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1. Introduction
\n
Magnetic resonance imaging (MRI) is a versatile non-invasive imaging technology that has been widely accepted for brain imaging (probing a magnetic state of brain interior). When applied to brain functional imaging, MRI produces a timeseries of images that are construed as an image representation of a brain functional activity. It is believed that any brain activity incurs a cerebral blood oxygenation level dependent (BOLD) magnetic state change that can be detected by MRI [1–4]. Brain functional imaging based on MRI and the endogenous BOLD contrast is termed BOLD fMRI.
\n
In principle, the MRI output is a complex-valued image consisting of a pair of magnitude and phase [5]. Nevertheless, only the MR magnitude image has been exploited for brain imaging (structural or functional). Recent research shows that neither the MR magnitude nor the phase could faithfully represent the brain magnetic state. This is due to a cascade of MRI transformations (including linear dipole-convolved magnetization and nonlinear complex modulo/argument operations [6]). Consequently, conventional BOLD fMRI that is based on MR magnitude imaging may deviate from the underlying brain magnetic source change due to nonlinear data transformations associated with MR magnitude image formation. Since there is a lack of analytic formulation for describing the imaging aspects of BOLD fMRI, we conduct numeric simulations to understand the BOLD fMRI model.
\n
In the past decades, there have been reports on single-voxel BOLD signal simulations [7–9] and multivoxel 3D BOLD imaging simulations [6, 10, 11]. In this chapter, we first provide a tutorial on the numeric simulations of single-voxel signals and multivoxel images and move forward to address implementing 4D BOLD fMRI simulations.
\n
\n
2. Models and methods
\n
An overview of a brain BOLD fMRI model is diagramed in Figure 1, which consists of a cascade of three modules (stages). Specifically, the “Source Magnetism” module provides the phenotypical χ expression of a brain functional biophysiological state, which serves as the source of the “MRI technology” module that produces a complex-valued MR image. Upon data acquisition of a 4D fMRI, a postprocessing stage of “Statistic image analysis” is performed to extract the brain functional map (fmap). A complete BOLD fMRI simulation implements the three cascaded stages in Figure 1 by numerical representations and computations.
\n
Figure 1.
A BOLD fMRI model consists of three stages. The stage of “Source Magnetism” provides a dynamic magnetic susceptibility source for the stage of “MRI Technology”. The MRI detection produces a 4D complex-valued fMRI dataset, which are used for functional imaging and mapping by “Statistical Image Analysis”.
\n
2.1. Definition of 3D vasculature and magnetic susceptibility source (χ)
\n
The initial step of BOLD fMRI simulation is to configure a χ-expressed BOLD activity, thereby providing a BOLD χ source for fMRI. We define a brain cortex volume of interest (VOI) with a tissue background and fill it with a cortex vasculature, thus simulating a brain cortex region. Let χ0(r) denote a static 3D χ distribution of parenchymal tissue in VOI and Δχ(r,t) the vascular blood χ change associated with a BOLD activity, with r = (x,y,z) denoting the spatial coordinates in VOI, then the dynamic 4D χ source is given by\n
where Hct denotes the blood hemocrit (Hct = 0.4 for normal blood), χdo the magnetic susceptibility difference between deoxygenated and oxygenated blood tissues (χdo = 0.27 × 4π ppm (in SI unit)), Y(t) the blood oxygenation level (Y ∈ [0,1]), NAB(r) the local neuroactive blob distribution, and V(r,t) the vasculature geometry in VOI. The explicit t variable indicates a possible change during a BOLD activity, such as cerebral blood volume change in V(r,t) and oxygenation level change in Y(t). For the sake of simulating fMRI signals, a pure BOLD activity is expressed by a dynamic blood magnetic susceptibility change, Δχ(r,t), which serves as the magnetic source for BOLD MRI simulation. In practice, the BOLD activity provides an additive term, Δχ(r,t) (a perturbation term), on a background distribution χ0(r) in Eq. (1).
\n
A local functional activity is defined by a 3D spatial distribution of NAB(r) (a neuroactive blob centered at r in VOI). For the sake of numerical representation, we assume a NAB by a Gaussian-shaped blob (with soft boundary) or a ball-shaped blob (with hard boundary). A NAB defines a local activity distribution in VOI, which presents with an ON state (active state) and vanishes with an OFF state (resting state) by a temporal modulation of a designed task paradigm. We may define an excitatory activity by a positive distribution (NAB(r) > 0) or an inhibitory activity by a negative distribution (NAB(r) < 0), in relation to the static background distribution. For the numerical simulation of a BOLD activity, we define a BOLD χ response by a spatiotemporal modulation model in Eq. (1). A brain active state gives rise to Δχ(r,t) ≠ 0 in NAB and at a task “ON” epoch, and a brain resting state is numerically characterized by Δχ(r,t) = 0 over the VOI in Eq. (1).
\n
It is mentioned that the BOLD χ expression in a brain activity is simply simulated by a spatial modulation model in Eq. (1), where a neuronal activity is defined by a local blob that shapes a local blood Δχ map by a spatial multiplication. We also simplify the BOLD χ source simulation by ignoring the hemodynamic response function (hrf), which otherwise could be accounted for by convoluting Δχ(r,t) with a kernel of hrf (usually adopting a canonical hrf that is characteristic of a high upshoot followed by a small undershoot).
\n
A BOLD χ change happens inside the vascular blood stream. We need to configure the vasculature geometry V(r,t) by filling the VOI with cluttered vessels with a blood volume fraction (bfrac), as expressed by\n
where the t variable is reserved to incorporate the change in cerebral blood volume as a result of vasodilation/vasoconstriction in a BOLD activity. A static vasculature is included as a binary volume V(r) that remains stationary during a BOLD activity. The random vascular geometry is generated under a control of bfrac = [0.02, 0.04] for cortex vasculature simulation [1, 8, 11–13].
\n
Figure 2.
Illustrations of VOI vasculature and BOLD Δχ source. The VOI is filled with (a1) random vessels (cylindrical segments) and (b1) spheric beads. The NAB-modulated Δχ distributions are shown in (a2) and (b2), respectively, with a y0-slice. It is noted Δχ may assume positive and negative values in local NAB regions.
\n
In order to maintain a control of constant bfrac for cortex vasculature over different regions or across multiresolution subregions, we may fill a VOI with random beads instead of cluttered vessels. In Figure 2 (a1,b1) are illustrated two brain local vasculature geometries with cluttered cylinders and random beads, under local stimuli by an excitatory blob (in red) and an inhibitory blob (in green). The NAB-modulated BOLD χ response distributions (in an active ON state) are shown in Figure 2(a2, b2) with a y0-slice in which the inactive regions (far from NAB) have little or no BOLD responses (Δχ ≈ 0).
\n
In order to numerically depict the vasculature geometry, we need to define the VOI with a large finely gridded 3D matrix with a tiny grid element (gridel) at a scale of micronmeter [14]. For example, a matrix of 2048 × 2048 × 2048 gridels, where a gridel = 2 × 2 × 2 μm3, is used to represent a small VOI of 4.1 × 4.1 × 4.1 mm3. The large matrix resulting from VOI gridel sampling offers a quasi-continuous representation of a continuous distribution over VOI. A gridel represents a spin packet (or isochromat) that contains numerous identical proton spins, serving as a mesoscopic representation (at micronmeter scale) between microscopic structure (at atomic and molecular angstrom scale) and macroscopic structure (at millimeter scale of MRI voxels) [15, 16].
\n
\n
2.2. Calculation of χ-induced fieldmap
\n
Upon determining the brain χ source configuration, we calculate the χ-induced magnetic field map (fieldmap for short) by a 3D spatial convolution with a dipole kernel. This is to simulate the brain tissue magnetization process in a main field B0 that produces an inhomogeneous fieldmap. Let b(x,y,z) represent the z-component of χ-induced 3D vector field; it is given by [10, 11]\n
where * denotes spatial convolution, and hdipole a 3D dipole field [17]. In a Fourier domain, the 3D dipole convolution can be efficiently implemented by multiplicative spatial filtering, as expressed by [18]\n
where (kx,ky,kz) denotes the coordinates in the Fourier domain. The fieldmaps induced by the Δχ distribution in a main field B0 are illustrated in Figure 3 (displayed with a y0-slice), which shows a conspicuous dipole effect in a manifestation of bipolar-valued quadruple lobes around vessels (with an orientation dependence [19]).
\n
Figure 3.
The fieldmaps calculated from the Δχ distributions in Figure 2(a2, b2). It is noted that the Δχ-induced fieldmap takes on a continuous inhomogenous bipolar-valued distribution over VOI, bearing a conspicuous dipole effect around large vessels (beads).
\n
Figure 4.
3D FFT implementation by 2D FFT and 1D FFT. The 3D FFT of a large 3D matrix (e.g., 2048 × 2048 × 2048) is achieved by first performing 2D FFT on each z-slice (xy-plane) and then 1D FFT along z columns. A large 3D matrix is decomposed into a number of small z-chunks to reduce the data file management (fwrite and fread).
\n
In computation implementation, the 3D FFT for fieldmap calculation for a finely-gridded 3D χ distribution matrix (e.g., 2048 × 2048 × 2048 gridels) may encounter an “out-of-memory” problem. We propose to solve this problem by decomposing 3D FFT into 2D FFT and 1D FFT. Specifically, we first conduct 2D FFT on each z-slice (or xy-plane) and save the data as data files, and then conduct 1D FFT along each of the z-axis columns of a 3D volume that is stacked from z-slices (processed by 2D FFT and saved in files). In order to reduce the data file management (fwrite and fread) of the 3D FFT decomposition, we decompose the 3D matrix into a handful of z-chunks (z-slabs) that each consists of multiple z-slices. The number of z-chunks is dependent upon the available computer RAM (random access memory). As illustrated in Figure 4, we only need to manage (fwrite and fread) a number of 32 z-chucks (each consists of 64 z-slices in a matrix of 2048 × 2048 × 64), instead of 2048 individual z-slices.
\n
\n
2.3. Multivoxel partition of VOI
\n
An MRI output is a discrete multivoxel image with the voxel size at a macroscopic millimeter scale, which implies that the MRI scanning process partitions a brain VOI into a small array of macroscopic voxels. We simulate a multivoxel MR image by rebinning mesoscopic gridels (at micronmeter scale) into macroscopic voxels (at millimeter scale). For example, we can reduce a large matrix of 2048 × 2048 × 2048 gridels to a small image matrix of 64 × 64 × 64 voxels with a voxel of 32 × 32 × 32 gridels. The multivoxel partition of VOI is in fact a spatial sampling by voxels, called voxelization. We denote the gridel-sampled representation of a continuous distribution over VOI by a spatial variable “(r)”, and the voxel-sampled discrete representation by an index variable “[r]”. Let Ω denote a voxel space, and |Ω| the voxel size (in terms of a number of gridels in Ω). The VOI voxelization is represented by\n
V[x,y,z]=1|Ω|∑(x′,y′,z′)∈Ω(x,y,z)V(x′,y′,z′)E5
\n
The VOI voxelization (voxel sampling) is necessary for MRI to produce a multivoxel image, due to the band limit of coil transmission and reception, which is designed as a parameter of voxel size in MRI protocol. The voxel size also represents a parameter of spatial resolution. In the MRI output, a high-resolution (corresponding to small voxel size) produces a large image matrix, and vice versa.
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\n
2.4. Calculation of intravoxel dephasing signals (Monte Carlo method)
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An MRI voxel signal (or a NMR signal) is formed by an intravoxel spin precession dephasing in a χ-induced fieldmap. A quadrature detection produces a complex-valued voxel signal, denoted by C[x,y,z] that is formulated by [5]\n
where γ denotes the gyromagnetic ratio, and the auxiliary variable ‘X’ is reserved to explicitly include the dependence of NMR signal upon a diverse set of factors. We are always concerned with the factors of echo time (TE), field strength (B0), spatial resolution (voxel size |Ω|), and vessel geometry in particular.
\n
A voxel contains a number of gridels that each represents a spin packet. The voxel signal calculation in Eq. (6) counts all the spin packets in the voxel space. For a voxel that contains a large number of gridels, we may select a smaller number of gridels to calculate the voxel signal and reduce the computation burden. The intravoxel dephasing signal calculation made by counting the spin packets is a Monte Carlo simulation, which is expressed by\n
C[x,y,z;X]=1N∑n=1N<|Ω|eiγb(xn,yn,zn)TE for (xn,yn,zn)∈Ω(x,y,z)E7
\n
For example, a voxel of 32 × 32 × 32 gridels consists of 32,768 spin packets, from which we may randomly select 3000 for the intravoxel average computation in Eq. (7) at a small computation cost of 10% (≈3000/32,768). It is noted that C[x,y,z;X] denotes a complex voxel signal at [x,y,z] in VOI, and we also use C[x,y,z;X] to represent a multivoxel complex-valued image in the context that [x,y,z] addresses all the voxels in VOI.
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From a complex signal (image), we can calculate its magnitude and phase components by\n
It is also noted that we use the magnitude loss and phase accrual to represent the pair of complex signal components and that the magnitude and phase calculations are different nonlinear operations.
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2.5. Intravascular (IV) and extravascular (EV) signal separation
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In an MRI experiment, it is difficult to separate intravascular (IV) signal from extravascular (EV) signal in an NMR signal. In numerical simulation, we can calculate the IV and EV signals separately based on the binary partition of voxel space according to the vessel geometry. Let ΩIV and ΩEV denote the IV and EV subspaces in a voxel space, which are partitioned by the vessel geometry by\n
ΩIV(x,y,z)={1 (x,y,z)∈vessel0 otherwise ΩEV(x,y,z)={1 (x,y,z)∉vessel0 otherwise =1−ΩIV(x,y,z)with Ω=ΩIV∪ΩEV and |Ω|=|ΩIV|+|ΩEV|E9
\n
Then, we calculate the IV signal by only counting the gridels that are within vessel space (ΩIV), and the EV signal by the gridels in ΩEV. That is, the IV and EV signals are given by\n
In Figure 5 are illustrated the IV/EV partition of a voxel space for IV/EV signal simulations. It is mentioned that the ΩIV only occupies a small fraction of Ω and the BOLD χ change is confined in ΩIV.
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Figure 5.
Illustration of extravascular (EV) and intravascular (IV) space partition in a voxel for intravoxel spin dephasing signal simulations (a) in absence of spin diffusions (static spins) and (b) in the presence of spin diffusions. A voxel space is partitioned by its intravoxel binary vasculature into IV (vessel=1) and EV (vessel=0) subspaces.
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Although a BOLD Δχ change is confined in ΩIV in a NAB, the vascular blood magnetization process in B0 establishes a long-range magnetic field distribution, not only in ΩIV but also in ΩEV, with a distant decay (∝1/r3) and a spatial modulation by NAB (see Figures 2 and 3). Obviously, a BOLD activity causes an IV signal and an EV signal simultaneously, which are generated from different field values over the IV and EV spaces, respectively. In Figure 5(a) is illustrated the IV/EV signal formations from spin particles in the IV/EV partition spaces.
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A voxel NMR signal is formed from its IV and EV signals by a convex combination according to the IV/EV occupancies, as represented by\n
Consequently, the IV signal contribution is greatly suppressed by a small weight of bfrac (<<1), as will be demonstrated later.
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2.6. Diffusion effect
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An NMR signal is formed via the carrier of hydrogen protons in tissue water. Since the water molecules undergo random motions, the water protons are non-stationary. We describe the proton random motion in 3D space by a trajectory r(t), which is represented by [9, 20]\n
where δt denotes the time interval of the random motion of water molecules (δt = 2 ms in simulation), D the diffusion coefficient (different for diffusions in IV and EV), and Gauss a Gaussian distribution of the random motions (with a standard deviation of σd). It is noted that water proton diffusion in IV space is twice faster than in EV space. In Figure 5(b) are illustrated the diffusion IV and EV signal simulations.
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2.7. Volumetric BOLD fMRI simulation
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Based on individual voxel signal calculation, we implement 3D volumetric BOLD fMRI simulation by calculating the voxel signals at a multivoxel image array. Given a 3D χ source, the 3D BOLD fMRI simulations produce a 3D complex-valued multivoxel image C[x,y,z; X]; here, we are concerned with the spatial pattern comparison between the χ source and the magnitude image. Since the phase image bears a conspicuous dipole effect that dooms the morphological mismatch with the χ source, we do not need to compare the phase image with the χ source. However, the phase image is directly related to the χ-induced fieldmap, and the phase image has been used for the fieldmap reconstruction in an inverse MRI solver [11, 21, 22]. In particular, in a small phase angle regime, the phase conforms the fieldmap with a difference of constant scale. In large phase angle scenarios, the unwrapped phase image resembles the fieldmap very well (albeit with somewhat nonlinear distortions). Therefore, we are also concerned with pattern comparison between MR phase image and the fieldmap. We suggest the spatial pattern comparisons by spatial correlations, which are defined by\n
It is noted that the spatial pattern correlations are applied to the multivoxel matrices (in notation of [r]) of the χ source, the fieldmap, and the images, which are all discretized at a spatial resolution of the same voxel size.
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2.8. 4D BOLD fMRI simulation
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It is straightforward to implement 4D BOLD fMRI simulation based on the repetition of volumetric BOLD fMRI simulations for each snapshot capture over a BOLD activity. First, we need to define a task-evoked 4D BOLD χ change, as illustrated in Figure 6. Specifically, we configure a 3D vasculature-laden VOI and provide a 3D χ distribution for a brain VOI state. A local χ change is simulated with a spatiotemporal modulation by a NAB and a task paradigm (in Eq. (1)). For the weak BOLD response detection, the task paradigm is usually designed as a boxcar waveform for repetition measurement of BOLD signals. We may define a positive NAB for an excitatory BOLD response and a negative NAB for an inhibitory response. The static background χ0 may be assigned to a water pool (χ0 = χwater) or be empty (χ0 = 0) with an additive Gaussian noise.
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Figure 6.
Illustration of 4D BOLD χ response simulations. A VOI is filled local Δχ change with positive and negative Δχ responses superimposed on a static background in the presence of noise. A BOLD event is represented by a timeseries of the 3D Δχ snapshot distributions in Eq. (1) through a spatiotemporal modulation by NAB(r) and task(t).
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The 4D BOLD fMRI simulation involves a predefined 4D source χ[r,t] and two output 4D images (A[r,t] for magnitude and P[r,t] for phase, as defined in Eq. (8)). Conventional BOLD fMRI exploits the 4D magnitude dataset A[r,t] for functional analysis. For a task-evoked BOLD fMRI simulation, the functional activity map can be extracted from a 4D dataspace, Λ[r,t] = {χ[r,t], A[r,t], P[r,t]} by a temporal correlation (tcorr) map that is defined by\n
where stdt denotes the standard deviation of the data with respect to the t variable, χtrue the predefined χ source, and χrecon the reconstructed χ source (by solving the inverse problem of MRI data). It is noted that the correlation coefficient is invariant to signal strength. Therefore, a strong response signal may have the same correlation value as a weak response does as long as the strong and weak responses take on the same timecourse profiles. Consequently, the scale invariance of correlation leads to correlation saturation (tcorr = 1 at regions with different response strengths). Nevertheless, the correlation saturation can be ruined by the presence of noise. Herein, by noise we mean any pattern difference between the response signal timecourse and task timecourse. In reality, the BOLD χ responses are subject to various noises (biological noise, physiological noise, detection noise) that spoil the task correlations at weak response regions. Only strong responses are immune to noise spoilage. It is the noise in the voxel response timecourse (extracted from a 4D dataset at a specific voxel) that shapes the tcorr map according to the response signal strength.
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3. Simulation results
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3.1. Single voxel signal simulations
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3.1.1. EV/IV signal separation
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By calculating the EV and IV signal portions separately and their convex linear combination in Eq. (11), we present the EV/IV signal behaviors with respect to a span of echo time (TE=[0, 60] ms) and for a range of field strength (B0=[1.5, 3, 4, 7, 9] Tesla). It is seen in Figure 7 that the IV signal changes quickly with a long echo time. However, the drastic IV signal changes are greatly suppressed in the voxel signals by the dominant EV signals. In particular, the IV signal may be developed into phase wrapping phenomenon for a long echo time (see Figure 7(b2)). With the dominance of EV signals in a large voxel, a voxel signal remains as a linear phase accrual with echo time (see Figure 7(b3)).
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Figure 7.
Intravascular (IV) and extravascular (EV) voxel signal simulations. The IV signal evolves drastically for a long TE and its contribution to the full voxel signal is relatively small.
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3.1.2. Multiresolution voxel signal behavior
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As a voxel size decreases, the voxel space contains less (or none) vessels, and there is less voxel average effect. In Figure 8, the four-level voxel subdivision and multiresolution voxel signal behaviors are demonstrated. At level =1, the parent voxel contains a clutter of vessels where the complex voxel signal appears as a short line-segment trajectory (with respect to TE). As the voxel is decomposed into an 8 × 8 × 8 array at level = 4, the subvoxel only contains a single vessel, and the voxel signal becomes turbulent due to the high field values for rapid Larmor precession [14, 23].
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Figure 8.
Multiresolution complex-valued voxel signals due to voxel subdivision. As the voxel size is dyadically reduced, the smaller voxels contain less vessels, and the voxel signal may become turbulent at vessel boundary (Adapted from [23]).
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3.1.3. Diffusion effects on magnitude and phase signals
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The numerical simulations on the diffusion effect on MR magnitude and phase are presented in Figure 9 for a span of TE = [0, 60] ms with different field strengths (in terms of ΔχB0 = [0.1, 3] ppmT). The results show that the diffusion has more effect on low field magnitude than on high field magnitude [20]. Nevertheless, the diffusion has little effect on MR phase signals.
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Figure 9.
Effects of diffusion and field strength on voxel signal magnitude and phase. It is seen that the diffusion has more effects on magnitude signal than on phase signal and that the diffusion effect decreases as the field strengths increases (Adapted from [20]).
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3.2. Volumetric BOLD fMRI simulations
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3.2.1. Cortex VOI configuration and voxelization
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We define a cortex VOI in a large matrix and fill it with random beads (radius = 3 μm, bfrac = 0.03), and simulate local BOLD response by a Gaussian-shaped NAB, which modulates the local χ distribution by a spatial multiplication. The VOI is partitioned into a coarse matrix by grouping the gridels into voxels. As a result of voxelization, we represent a distribution over VOI by a multivoxel image matrix. The voxelization with a large voxel size produces a small image matrix, and vice versa. Figure 10 shows a VOI that is represented by a large matrix in gridel sampling (a) with a zoomed region for substructure visualization (b). The VOI voxelization by a voxel of 32 × 32 × 32 gridels produces a matrix of 64 × 64 × 64 voxels (c) and produces a matrix of 32 × 32 × 32 voxels (d) by a voxel of 64 × 64 × 64 gridels. It is seen that a larger voxel size is comprised of more spatial smoothing.
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Figure 10.
Illustration of VOI configuration and voxelization. A VOI is represented by a large matrix for subvoxel structure representation. The VOI voxelization produces a small multivoxel matrix, depending on the voxel size.
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3.2.2. Multivoxel image calculation
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Given a 3D χ distribution in Figure 11(a), we calculated the χ-induced fieldmap by Eq. (2) and presented the results (b). In the absence of diffusion, we calculated the complex-valued T2* images (c, d). In the presence of diffusion (Eq. (12)), we recalculated the complex-valued T2* images (e, f). The diffusion simulation on multivoxel fMRI shows that the diffusion effect is insignificant on image formation.
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Figure 11.
Illustration of volumetric BOLD fMRI simulation, displayed with a z-slice (with B0//z-axis). (a) 3D Δχ source (in a matrix of 64 × 64 × 64 voxels resulting from a VOI of 2048 × 2048 × 2048 gridels); (b) the Δχ-induced fieldmap; (c, d) the magnitude and phase images with static spins (at TE = 30 ms); and (e, f) the magnitude and phase images with diffusion spins.
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3.2.3. Morphological distortions associated with 3D BOLD fMRI
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We performed volumetric BOLD fMRI simulations for a span of echo times (TE= [0, 30] ms) with different parameter settings with respect to voxel size, field strength, and with and without diffusion. With the datasets of numerical BOLD fMRI simulations, we compared the magnitude images with the predefined χ source and the phase images with the fieldmaps. The results are presented in Figure 12. Note that the pattern correlations are plotted in a small display window ([0.9, 1]) out of the full range of corr ∈ [–1, 1] for scrutiny.
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Figure 12.
Spatial correlation measurements (a) between χ source and magnitude image and (b) between χ-induced fieldmap and phase image, for static intravoxel dephasing and diffusive intravoxel dephasing. Note the small display windows for corr values in the range of [–1,1] (Adapted from [11]).
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3.3. 4D BOLD fMRI simulations
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The 4D BOLD fMRI simulations are presented in Figures 13 through 15. Specifically, in Figure 13 are shown (a) the VOI configuration with two local neuroactive blobs (NAB), (b) the NAB-modulated BOLD χ distribution at an ON state (or active state), and (c) the NAB-absent χ distribution at an OFF state (or resting state), displayed with a y0-slcie. We designed a task paradigm by a pattern of 5 ON states and 5 OFF states, simulating the brain active state measurement by 5 repetitions and the brain resting state measurement by another 5 repetitions. (In practice, a multiple repetition of the “ON/OFF” pattern is used to design the task paradigm). The bead-represented vasculature structure in a voxel in VOI is shown in zoom (d) with a 3D display. It is noted that the VOI is represented in a matrix of 2048 × 2048 × 2048 gridels (a), the voxelization on VOI is represented by a multivoxel matrix of 64 × 64 × 64 voxels (b) and (c) with a voxel = 32 × 32 × 32 gridels (d), and that the cortex vasculature in a VOI is simulated by a uniform random distribution (background) that is independent of the BOLD NAB and task paradigm. The 4D χ(r,t) representation for a local BOLD activity is related to the NAB and the task through a spatiotemporal model in Eq. (1).
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Figure 13.
Numerical representation of a local BOLD activity in terms of 4D χ(r,t). (a) A Gaussian-shaped NAB and a ball-shaped NAB in VOI; (b) an ON state χ[r,tON]; (c) an OFF state χ[r,tOFF]; and (d) the bead-laden structure in a voxel.
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Upon the numerical representation of 4D χ(r,t), we performed 4D BOLD fMRI simulations by repeating the 3D BOLD fMRI simulation for each snapshot time point (there are 10 timepoints for the task pattern of 5 ONs and 5 OFFs), with the settings (TE = 30 ms, B0 = 3 T, VOI matrix = 64 × 64 × 64 voxels, 1 voxel = 32 × 32 × 32 gridels, 1 gridel = 2 × 2 × 2 μm3). Figure 14 shows (a1, a2) the magnitude images, (b1, b2) the phase images captured at an ON and OFF state, and (a3, b3) the timecourses of magnitude signal changes, and phase signal changes at two voxels: one voxel inside an active blob (marked by “x” in (a1)) and another outside the active at blob (marked by “o”). It is noted the ripples in the signal timecourses in (a3, b3) are attributed to the additive Gaussian random noise in the data acquisition simulations.
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Figure 14.
Numerical simulations of 4D BOLD fMRI data acquisition. (a1, a2) BOLD magnitude images captured at an ON and OFF state and (a3) the magnitude signal timecourses at two voxels (marked by x and o (a1, a2), extracted from the 4D magnitude dataset A[r,t]). (b1, b2, b3) for the BOLD phase images in P[r,t] and the voxel phase timecourses.
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By arranging the timeseries of images according to the task timecourse, we can play a movie for a BOLD activity. In reality, the BOLD response is too weak and noisy to be perceived between an ON and OFF state. For the sake of BOLD response pattern representation, we need to extract the BOLD activity blobs from the timeseries of images by statistical parameter mapping method, which consists of an essential task correlation map as defined in Eq. (14).
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Figure 15.
Numerical simulations of fmap extractions from 4D BOLD fMRI datasets in the presence of additive Gaussian noises at different noise level = {0.001,0.01,0.05,0.1}. (a) Magnitude fmap and (b) phase fmap.
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Upon the completion of 4D BOLD magnitude and phase image datasets (A[r,t], P[r,t]), we calculated the task- correlated fmap using Eq. (14). In the results, we obtained 3D Atcorr for BOLD magnitude fmap from the 4D magnitude image dataspace, and a 3D Ptcorr for BOLD phase fmap from the 4D phase image dataspace. By repeating the 4D BOLD fMRI simulations with different noise levels, we show that Atcorr or Ptcorr is sensitive to the additive Gaussian noise. In Figure 15 are showed the Atcorr and Ptcorr (displayed with a y0-slice out of the 64 × 64 × 64 matrix volume) for the Gaussian noise at different noise levels = {0.001, 0.01, 0.05, 0.1}. It is seen that either the magnitude or phase fmap suffers from correlation saturation in little noise (noise level < 0.01) or tends to be buried in severe noises (noise level > 0.05) for our spatiotemporal modulation model in Eq. (1). In particular, our simulation shows the correlation saturation in extreme cases of little noise or noiseless settings; this phenomenon may be explained by the scale invariance of correlation coefficient. On the other extreme case, a severe noise may destroy the task-correlated activity blob; this explains the pursuit on high-SNR image acquisition.
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Our 4D BOLD fMRI simulations show that the predefined BOLD NAB in Figure 13(a) could be largely reproduced by a task-correlation magnitude fmap (Atcorr in Figure 15(a)) as extracted from a 4D BOLD fMRI magnitude dataset, thus justifying the BOLD fMRI experiment for brain functional mapping. In comparison, the phase fmap (in Ptcorr) is spatially dissimilar to the predefined BOLD NAB due to the conspicuous dipole effect in the phase images [6, 11]. Nevertheless, our 4D BOLD fMRI simulations also show that the imaging noise has a strong effect on the fmap extracted from the magnitude or phase image dataset due to the simplified spatiotemporal modulation model for numerical BOLD χ expressions.
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4. Discussion
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The data acquisition of BOLD fMRI is not analytically tractable due to the involvement of diversified parameters. The BOLD fMRI simulations provide a means to observe the effect of MRI transformations on the MR data acquisition; spatial distortions between the underlying magnetic source and MR images; and reproducibility of functional activity extraction from a 4D BOLD fMRI dataset.
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Since MRI is designed to measure a magnetic field distribution, the BOLD fMRI only measures the χ-expressed BOLD response during a functional activity, a phenotypic numeric expression of a biophysiological brain functional activity in terms of tissue magnetism. It is believed that a functional activity causes IV blood magnetism change in terms of oxygenated and deoxygenated blood magnetic susceptibility change. Therefore, our simulation begins with a configuration of magnetic source by a vasculature-laden VOI with a 3D χ source distribution. Through a spatiotemporal modulation by a predefined local neuroactive blob (numerically NAB(r)) and a task paradigm (numerically task(t)), we define a dynamic χ source to represent a χ-expressed BOLD activity (in Eq. (1)). It is pointed out in Eq. (1) that the BOLD χ response may incorporate the factors of cerebral metabolic rate of oxygen consumption (CMRO2), cerebral blood volume (CBV), and cerebral blood flow (CBF) through the parameters of Y(t) and V(r,t), thereby enabling the numeric simulations of MRI-detected BOLD activity. In reality, the biophysiological aspects for neurovascular coupling are far more complicated than the spatiotemporal modulation model in Eq. (1), which deserves a long-term exploration.
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Upon a predefined χ source map, we implement 3D BOLD fMRI numerical simulation based on MRI principles. In the results, we are concerned with pattern comparison between the source distribution and the output images (magnitude and phase). Our simulations show that neither the magnitude image nor the phase image is a faithful representation of the χ source distribution. In the context of volumetric medical imaging, the MRI output image is not a tomographic reproduction (quantitative spatial mapping) of the χ source. Since the source-image mismatch is due to a cascade of MRI transformations that cause distortions during data acquisition, this inspires us to reconstruct the χ source by solving an inverse MRI problem [21, 22].
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In NMR principle, a voxel signal is formed from numerous hydrogen proton precessions in a magnetic field. The signal formation involves a huge space scale span from a microscopic atomic scale to macroscopic millimeter scale. For numerical simulations, we implement the mesoscopic micrometer scale through gridel sampling [14, 15]. A gridel is a tiny grid element (at micronmeter scale) smaller than vessel size with which we may digitally depict a vessel geometry. On the other hand, a gridel consists of numerous protons at microscopic atomic scale. The collective proton spins in a gridel are denoted by a spin packet [14, 15]. We define a cortex VOI in a large finely-gridded matrix and partition the VOI into a coarse multivoxel matrix, with each voxel containing an adequate number of gridels for subvoxel structure representation. The VOI partition and gridel rebinning for multivoxel image formation is a topic of multiresolution BOLD signal analysis [15, 23].
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In the past decades, the BOLD fMRI mechanism was numerically simulated with signal voxel signals, [7–9], offering an understanding of BOLD fMRI signal formation with respect to a diverse set of parameter settings. However, the single-voxel signal simulation cannot reveal the spatial context for source-image mapping study. Therefore, we were motivated to use multivoxel image simulations for revealing the spatial mismatches between the source and the image [9–11]. Based on 3D BOLD fMRI simulations, it is a straightforward process to implement 4D BOLD fMRI simulations. Our 4D BOLD fMRI simulations for a task-evoked brain functional activity, based on a simple spatiotemporal modulation model in Eq. (1), show that the fmap extraction from a 4D BOLD fMRI dataset is sensitive to the additive Gaussian noise. The noise dependence of the task-correlation-based fmap extraction is attributed to the scale invariance of the correlation coefficient.
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One factor for the source-image mismatch is the dipole effect that is introduced during the tissue magnetization in a main field B0, which is unavoidable for MRI data acquisition. The dipole effect is introduced to the χ-induced fieldmap, which is propagated to the MR magnitude and phase images (signals) via different data transformations. The dipole effect on the χ-induced fieldmap manifests bipolar-valued quadruple lobes around vessels. Upon MRI data acquisition, the magnitude image is a nonnegative nonlinear spatial mapping of the fieldmap and the phase image is an arctan nonlinear spatial mapping. It is interesting to show in our numeric simulations that the nonnegative magnitude image resembles the predefined χ source distribution, except for the negative inversions at negative χ regions (not reported herein), and we have found that the (unwrapped) bipolar-valued phase image conforms very well with the bipolar-valued fieldmap [6, 11]. The phase image bears a conspicuous dipole effect that makes a striking difference between the phase image and the predefined χ source.
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BOLD fMRI simulation is a time-consuming computation job. In a computer cluster (a Kernel Linux system with 16 CPUs and 252 GB memory), the single-voxel signal simulation requires about 1 hour, and 3D multivoxel simulation requires more than 10 hours, and 4D BOLD fMRI simulation requires a few days, depending on the sizes of gridel, voxel, and VOI. The computation burden may be greatly reduced by a Bloch technique [24], which implements intravoxel dephasing signal calculation by a linear approximation. The fast Bloch simulation method is good for MR phase image simulation, but not good for MR magnitude simulation due to an accentuated edge effect. Moreover, the IV and EV signal separation and the diffusion simulations are not implementable by the Bloch method.
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5. Conclusion
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We conclude our numerical BOLD fMRI simulations by the following findings (albeit qualitative):
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Both the MR magnitude and the phase images are spatially different from the predefined magnetic susceptibility distribution. This image-source distortion is due to the inevitable data transformations associated with MRI data.
By numerical simulation, we can separate the intravascular (IV) signal from the extravascular (EV) signal in a voxel signal. The IV signal is much stronger than the EV signal as a result of a BOLD χ change. However, the drastic IV signal evolution is usually greatly suppressed in a voxel signal by a small proportion of blood volume fraction (bfrac ≈ [0.02, 0.04]).
As voxel size decreases, the voxel signals evolve more drastically and turbulently inside and around the large vessels.
The proton diffusion effect due to nonstationary water molecules in brain tissues incurs more MR magnitude signal decays in a low field than in a high field. In comparison, the proton diffusion has little effect on MR phase signals.
The numerical simulation on 4D BOLD fMRI for task-evoked functional mapping shows that the functional activity extraction by a task correlation technique is sensitive to data noise.
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Overall, the numerical simulations on BOLD fMRI allow us to look into the insights of a single-voxel signal, a multivoxel image, and a video of brain functional BOLD activity with respect to various parameter settings. The finding in source-image mismatch inspires us to seek for the underlying magnetic source of BOLD fMRI for more accurate brain functional mapping. The finding in the noise sensitiveness of task-correlated fmap raises a caveat to the correlation-based functional mapping.
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Abbreviations:
1D: one dimensional; 2D: two dimensional; 3D: three dimensional (spatial); 4D: four dimensional (spatiotemporal); BOLD: blood oxygenation level dependent; MR: magnetic resonance; MRI: magnetic resonance imaging; fMRI: functional MRI; FFT: fast Fourier transform; NAB: neuroactive blob; VOI: volume of interest; IV: intravascular; EV: extravascular; gridel: grid element; bfrac: blood volume fraction; fmap: functional map; corr: correlation (coefficient); tcorr: temporal correlation or task correlation.
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\n',keywords:"magnetic resonance imaging (MRI), blood oxygenation level dependence (BOLD), magnetic susceptibility source, dipole effect, voxelization, complex-valued magnetic resonance signal (image), intravoxel dephasing signal, multivoxel image, BOLD fMRI simulation, task correlation",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/50911.pdf",chapterXML:"https://mts.intechopen.com/source/xml/50911.xml",downloadPdfUrl:"/chapter/pdf-download/50911",previewPdfUrl:"/chapter/pdf-preview/50911",totalDownloads:1152,totalViews:366,totalCrossrefCites:0,totalDimensionsCites:3,hasAltmetrics:0,dateSubmitted:"October 15th 2015",dateReviewed:"March 24th 2016",datePrePublished:null,datePublished:"August 24th 2016",dateFinished:null,readingETA:"0",abstract:"Background: Brain functional magnetic resonance imaging (fMRI) is sensitive to changes in blood oxygenation level dependent (BOLD) brain magnetic states. The fMRI scanner produces a complex-valued image, but the calculation of the original BOLD magnetic source is not a mathematically tractable problem. We conduct numeric simulations to understand the BOLD fMRI model.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/50911",risUrl:"/chapter/ris/50911",book:{slug:"numerical-simulation-from-brain-imaging-to-turbulent-flows"},signatures:"Zikuan Chen and Vince Calhoun",authors:[{id:"179437",title:"Ph.D.",name:"Zikuan",middleName:null,surname:"Chen",fullName:"Zikuan Chen",slug:"zikuan-chen",email:"zchen@mrn.org",position:null,institution:{name:"Mind Research Network",institutionURL:null,country:{name:"United States of America"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Models and methods",level:"1"},{id:"sec_2_2",title:"2.1. Definition of 3D vasculature and magnetic susceptibility source (χ)",level:"2"},{id:"sec_3_2",title:"2.2. Calculation of χ-induced fieldmap",level:"2"},{id:"sec_4_2",title:"2.3. Multivoxel partition of VOI",level:"2"},{id:"sec_5_2",title:"2.4. Calculation of intravoxel dephasing signals (Monte Carlo method)",level:"2"},{id:"sec_6_2",title:"2.5. Intravascular (IV) and extravascular (EV) signal separation",level:"2"},{id:"sec_7_2",title:"2.6. Diffusion effect",level:"2"},{id:"sec_8_2",title:"2.7. Volumetric BOLD fMRI simulation",level:"2"},{id:"sec_9_2",title:"2.8. 4D BOLD fMRI simulation",level:"2"},{id:"sec_11",title:"3. Simulation results",level:"1"},{id:"sec_11_2",title:"3.1. Single voxel signal simulations",level:"2"},{id:"sec_11_3",title:"3.1.1. EV/IV signal separation",level:"3"},{id:"sec_12_3",title:"3.1.2. Multiresolution voxel signal behavior",level:"3"},{id:"sec_13_3",title:"3.1.3. Diffusion effects on magnitude and phase signals",level:"3"},{id:"sec_15_2",title:"3.2. Volumetric BOLD fMRI simulations",level:"2"},{id:"sec_15_3",title:"3.2.1. Cortex VOI configuration and voxelization",level:"3"},{id:"sec_16_3",title:"3.2.2. Multivoxel image calculation",level:"3"},{id:"sec_17_3",title:"3.2.3. Morphological distortions associated with 3D BOLD fMRI",level:"3"},{id:"sec_19_2",title:"3.3. 4D BOLD fMRI simulations",level:"2"},{id:"sec_21",title:"4. Discussion",level:"1"},{id:"sec_22",title:"5. Conclusion",level:"1"},{id:"sec_23",title:"Abbreviations:",level:"1"}],chapterReferences:[{id:"B1",body:'J. L. Boxerman, L. M. Hamberg, B. R. Rosen et al., “MR contrast due to intravascular magnetic susceptibility perturbations,” Magn Reson Med, vol. 34, no. 4, pp. 555-66, Oct, 1995.'},{id:"B2",body:'S. Ogawa, R. S. Menon, D. W. Tank et al., “Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model,” Biophys J, vol. 64, no. 3, pp. 803-12, Mar, 1993.'},{id:"B3",body:'S. Ogawa, D. W. Tank, R. Menon et al., “Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging,” Proc Natl Acad Sci U S A, vol. 89, no. 13, pp. 5951-5, Jul 1, 1992.'},{id:"B4",body:'O. J. Arthurs and S. Boniface, “How well do we understand the neural origins of the fMRI BOLD signal?” Trends Neurosci, vol. 25, no. 1, pp. 27-31, Jan, 2002.'},{id:"B5",body:'E. M. Haacke, R. Brown, M. Thompson et al., Magnetic Resonance Imaging Physical Principles and Sequence Design, John Wiley & Sons, Inc, 1999.'},{id:"B6",body:'Z. Chen and V. Calhoun, “Nonlinear magnitude and linear phase behaviors of T2* imaging: theoretical approximation and Monte Carlo simulation,” Magn Reson Imaging, vol. 33, no. 4, pp. 390-400, May, 2015.'},{id:"B7",body:'J. L. Boxerman, P. A. Bandettini, K. K. Kwong et al., “The intravascular contribution to fMRI signal change: Monte Carlo modeling and diffusion-weighted studies in vivo,” Magn Reson Med, vol. 34, no. 1, pp. 4-10, Jul, 1995.'},{id:"B8",body:'J. Martindale, A. J. Kennerley, D. Johnston et al., “Theory and generalization of Monte Carlo models of the BOLD signal source,” Magn Reson Med, vol. 59, no. 3, pp. 607-18, Mar, 2008.'},{id:"B9",body:'A. P. Pathak, B. D. Ward, and K. M. Schmainda, “A novel technique for modeling susceptibility-based contrast mechanisms for arbitrary microvascular geometries: the finite perturber method,” Neuroimage, vol. 40, no. 3, pp. 1130-43, Apr 15, 2008.'},{id:"B10",body:'Z. Chen, and V. Calhoun, “Volumetric BOLD fMRI simulation: from neurovascular coupling to multivoxel imaging,” BMC medical imaging, vol. 12, pp. 8, 2012.'},{id:"B11",body:'Z. Chen, and V. Calhoun, “Understanding the morphological mismatch between magnetic susceptibility source and T2* image,” Magnetic Resonance Insights, vol. 6, pp. 65-81, 2013.'},{id:"B12",body:'Z. Chen, A. Caprihan, and V. Calhoun, “Effect of surrounding vasculature on intravoxel BOLD signal,” Medical physics, vol. 37, no. 4, pp. 1778-87, Apr, 2010.'},{id:"B13",body:'W. M. Spees, D. A. Yablonskiy, M. C. Oswood et al., “Water proton MR properties of human blood at 1.5 Tesla: magnetic susceptibility, T(1), T(2), T*(2), and non-Lorentzian signal behavior,” Magn Reson Med, vol. 45, no. 4, pp. 533-42, Apr, 2001.'},{id:"B14",body:'Z. Chen, and V. D. Calhoun, “Magnitude and phase behavior of multiresolution BOLD signal,” Concepts Magn Reson, vol. 37B, no. 3, pp. 129-35, 2010.'},{id:"B15",body:'Z. Chen, and V. Calhoun, “A computational multiresolution BOLD fMRI model,” IEEE Trans. BioMed. Eng, vol. 58, no. 10, pp. 2995-9, 2011.'},{id:"B16",body:'D. A. Yablonskiy, “Quantitation of intrinsic magnetic susceptibility-related effects in a tissue matrix. Phantom study,” Magn Reson Med, vol. 39, no. 3, pp. 417-28, Mar, 1998.'},{id:"B17",body:'J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory, New York: Addison-Wisley, 1993.'},{id:"B18",body:'J. P. Marques and R. Bowtell, “Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility,” Concepts Magn. Reson, vol. B 25, pp. 65-78, 2005.'},{id:"B19",body:'Z. Chen and V. Calhoun, “Effect of object orientation angle on T2* image and reconstructed magnetic susceptibility: numerical simulations,” Magn. Reson. Insight, vol. 6, pp. 23-31, 2013.'},{id:"B20",body:'Z. Chen and V. Calhoun, “Computed diffusion contribution in the complex BOLD fMRI signal,” Conc. Magn. Reson. Part A, vol. 40A, no. 3, pp. 128-145, 2012.'},{id:"B21",body:'Z. Chen and V. Calhoun, “Computed inverse resonance imaging for magnetic susceptibility map reconstruction,” J. Comp. Assist. Tomo, vol. 36, no. 2, pp. 265-74, Mar, 2012.'},{id:"B22",body:'Z. Chen and V. Calhoun, “Reconstructing brain magnetic susceptibility distributions from T2* phase images by TV-reguarlized 2-subproblem split Bregman iterations,” Rep. Med. Imag, vol. 7, pp. 41-53, 2014.'},{id:"B23",body:'Z. Chen, Z. Chen, and V. Calhoun, “Blood oxygenation level-dependent functional MRI signal turbulence caused by ultrahigh spatial resolution: numerical simulation and theoretical explanation,” NMR Biomed, vol. 26, no. 3, pp. 248-64, Mar, 2013.'},{id:"B24",body:'P. Latta, M. L. Gruwel, V. Jellus et al., “Bloch simulations with intra-voxel spin dephasing,” J. Magn. Reson, vol. 203, no. 1, pp. 44-51, Mar, 2010.'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Zikuan Chen",address:"zchen@mrn.org",affiliation:'
The Mind Research Network and LBERI, Albuquerque, New Mexico, USA
The Mind Research Network and LBERI, Albuquerque, New Mexico, USA
University of New Mexico, ECE Department, Albuquerque, New Mexico, USA
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\n
1. Introduction
\n
Machine translation (MT) investigates the approaches to translating text from one natural language to another. It is a subfield of computational linguistics that draws ideas from linguistics, computer science, information theory, artificial intelligence, and statistics. For a long time, it had a bad reputation because it was perceived as low quality. Especially in the last two decades, we have been witnessing great progress in MT quality, which made it interesting also for the use in the translation industry. Its quality is still lower than human translation, but that does not mean it does not have good practical uses. In the past, translation agencies and other professional translators were the only actors in the translation industry, but, in recent years, we have been faced with the rapidly growing range of machine translation solutions entering the market and being of practical use. There is increasing pressure on the translation industry in terms of price, volume, and turnaround time. The emergence of commercial applications for MT is a welcome change in translation processes. In professional or official circumstances, human translation is inevitable, as humans are essential to making sure a translation is grammatically correct and carries the same meaning as the original text. Machine translation is appropriate in different circumstances, mainly for unofficial purposes or for providing content for a human translator to improve upon it. MT has proved to be able to speed up the whole translation process, but it cannot replace the human translator. The questions that researchers in the translation industry are trying to answer today are: How much can human translators benefit from using MT? How could MT be integrated efficiently into translation processes? If MT is integrated into the translation workflow, will the quality of translation remain at the same level? These questions will not be answered explicitly in this chapter, but an effort will be made to show that MT is worth being part of the translation process, as its quality can be evaluated reliably. MT opens new opportunities for translators through using MT output only as a suggestion and, if necessary, post-editing it to the desired quality. It could be much faster than translation from scratch. This process is further discussed in the penultimate section of the chapter.
\n
The aim of this chapter is to overview the methods of machine translation and the methods of the evaluation of its quality. This chapter is organised as follows. In Section 2, different approaches for machine translation are described: rule-based MT in Section 2.1, example-based MT in Section 2.2, statistical MT in Section 2.3, hybrid MT in Section 2.4, and neural MT in Section 2.5. Not all languages are equally difficult for MT. Section 3 exposes common problems when dealing with morphologically rich languages. Sections 4–7 are devoted to MT evaluation. In Section 5, basic metrics for automatic MT evaluation are described and in Section 6, the more advanced ones. Automatic MT evaluation makes sense if it gives similar results as manual evaluation. Section 7 discusses how the correlation between automatic and manual MT evaluation is determined. MT is never perfect. Section 8 discusses post-editing MT to correct the mistakes and make MT of practical use. Section 9 concludes this chapter.
\n
\n
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2. Machine translation
\n
Computer scientists began trying to solve the problem of MT in the 1950s. The first published machine translation experiment was performed by the Georgetown University and IBM. It involved automatic translation of more than 60 Russian sentences into English. The system had only 6 grammar rules and 250 lexical items in its vocabulary. It was by no means a fully featured system. The sentences for translation were selected carefully, as the idea of the experiment was to attract governmental and public interest and funding by showing the possibilities of MT. Many problems of MT had come to light right after, and, consequently, for a long time, MT was present only as a research area in computational linguistics. Overtime, different approaches for MT were defined and gained maturity for practical use today. The history of the development of MT approaches is given in \nFigure 1\n. In [1], it has been shown that 22% of the MT users in the translation industry use rule-based MT systems, 50% use statistical MT systems, and 36% of them use hybrid MT systems.
\n
Figure 1.
Timeline of MT evolution.
\n
\n
2.1 Rule-based machine translation
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The first approaches for MT were based on linguistic rules that were used to parse the source sentence and create the intermediate representation, from which the target language sentence was created. Such approaches are appropriate to translate between closely related languages. The rule-based machine translation methods include dictionary-based MT, transfer-based MT, and interlingual MT.
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Dictionary-based MT uses entries in a language dictionary to find a words equivalent in the target language. Using a dictionary as the sole information source for translation means that the words will be translated as they are translated in a dictionary. As this is, in many cases, not correct, grammatical rules are applied afterwards.
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Transfer-based MT belongs to the next generation of machine translation. The source sentence is transformed into an intermediate, less language-specific structure. This structure is then transferred into a similar structure of the target language, and, finally, the sentence is generated in the target language. The transfer uses morphological, syntactic, and/or semantic information about the source and target languages.
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In interlingual MT, the source sentence is transformed into an intermediate, artificial language. It is a neutral representation that is independent of any language. The target sentence is then generated out of the interlingua.
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To be useful in practice, rule-based MT systems consist of large collections of rules, developed manually over time by translation experts, mapping structures from the source language to the target language. They are costly and time-consuming to implement and maintain. As rules are added and updated, there is the potential of generating ambiguity and translation degradation. Rule-based MT requires linguistic experts to apply language rules to the system.
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2.2 Example-based machine translation
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Example-based MT is based on the idea of analogy. It is grounded upon a search for analogous examples of sentence pairs in the source and target languages. Example-based MT belongs to corpus-based approaches because examples are extracted from large collections of bilingual corpora. Given the source sentence, sentences with similar sub-sentential components are extracted from the source side of the bilingual corpus, and their translations to the target language are then used to construct the complete translation of the sentence.
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2.3 Statistical machine translation
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Statistical MT is based on statistical methods [2]. It also belongs to corpus-based approaches, as statistical methods are applied on large bilingual corpora. Building a statistical MT system does not require linguistic knowledge. Statistical MT utilises statistical models generated from the analysis of texts, being either monolingual or bilingual. It is called training data. If more training data are available, better and larger MT systems can be built. Statistical MT systems are computationally expensive to build and store. Statistical MT can be adapted easily to a specific domain if enough bilingual and/or monolingual data from that domain are available.
\n
Statistical MT is defined using the noisy-channel model from the information theory:
where \n\nf\n\n is the source sentence and \n\ne\n\n is the target sentence. The source sentence consists of words \n\n\nf\nj\n\n\n and the target sentence of words \n\n\ne\ni\n\n\n. Words \n\n\nf\nj\n\n\n belong to the source vocabulary F and the words ei\n to the target vocabulary E. In the phrase-based model, the source sentence f is broken down into I phrases \n\n\n\nf\n¯\n\ni\n\n\n, and each source phrase \n\n\n\nf\n¯\n\ni\n\n\n is translated into a target phrase \n\n\n\ne\n¯\n\ni\n\n\n.
\n
Standard phrase-based SMT models consist of three components:
A translation model of phrases (denoted as \n\nϕ\n(\n\n\nf\n¯\n\n|\n\ne\n¯\n\n)\n\n). In practice, both translation directions, with the proper weight setting, are used: \n\nϕ\n(\n\n\nf\n¯\n\n|\n\ne\n¯\n\n)\n\n and \n\nϕ\n(\n\n\ne\n¯\n\n|\n\n\nf\n¯\n\n)\n.\n\n\n
A reordering model (denoted as d). It is based on distance. The reordering distance is computed as \n\n\nstart\ni\n\n−\n\nend\n\ni\n−\n1\n\n\n−\n1\n\n, where \n\n\nstart\ni\n\n\n is the position of the first word in phrase \n\ni\n\n, \n\n\nend\n\ni\n−\n1\n\n\n\n is the position of the last word of phrase \n\ni\n−\n1\n\n, and d is the probability distribution of reordering.
A language model (denoted as \n\n\np\nLM\n\n\ne\n\n\n). It makes the output a fluent sequence of words in the target language and is most commonly an n-gram language model.
\n\n
Log-linear models of phrase-based SMT are most commonly used:
where a is an alignment between source and target sentences and N is the length of the target sentence.
\n
Statistical MT faces many obstacles. Data sparsity of highly inflected languages limits the effectiveness of statistical MT. Advanced statistical MT systems try to overcome the limitations by introducing data preprocessing and data post-processing. In \nFigure 2\n data preprocessing is used, where morphosyntactic tags (MSD) and lemmas are assigned to words and used in translation and language models. Reordering model captures short-term dependencies. The operation sequence model (OSM) is able to capture long-distance dependencies [3]. It models translation by a linear sequence of operations. The operation generates translation, performs reordering, jumps forward and backward, etc. Having morphosyntactic tags and lemmas available, OSM could be constructed based on them, as depicted in \nFigure 2\n.
\n
Figure 2.
Statistical machine translation system using a language model based on surface forms, a language model based on MSD tags, a language model based on lemmas, and three OSMs.
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\n
\n
2.4 Hybrid machine translation
\n
While statistical methods still dominate research work in MT, most commercial MT systems were, from the beginning, only rule-based. Recently, boundaries between the two approaches have narrowed, and hybrid approaches emerged, which try to gain benefit from both of them. We distinguish two groups of hybrid MT, those guided by rule-based MT and those guided by statistical approaches. Hybrid systems, guided by rule-based MT, use statistical MT to identify the set of appropriate translation candidates and/or to combine partial translations into the final sentence in the target language. Hybrid systems, guided by statistical MT, use rules at pre-/post-processing stages.
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\n
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2.5 Neural machine translation
\n
Neural MT emerged as a successor of statistical MT. It has made rapid progress in recent years, and it is paving its way into the translation industry as well. Neural MT is a deep learning-based approach to MT that uses a large neural network based on vector representations of words. If compared with statistical MT, there is no separate language model, translation model, or reordering model, but just a single sequence model, which predicts one word at a time. The prediction is conditioned on the source sentence and the already produced sequence in the target language. The prediction power of neural MT is more promising than that of statistical MT, as neural networks share statistical evidence between similar words. In \nFigure 3\n one of the proposed topology for neural machine translation is given with the same example sentence as in \nFigure 2\n. The input words are passed through the layers of the encoder (blue circles) to its last layer, the context vector, updating it for every input word. The context layer is then passed through the decoder layers (red circles) to output words, and it is again updated for each output word.
\n
Figure 3.
Neural machine translation system using the encoder-decoder topology.
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The encoder-decoder recurrent neural network architecture with attention is currently the state of the art for machine translation.
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Although effective, the neural MT systems still suffer some issues, such as scaling to larger vocabularies of words and the slow speed of training the models. In addition, large corpus is needed to train neural MT systems with performance comparable to statistical machine translation. Researchers continue to work on solving open problems.
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3. Problems in machine translation
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The fast progress of MT has boosted translation quality significantly, but, unfortunately, machine translation approaches are not equally successful for all language pairs. Morphologically rich languages are problematic in MT, especially if the translation is from a morphologically less complex to a morphologically more complex language. Morphological distinctions not present in the source language need to be generated in the target language. Much work on morphology-aware approaches relies heavily on language-specific tools, which are not always available. Many morphologically rich languages fall in the category of low-resource languages.
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One group of morphologically rich languages is a group of highly inflected languages. They are difficult not only for MT but also for other language technology applications [4, 5]. The main problem in highly inflected languages is that the large number of inflected word forms lead to data sparsity (see example in \nTable 1\n), which results in unreliable estimates in statistical MT [6]. Most words in a given corpus occur at most a handful of times. Therefore, the translation rule coverage is partial, and the estimation of translation probabilities is poor. Some approaches try to reduce the problem of data sparsity by using modelling units other than words; for example, stems and endings, lemmas and morphosyntactic tags, etc. Relaxed word order in inflectional languages poses another problem (see example in \nTable 2\n). Usually, very little information about the target word order is obtainable from the source sentence. Pre-ordering approaches learn to preprocess the source sentence during training in such a way that the words on the source side appear closer to their final positions on the target side. A frequent problem of inflectional languages is also an inaccurate translation of pronouns. There are also many cases in inflectional languages where the subject is dropped completely. Problematic also is differences in the expression of negation. Slavic languages fall into the category of highly inflected languages, and they cause many problems in machine translation [7, 8].
\n
\n
\n
\n
\n
\n\n
\n
\n
Singular
\n
Dual
\n
Plural
\n
\n\n\n
\n
Nominative
\n
študent
\n
študenta
\n
študenti
\n
\n
\n
Genitive
\n
študenta
\n
študentov
\n
študentov
\n
\n
\n
Dative
\n
študentu
\n
študentoma
\n
študentom
\n
\n
\n
Accusative
\n
študenta
\n
študenta
\n
študente
\n
\n
\n
Locative
\n
študentu
\n
študentih
\n
študentih
\n
\n
\n
Instrumental
\n
študentom
\n
študentoma
\n
študenti
\n
\n\n
Table 1.
Inflected word forms of the word “student” (masculine) in Slovene.
In the example, the word has nine different endings.
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1.
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Angleščino študiram dve leti.
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2.
\n
Dve leti študiram angleščino.
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3.
\n
Študiram angleščino, dve leti.
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\n\n
Table 2.
Word permutations of the English sentence “I have been studying English for two years” in Slovene.
Third example is used in colloquial speech.
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Another group of morphologically rich languages is a group of agglutinative languages, which are even more difficult to use in machine translation. In an agglutinative language, words may consist of more than one, and possibly many, morphemes. Each morpheme in a sequence indicates a particular grammatical meaning. Morphemes are used commonly as basic units in MT for those groups of languages. All these phenomena cause errors in translations produced by MT systems and make the use of MT questionable. It is necessary to evaluate MT quality before use in practice.
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4. Machine translation evaluation
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As MT emerges as an important mode of translation, its quality is becoming more and more important. Judging translation quality is called machine translation evaluation. It is defined commonly by technical terms. It means, with the exception of human (i.e. manual) evaluation, that it is defined as an algorithm that can be coded into a programme and run by a computer that calculates the evaluation score, which tells the user how good a translation is. Translation evaluation methods count word- and/or sentence-based errors that can be detected automatically, while general text-level aspects are not taken into account. This weakness of automatic MT evaluation is one of the main criticisms in the translation community. Despite that, in the last decade, we have been witnessing great progress in automatic MT evaluation.
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MT quality can be measured in many different ways, depending on the goal of the evaluation and the means available. Traditionally, there are two paradigms of machine translation evaluation: Glass-box evaluation and black-box evaluation. Glass-box evaluation measures the quality of a system based on internal system properties. Black-box evaluation examines only the system output, without connecting it to the internal mechanisms of the translation system. The focus in this section will be on black-box evaluation. It is concerned only with the objective behaviour of the system upon a predetermined evaluation set. An evaluation set is a set of sentences in the source language and their translations into the target language, obtained by the translation system. These sentence pairs are then exposed to the evaluation. An evaluation set needs to be selected carefully to cover all data features important for future use of the translation system. The same translation quality can then be expected on the other data that is of the same type as the evaluation set; if not, translations of quite different quality could be obtained. The reason is in the fact that MT systems are trained on translation examples. If these examples are of a different type to the text that is afterwards translated by the system, the system has only weak knowledge about its translation and, consequently, produces poor translations. Different types of data mean variations in structure, genre, and style. Evaluation, on the other hand, can focus on testing the systems’s robustness. In this case, the evaluation set is composed of subsets of different data types. One should be aware that obtaining a robust MT system means at least training it with translation examples of different data types.
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There is also a difference between judging and measuring the quality of MT output as a final product and judging and measuring the usability of MT output for subsequent corrections by humans, called post-editing (PE). As regards the latter, it is interesting to know how much editing effort is needed to make the MT output match a reference translation or to become an acceptable translation. What is acceptable translation is left to be decided by the translation expert. In the MT community, there are no criteria for it.
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For a long time, methods for evaluating human and MT quality have been disconnected. The comparison between them was impossible. In recent years, a framework called multidimensional quality metrics (MQM) [9] was developed for evaluating the quality of both human and machine translations. It includes over 100 issue types that cover all of the major translation quality evaluation metrics. For the specific translation quality judgement task, relevant issues may be chosen from MQM. The focus of this section is only on the evaluation of MT quality, whereas human translation is taken as the gold standard.
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4.1 Manual evaluation
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The most common option for judging and measuring machine translation quality is human evaluation. The quality of MT output is judged by experts in translation and linguistics from two different perspectives. The first perspective is the degree of adherence to the target text and target language norms, referring, for example, to features such as grammaticality and clarity. This quality evaluation perspective is known as fluency. When judging fluency, the source text is not relevant. The evaluators have access to only the translation being judged and not the source data. Fluency requires an expert fluent only in the target language. On the other hand, source text adherence is judged to the source text norms and meaning, in terms of how well the target text represents the informational content of the source text. It is known as accuracy. The evaluators have access to the source text and translations being judged. Frequently, the context of a sentence is also taken into account. The evaluators must be bilingual in both the source and target languages. The adequacy and fluency are usually judged on a 5-point scale, as given in \nTable 3\n.
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\n
\n
\n
\n
\n\n
\n
Adequacy
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Fluency
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\n\n\n
\n
5
\n
All meaning
\n
5
\n
Flawless language
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\n
\n
4
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Most meaning
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4
\n
Good language
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\n
\n
3
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Much meaning
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3
\n
Non-native language
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\n
\n
2
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Little meaning
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2
\n
Disfluent language
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\n
\n
1
\n
None
\n
1
\n
Incomprehensible
\n
\n\n
Table 3.
Numeric scale for judging adequacy and fluency.
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Human evaluation is time-consuming and expensive. It is also inherently subjective. To alleviate the problem of subjectivity, more experts are usually asked to evaluate the translations in the same evaluation set, and their evaluations are, finally, justified statistically.
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4.2 Automatic evaluation
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MT systems are rarely static, and they tend to be improved over time as resources grow and bugs are fixed. The evaluation needs to be repeated many times. Automatic evaluation metrics are cost-free alternatives to human evaluation. They are used commonly during the development of MT systems to estimate improvement. They are also applicable to compare different MT systems. While using automatic metrics to judge the translation quality, it is important to understand what their scores mean. They rely on the idea that MT quality in itself should approach human quality. Automatic metrics depend on the availability of human reference translation. They evaluate the output of MT systems by comparing it to the reference translation. As there is a great variability even in human translation, it is important to have more human reference translations for each machine-translated sentence to be evaluated. Evaluation metrics then provide evaluation scores based on the most similar reference translation.
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Standard and recently proposed automatic metrics for MT evaluation will be discussed in the continuation of this section. Statistical correlation coefficients are used to see how close automatic evaluation is to manual judgements. Three correlation coefficients will be described later in the section. Machine translation, coupled with subsequent post-editing, has become a widely accepted method in the translation industry. This type of translation workflow will be discussed at the end of this section.
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5. Basic metrics for translation evaluation in MT
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An obvious method for evaluation is to look at the translation and judge by hand, whether it is correct or not. To get reliable judgements, the evaluators should be appropriately qualified. From a practical point of view, manual evaluation, performed by translation experts, is expensive and takes time. What is needed are automatic metrics that are quick and cheap to use and approximate human judgements accurately. De facto metrics, used in the MT community, are BLEU, NIST, METEOR, and TER. All these metrics need reference translations because they compare the MT output with reference translations and provide comparison scores. If reference translations are available, these metrics can be used to evaluate the output of any number of systems quickly, without the need for human intervention. Let us take an example where the reference translation is “Dve leti že študiram angleščino” and the MT output to be evaluated is “Angleščino študiram dve leti”. If we compute the precision, we get:
\n\n\ncorrect\n\n counts the number of correctly translated words, and \n\n\nlength\no\n\n\n is the length of machine translation output. For the same example, the recall is:
Based on given measures, the quality of translation is good, as reordering is not penalised. It is not always a good decision. For example, the MT output “Dve angleščino študiram leti” will get the same evaluation result, even though the translation is disfluent.
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BLEU [10] measures the overlap of unigrams (single words) and high-order n-grams between MT output and reference translations. It is defined as follows:
The main component of BLEU is n-gram precision, i.e. precisioni\n. It is calculated as the ratio between matched n-grams and the total number of n-grams in the evaluated translation. Precision is calculated separately for each n-gram order, and the precisions are combined via a geometric averaging. The highest n-gram order is defined commonly to be four (four words in a sequence). Higher-order n-grams are used as an indirect measure of a translations level of grammatical well-formedness. The BLEU metric computes the modified precision score, weighted by the brevity penalty, which punishes sentences that are shorter than the reference. The final scores range from 0 to 1. \nTable 4\n contains the calculation of BLEU score for our example.
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\n\n
\n
Metric
\n
Score
\n
\n\n\n
\n
1-gram precision
\n
\n\n\n\n\n4\n4\n\n\n\n\n
\n
\n
\n
2-gram precision
\n
\n\n\n\n\n1\n3\n\n\n\n\n
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\n
\n
3-gram precision
\n
\n\n\n\n\n0\n2\n\n\n\n\n
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\n
\n
4-gram precision
\n
\n\n\n\n\n0\n1\n\n\n\n\n
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\n
\n
Brevity penalty
\n
\n\n\n\n\n4\n5\n\n\n\n\n
\n
\n
\n
BLEU
\n
0%
\n
\n\n
Table 4.
BLEU score computation for the MT output “Angleščino študiram dve leti”, if the reference is “Dve leti že študiram angleščino”.
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BLEU is typically computed over the entire corpus, not single sentences. It is important to point out that very few translations will attain a score of 1 unless they are identical to a reference translation. For this reason, even a human translator will not necessarily score 1, as there is great variability of possible correct translations. In this sense, it is also important to note that having more reference translations per sentence is highly welcome. It will increase the BLEU score. NIST [11] is a close derivate of BLEU.
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Both metrics, BLEU and NIST, focus only on n-gram precision and disregard recall. Recall is the ratio between matched n-grams and the total number of n-grams in the reference translation. METEOR metric [12] combines precision and recall. The authors of METEOR argue that the brevity penalty in BLEU does not compensate adequately for the lack of recall. METEOR computes a score only for unigram matching. Matching is done in three stages. The first stage is exact matching. Strings are aligned, which are identical in the reference and the translation. Words that are not matched are stemmed in the second stage. Stemming is the process of reducing inflected words to their word stem by cutting off the ends of words. Words with the same morphological root are aligned after stemming. In the last stage, unaligned words which are found to be synonyms are aligned, according to WordNet. WordNet [13] is a large lexical database of synonyms (called synsets). In WordNet, synsets are interlinked by means of conceptual-semantic and lexical relations. METEOR does not use higher-order n-grams, as n-gram counts do not require an explicit word-to-word matching. In METEOR, an explicit measure of the level of grammaticality is used. It captures directly how good the structure of the matched words in the machine translation is in relation to the reference.
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Word error rate (WER) metric was first used to evaluate automatic speech recognition. It counts the minimum number of edits needed to change the evaluated translation so that it matches the references exactly, normalised by the average length of the references. The minimum number of edits is also called Levenshtein distance. Possible edits are insertion (I), deletion (D), and substitution (S) of single words. Matched words are denoted with M. Different edits can have different weights. For example, substitution is usually weighted at unity, but deletion and insertion are both weighted at 0.5:
\n\nTable 5\n contains the calculation of WER for our example.
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Translation edit rate (TER) metric [14] is a derivate from the WER. It uses an additional edit step, namely, shifts of word sequences (Shift). A shift moves a contiguous sequence of words within the evaluated translation to another location within the translation. All edits have equal cost. If more than one reference is available, and since the minimum number of edits needed to modify the translation is called for, only the number of edits to the closest reference is measured. TER is normalised by the average length of the reference. Position-independent error rate (PER) is another derivate from WER, which treats the reference and translation output as bags of words. Words from the translation are aligned to words in the reference, ignoring the position.
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6. Advanced metrics for translation evaluation in MT
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Although BLEU, NIST, METEOR, and TER metrics are used most frequently in the evaluation of MT quality, new metrics emerge almost every year. There is a metrics-shared task, held annually at the WMT Conference where new evaluation metrics are proposed [15, 16, 17]. Those which exhibit high correlation with human judgement will be presented from the pool of recently defined metrics.
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CDER [18] is a more advanced metric that is concerned with edits and Levenshtein distance. It calculates the distance between two strings \n\n\ne\ni\nI\n\n\n and \n\n\ne\ni\n\n\n\n\n∼\n\nL\n\n\n\n using the auxiliary quantity \n\nD\n\ni\nl\n\n\n, defined as:
In addition to classical edit operations (i.e. insertion, deletion, and substitution), it models block reordering explicitly as an additional edit operation. As a further improvement, it introduces word dependent substitution costs \n\n\nc\nSUB\n\n\n\ne\ni\n\n\n\ne\n˜\n\nl\n\n\n\n. The observation that the substitution of a word with a similar one is likely to affect translation quality less than the substitution with a completely different word is accounted for in a metric score.
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Tolerant BLEU [19] and LeBLEU [20] are derivates of BLEU with a relaxation of the strict word n-gram matching that is used in standard BLEU. Tolerant BLEU applies a specific distance measure that requires an exact match only in the middle of words, not in words as a whole. LeBLEU uses a distance measure based on characters. It also facilitates a fuzzy matching of longer chunks of text that allows, for example, to match two independent words with a compound.
It calculates the edit rate on character level, whereas shift edits are still performed on word level. First, a technique for word-level shifts is performed, words are then split into characters, and, finally, the edit distance is calculated based on characters, and \n\nShift Cost\n\n is calculated. In addition, the lengths of translations in characters (\n\n\nlength\n\no\nchar\n\n\n\n) instead of references are used for normalising the edit distance, which effectively counters the issue that shorter translations normally achieve lower TER. If we have two translations of different lengths, but with the same edit distance, they will obtain the same TER, as the length of the reference remains unchanged. In the same case, the longer translation will obtain lower TER if the edit distance is normalised by the length of translation.
\n
METEOR universal [22] is a derivate of METEOR. It adds the fourth stage to matching. It is paraphrase matching. For each target phrase e\n1, all source phrases f that e\n1 translates are found. Each alternate phrase (\n\n\ne\n2\n\n≠\n\ne\n1\n\n\n) that translates f is considered a paraphrase with probability \n\nP\n\n\n\nf\n\n\ne\n1\n\n\n⋅\nP\n\n\ne\n2\n\n\n\nf\n\n\n\n. The cumulative probability of e\n2 being a paraphrase of e\n1 is the sum over all possible pivot phrases f:
Phrases are matched if they are listed as paraphrases in a language appropriate paraphrase table. Paraphrases are extracted automatically from the parallel corpora used to train statistical MT systems.
\n
The BEER [23] metric provides a linear combination of different features:
where h is the system output and r is the reference. Each feature \n\n\nϕ\ni\n\n\nh\nr\n\n\n has a weight wi\n assigned to it. The first group of features consists of adequacy features. These features use precision, recall, and F1-score for different counts. F1-score is the harmonic mean of precision and recall multiplied by the constant of 2. The constant of 2 scales the F1-score to 1 when both recall and precision are 1. In BEER, function words and content words (nonfunction words) are counted separately. By differentiating function and nonfunction words, a better estimate is obtained of which words are more important and are less. The most important adequacy feature is a count of matching character n-grams. Using it, the translations are considered partially correct even if they did not get the morphology completely right. Character n-grams of order 6 are used. The second group of features comprises ordering features. Word order is evaluated by presenting the reordering as a permutation and calculating the distance to the ideal monotone permutation. Permutation trees are used to estimate long-distance reordering.
\n
ChrF [24] is another, even simpler, metric based on character n-grams. It computes an F-score, based on precision and recall, using character n-grams:
\n\n\nChrP\n\n and \n\nChrR\n\n are character n-gram precision and recall, averaged over all n-grams. \n\nChrP\n\n is the percentage of n-grams in the translation, which have a counterpart in the reference. \n\nChrR\n\n is the percentage of character n-grams in the reference, which are also present in the translation. In the final score, the parameter is used, which gives more importance to recall than to precision. In [25], the optimal value for β is found to be 2, and the metric is called chrF2. In this metric, a recall has two times more importance than precision. WordF2 is a similar metric, where words are used instead of characters. Different weightings for n-grams were also investigated. Uniform weights are the most promising for machine translation evaluation.
\n
DREEM [26] is a new metric based on distributed representations of words and sentences generated by deep neural networks. Neural networks are models that imitate human brains to recognise patterns in sequences. DREEM employs three different types of word and sentence representations: One-hot representations, distributed word representations learned from a neural network model, and distributed sentence representations computed with a recursive autoencoder. The final score is the cosine similarity of the representation of the translation and the reference, multiplied with a length penalty.
\n
RATATOUILLE [27] is a metric combination of BLEU, BEER, METEOR, and few more metrics, out of which METEOR-WSD is a novel contribution. METEOR-WSD is an extension of METEOR that includes synonym mappings.
\n
In this section, state-of-the-art MT evaluation metrics were investigated briefly. Only the most important characteristics of them were exposed. For a more elaborate description of each metric, the reader is advised to use the provided references to literature.
\n
It should be noted that despite the well-known problems with BLEU, and the availability of many other metrics, MT system developers have continued to use BLEU as the primary measure of translation quality.
\n
Today, different MT systems are available for use in practice. Usually, the qualities of different MT systems are compared between themselves by computing the translation quality scores on a predetermined evaluation set. The question arises whether, if there is a difference in quality on the evaluation set, one can be ensured that different MT systems indeed own different system quality. A difference in quality on an evaluation set may be just the result of happenstance. Research work on the statistical significance test for MT evaluation was done by Koehn [28], and the bootstrap resampling method is proposed to compute the statistical significance intervals for evaluation metrics on evaluation data. Statistical significance usually refers to the notions of the p-value, the probability that the observed difference in quality will occur by chance given the null hypothesis.
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\n
\n
7. Correlation between automatic and human evaluation
\n
Human judgements of translation quality are usually trusted as the gold standard, and the aim of an automatic evaluation metric is to produce quality estimates that are as close as possible to human judgements. As there are many different evaluation metrics, the user needs to decide which automatic evaluation metric he trusts the most. Correlation coefficients are used commonly to measure the closeness of automatic metric scores and manual judgements. Manual MT quality judgements on a number of test data are needed for comparison. Correlation coefficients are then computed on system level and/or segment level.
\n
System-level comparison is done to compare different MT systems in general. First, each system gets a cumulative rank that reflects how high the annotators ranked that system. The metric scores of systems are also converted into ranks, and then the Spearman’s rank correlation coefficient \n\nρ\n\n is computed as [16]:
\ndi\n is the difference between the annotator’s rank and metric’s rank for system \n\ni\n\n. The number of systems is denoted with n. The possible values of \n\nρ\n\n range between 1 (where all systems are ranked in identical order) and − 1 (where the systems are ranked in the reverse order). Metrics with values of Spearman’s \n\nρ\n\n closer to 1 are better. The Spearman’s correlation coefficient \n\nρ\n\n is sometimes too harsh [17]: If a metric disagrees with humans in ranking two systems of a very similar quality, the \n\nρ\n\n coefficient penalises this equally as if the systems were very distant in their quality. Pearson’s correlation coefficient r is sometimes preferred [17]. It measures the strength of the linear relationship between a metric’s scores and human scores:
H is the vector of annotator’s scores of all systems, and M is the vector of the corresponding scores as predicted by the given metric. \n\n\nH\n¯\n\n\n and \n\n\nM\n¯\n\n\n are their means, respectively. \nFigure 4\n shows Pearson’s correlations of selected system-level metrics and MT systems built for different language pairs [15]. We can see that in majority of cases metrics correlate well with human judgements.
\n
Figure 4.
Pearson’s correlation coefficient r for selected evaluation metrics used for different MT systems.
\n
The quality of a metric’s segment level scores is usually measured by means of Kendall’s \n\nτ\n\n rank correlation coefficient [17]. Let \n\nr\n\n⋅\n\n\n denotes annotator’s rank and \n\nm\n\n⋅\n\n\n metric’s rank. To compute Kendall’s \n\nτ\n\n, the annotators rank all the translations of each segment from the best to the worst. Pairs \n\n\na\nb\n\n\n are then built where one system’s translation \n\nr\n\na\n\n\n of a particular segment is judged to be (strictly) better than the other system’s translation \n\nr\n\nb\n\n\n:
In a concordant pair, a human annotator and an automatic metric agree in ranking, and in a discordant pair, they disagree. Finally, Kendall’s \n\nτ\n\n is computed as:
\n\n\nτ\n\n value is between −1 (a metric always predicted a different order than humans did) and 1 (a metric always predicted the same order as humans). Metrics with higher \n\nτ\n\n are better.
\n
In this section, no analysis of correlations for automatic metrics is presented, as it depends on many parameters. In general, all evaluation metrics presented in this chapter correlate well with human judgements. It is only worth mentioning that, for inflected languages, metrics that work on character level correlate better with human judgements than metrics that work only on word level.
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\n
\n
8. Post-editing machine translation
\n
In recent years, MT has become accepted more widely in the translation industry [29]. The most common workflow involves the use of machine-translated text as a raw translation that is corrected or post-edited by a translator. Post-editing (PE) tools and practices for such workflows are being developed in large multilingual organisations, such as the European Commission [30]. The researchers in [31] report that 30% of the companies in the translation industry currently use MT. The majority (70%) of the MT users combine MT with PE at least some of the time.
\n
Post-editing MT is attractive because it has been shown to be faster than human translation. It is faster than translation from scratch and even faster than translation assisted by a translation memory [32]. Speed is not the only factor that should be taken into account when assessing the post-editing process. More recent studies have looked at ways of determining post-editing effort. In [33], three levels of post-editing effort are defined: Temporal effort, cognitive effort, and technical effort. The temporal effort is the time needed to post-edit a given text, cognitive effort is the activation of cognitive processes during post-editing, and the technical effort means the operations such as insertions and deletions that are performed during post-editing. All three levels of post-editing effort are influenced greatly by the translation quality. The use of PE and MT also raises the question about the quality of final translations. Has the quality improved, or is it worse?
\n
As PE effort is related strongly to MT quality, derivatives of standard quality metrics are developed, which are concerned more with PE effort. Human-mediated translation error rate (HTER) [14] is a human-in-the-loop variant of TER. Instead of a reference, post-edited translation is used in the comparison. HTER centres on what edits are to be made to convert a translation into its post-edited version. It is computed as the ratio between the number of edit steps and the number of words in the post-edited version. HTER can be used as a measure of technical PE effort: The fewer changes necessary to convert the translation into its post-edited version, the less the effort required from the translator.
\n
HTER is concerned more with the final translation and not the process. In [34] a metric called actual edit rate (AER) is proposed, which measures the translator’s actual edit operations, which may involve more complex tasks, for example, applying corrections to previously post-edited parts of the text.
\n
A study on PE of MT confirmed the relation between HTER and MT qualities [34]. An increase in HTER was evident as the quality of the MT system decreased. In contrast, they did not establish any significant association between AER and MT qualities. Keyboard activity may not be as sensitive to MT quality as PE time. They also found a linear relationship between MT quality and post-editing speed. MT quality was measured by the BLEU score of the system. The increase of BLEU score by one point resulted in a decrease of post-editing speed of about 0.16 seconds/word post-editing time. Their study also shows the correlation between the quality of machine translation output and the quality after post-editing. They confirmed that worse translation almost always leads to worse result after post-editing. As the use of MT and PE workflows has increased, there is a growing demand for expertise in PE skills. The research on and teaching of skills specific to post-editing has become necessary. The authors in [31] emphasise the impact of “familiarity with translation technology” on the employability of future translators.
\n
\n
\n
9. Conclusion
\n
Machine translation is being used by millions of people on a daily basis. This chapter discusses different MT approaches that were developed over time. Currently, the most promising approach is neural machine translation. Although effective, it also suffers some issues, such as scaling to larger vocabularies of words and the slow speed of training the models. Researchers continue to work on solving the problems and making translation a better service accessible to everyone.
\n
The second part of the chapter describes how machine translation output is evaluated. The main characteristics of human and automatic MT evaluation were outlined. Human evaluation of MT output remains crucial to look for ideas to improve MT systems still further. On the other hand, automatic MT evaluation is cheap and fast. In the chapter, traditional and advanced metrics for automatic MT evaluation were presented. Despite the well-known problems with BLEU, and the availability of many other metrics, MT system developers have continued to use BLEU as the primary measure of translation quality.
\n
MT quality is continually improving. Despite that, there are still a number of flaws in machine translation output. To make the translation correct, post-editing machine translation output is proposed to be integrated into the translation processes. It is discussed at the end of the chapter.
\n
Future research in MT will be devoted to neural machine translation. It is still not very well understood. Its inner workings are commonly seen as a black-box, which works as the neurons of the human brain. As the computing power NMT requires becomes more widely available, many different configurations can be examined to further improve the accuracy of machine translation.
\n
Future effort in machine translation evaluation will be directed toward character-based metrics which show the highest correlation with human judgement at the system and segment levels.
\n
Human translators are worried to be replaced by machines. Machine translation, no matter how sophisticated, cannot match the accuracy of people. Human translators are also an important segment in MT evolution not only as post-editors but also as teachers for MT systems to become better and better.
\n
\n
Acknowledgments
\n
The authors acknowledge the financial support from the Slovenian Research Agency (research core funding No. P2-0069).
\n
\n',keywords:"machine translation, statistical machine translation, neural machine translation, evaluation, post-editing",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/68953.pdf",chapterXML:"https://mts.intechopen.com/source/xml/68953.xml",downloadPdfUrl:"/chapter/pdf-download/68953",previewPdfUrl:"/chapter/pdf-preview/68953",totalDownloads:684,totalViews:0,totalCrossrefCites:0,dateSubmitted:"May 16th 2019",dateReviewed:"August 7th 2019",datePrePublished:"September 7th 2019",datePublished:"May 6th 2020",dateFinished:null,readingETA:"0",abstract:"Machine translation has already become part of our everyday life. This chapter gives an overview of machine translation approaches. Statistical machine translation was a dominant approach over the past 20 years. It brought many cases of practical use. It is described in more detail in this chapter. Statistical machine translation is not equally successful for all language pairs. Highly inflectional languages are hard to process, especially as target languages. As statistical machine translation has almost reached the limits of its capacity, neural machine translation is becoming the technology of the future. This chapter also describes the evaluation of machine translation quality. It covers manual and automatic evaluations. Traditional and recently proposed metrics for automatic machine translation evaluation are described. Human translation still provides the best translation quality, but it is, in general, time-consuming and expensive. Integration of human and machine translation is a promising workflow for the future. Machine translation will not replace human translation, but it can serve as a tool to increase productivity in the translation process.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/68953",risUrl:"/chapter/ris/68953",signatures:"Mirjam Sepesy Maučec and Gregor Donaj",book:{id:"8465",title:"Recent Trends in Computational Intelligence",subtitle:null,fullTitle:"Recent Trends in Computational Intelligence",slug:"recent-trends-in-computational-intelligence",publishedDate:"May 6th 2020",bookSignature:"Ali Sadollah and Tilendra Shishir Sinha",coverURL:"https://cdn.intechopen.com/books/images_new/8465.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"147215",title:"Dr.",name:"Ali",middleName:null,surname:"Sadollah",slug:"ali-sadollah",fullName:"Ali Sadollah"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"305414",title:"Associate Prof.",name:"Mirjam",middleName:null,surname:"Sepesy Maučec",fullName:"Mirjam Sepesy Maučec",slug:"mirjam-sepesy-maucec",email:"mirjam.sepesy@um.si",position:null,institution:null},{id:"309288",title:"Dr.",name:"Gregor",middleName:null,surname:"Donaj",fullName:"Gregor Donaj",slug:"gregor-donaj",email:"gregor.donaj@um.si",position:null,institution:{name:"University of Maribor",institutionURL:null,country:{name:"Slovenia"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Machine translation",level:"1"},{id:"sec_2_2",title:"2.1 Rule-based machine translation",level:"2"},{id:"sec_3_2",title:"2.2 Example-based machine translation",level:"2"},{id:"sec_4_2",title:"2.3 Statistical machine translation",level:"2"},{id:"sec_5_2",title:"2.4 Hybrid machine translation",level:"2"},{id:"sec_6_2",title:"2.5 Neural machine translation",level:"2"},{id:"sec_8",title:"3. Problems in machine translation",level:"1"},{id:"sec_9",title:"4. Machine translation evaluation",level:"1"},{id:"sec_9_2",title:"4.1 Manual evaluation",level:"2"},{id:"sec_10_2",title:"4.2 Automatic evaluation",level:"2"},{id:"sec_12",title:"5. Basic metrics for translation evaluation in MT",level:"1"},{id:"sec_13",title:"6. Advanced metrics for translation evaluation in MT",level:"1"},{id:"sec_14",title:"7. Correlation between automatic and human evaluation",level:"1"},{id:"sec_15",title:"8. Post-editing machine translation",level:"1"},{id:"sec_16",title:"9. Conclusion",level:"1"},{id:"sec_17",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'\nDoherty S, Gaspari F, Groves D, van Genabith J. Mapping the industry. I: Findings on translation technologies and quality assessment. In: GALA. 2013\n'},{id:"B2",body:'\nKoehn P, Och FJ, Marcu D. Statistical phrase-based translation. In: Proceedings of the 2003 Conference of the North American Chapter of the Association for Computational Linguistics on Human Language Technology, Vol. 1. Association for Computational Linguistics; 2003. pp. 48-54\n'},{id:"B3",body:'\nDurrani N, Schmid H, Fraser A. A joint sequence translation model with integrated reordering. In: Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies. Vol. 1. Association for Computational Linguistics; 2011. pp. 1045-1054\n'},{id:"B4",body:'\nDonaj G, Kačič Z. Language Modeling for Automatic Speech Recognition of Inflective Languages: An Applications-Oriented Approach Using Lexical Data. Springer; 2016\n'},{id:"B5",body:'\nDonaj G, Kačič Z. Context-dependent factored language models. EURASIP Journal on Audio, Speech, and Music Processing. 2017;2017(1):6\n'},{id:"B6",body:'\nMaučec MS, Donaj G. Morphosyntactic tags in statistical machine translation of highly inflectional language. In: Proceedings of the Artificial Intelligence and Natural Language Conference (AINL FRUCT); Saint-Petersburg, Russia. 2016. pp. 99-102\n'},{id:"B7",body:'\nMaučec MS, Brest J. Slavic languages in phrase-based statistical machine translation: A survey. Artificial Intelligence Review. 2019;51(1):77-117\n'},{id:"B8",body:'\nMaučec MS, Donaj G. Morphology in statistical machine translation from english to highly inflectional language. Information Technology and Control. 2018;47(1):63-74\n'},{id:"B9",body:'\nLommel AR, Burchardt A, Uszkoreit H. Multidimensional quality metrics: A flexible system for assessing translation quality. In: Proceedings of ASLIB: Translating and the Computer. Vol. 35. 2013\n'},{id:"B10",body:'\nPapineni K, Roukos S, Ward T, Zhu W-J. Bleu: A method for automatic evaluation of machine translation. In: Proceedings of the 40th Annual Meeting on Association for Computational Linguistics. Association for Computational Linguistics; 2002. pp. 311-318\n'},{id:"B11",body:'\nDoddington G. Automatic evaluation of machine translation quality using n-gram co-occurrence statistics. In: Proceedings of the Second International Conference on Human Language Technology Research. Morgan Kaufmann Publishers Inc; 2002. pp. 138-145\n'},{id:"B12",body:'\nLavie A, Agarwal A. Meteor: An automatic metric for MT evaluation with high levels of correlation with human judgments. In: Proceedings of the Second Workshop on Statistical Machine Translation. 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Proceedings of the Ninth Workshop on Statistical Machine Translation. 2014:293-301\n'},{id:"B18",body:'\nLeusch G, Ueffing N, Ney H. Cder: Efficient MT evaluation using block movements. In: 11th Conference of the European Chapter of the Association for Computational Linguistics. 2006\n'},{id:"B19",body:'\nLibovickỳ J, Pecina P. Tolerant bleu: A submission to the wmt14 metrics task. In: Proceedings of the Ninth Workshop on Statistical Machine Translation. 2014. pp. 409-413\n'},{id:"B20",body:'\nVirpioja S, Grönroos S-A. Lebleu: N-gram-based translation evaluation score for morphologically complex languages. In: Proceedings of the Tenth Workshop on Statistical Machine Translation. 2015. pp. 411-416\n'},{id:"B21",body:'\nWang W, Peter J-T, Rosendahl H, Ney H. Character: Translation edit rate on character level. In: Proceedings of the First Conference on Machine Translation: Volume 2, Shared Task Papers, Volume 2. 2016. pp. 505-510\n'},{id:"B22",body:'\nDenkowski M, Lavie A. 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Alignment-based sense selection in meteor and the ratatouille recipe. Proceedings of the Tenth Workshop on Statistical Machine Translation. 2015:385-391\n'},{id:"B28",body:'\nKoehn P. Statistical significance tests for machine translation evaluation. In: Proceedings of the 2004 Conference on Empirical Methods in Natural Language Processing. 2004\n'},{id:"B29",body:'\nWay A. Quality expectations of machine translation. In: Translation Quality Assessment. Springer; 2018. pp. 159-178\n'},{id:"B30",body:'\nBonet J. No rage against the machine. Languages and Translation. 2013;6(2)\n'},{id:"B31",body:'\nGaspari F, Almaghout H, Doherty S. A survey of machine translation competences: Insights for translation technology educators and practitioners. Perspectives. 2015;23(3):333-358\n'},{id:"B32",body:'\nPlitt M, Masselot F. A productivity test of statistical machine translation post-editing in a typical localisation context. The Prague Bulletin of Mathematical Linguistics. 2010;93:7-16\n'},{id:"B33",body:'\nKrings HP, Shreve GM. Repairing Texts: Empirical Investigations of Machine Translation Post-Editing Processes. Vol. 5. Kent State University Press; 2001\n'},{id:"B34",body:'\nSanchez-Torron M, Koehn P. Machine translation quality and post-editor productivity. In: AMTA 2016 Vol. 2016. p. 16\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Mirjam Sepesy Maučec",address:"mirjam.sepesy@um.si",affiliation:'
Faculty of Electrical Engineering and Computer Science, University of Maribor, Slovenia
Faculty of Electrical Engineering and Computer Science, University of Maribor, Slovenia
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