Cloverleaf Clusters: A Common Macrostructural Organization across Human Visual and Auditory Cortex Cloverleaf Clusters: A Common Macrostructural Organization across Human Visual and Auditory Cortex

One of the fundamental properties of mammalian brains is that sensory regions of cor- tex are organized into multiple, functionally specialized cortical field maps (CFMs). An individual CFM is composed of two orthogonal topographical representations, reflect - ing two essential aspects of a sensory feature space. Each CFM is thought to subserve a specific computation or set of computations that underlie particular perceptual behaviors by enabling the comparison and combination of the information carried by the various specialized neuronal populations within this cortical region. Multiple adjacent CFMs, in turn, have now been shown by multiple laboratories to be organized in visual and auditory cortex into a macrostructural pattern called the cloverleaf cluster. CFMs within cloverleaf clusters tend to share properties such as receptive field distribution, cortical magnification, and processing specialization. This chapter will review the evidence for CFM and cloverleaf cluster organization across human visual and auditory cortex and will discuss the utility of these measurements for determining cortical structure and function and for investigating what changes occur in sensory cortex following various types of trauma or disease.


Introduction
Measurements in visual, auditory, and somatosensory cortices across numerous species of mammals have demonstrated that cortical field maps (CFMs) are a fundamental way for the brain to represent sensory information [1][2][3][4][5]. CFMs arise from organized inputs from sensory organs (e.g., retina, cochlea, skin) that maintain the topographic organization of the sensory receptors in the cortex. Thus neurons whose sensory receptive fields are positioned next to one another in sensory feature space are located next to one another in cortex within a CFM. Knowledge of the properties of these CFMs is vital for understanding how specific sensory computations are processed across the brain. Basic stimulus features are processed in lower-level cortical regions, which then send information onto the next stage in the cortical hierarchy to undergo progressively more complex computations [6]. A common aspect of these sensory pathways is that the topography of the sensory receptors embodies the most fundamental stimulus information, which is conserved throughout most of the cortical hierarchy [7,8].
A growing number of measurements in the visual and auditory systems have shown sensory CFMs to be organized into a macrostructural pattern called cloverleaf clusters, indicating that CFMs and cloverleaf clusters may both be fundamental organizing principles in cortical sensory processing [2,4,[7][8][9][10][11]. Such organization may provide a basic framework for the complex processing and analysis of input from sensory receptors [12]. CFMs within clusters tend to share properties such as receptive field distribution, processing specialization, and cortical magnification (e.g., [10,11,13]). It is likely that this cluster organization, like the topographic organization of CFMs, allows for efficient connectivity among neurons that represent neighboring aspects in sensory feature space [14][15][16][17]. Since the axons contained within one cubic millimeter of cortex can extend 3-4 km in length, efficient connectivity is vital for sustainable energetics in cortex [18]. The cloverleaf cluster organization may thus be important for minimizing the length of axons connecting sensory maps within and between clusters, allowing for a more efficient ratio of brain matter to skull capacity.
The definition and characterization of CFMs and cloverleaf clusters have been indispensable in the investigation of the structure and function of human cortex, as these in vivo measurements allow for the systematic exploration of computations across a particular sensory cortex (for reviews, see [8,12]). In addition, they can serve as excellent and dependable independent localizers for investigations of particular functions across individuals (e.g., [3,4,10,13,19,20]). Thus, measuring the organization of individual CFMs helps elucidate the stages of distinct sensory processing pathways and can be used to track how the cortex changes under various disorders [21][22][23][24][25][26][27][28]. This chapter will review our current knowledge of the CFM and cloverleaf cluster organization across human visual and auditory cortex.

Techniques for measuring cortical field maps and cloverleaf clusters 2.1. Phase-encoded fMRI paradigms are used for measuring visual and auditory field maps
Obtaining a high quality measurement of topographic responses is the first step in accurately defining CFMs and requires choosing a set of stimuli that is appropriate for the sensory domain of interest. A highly accurate and powerful paradigm for measuring human CFMs in vivo relies on phase-encoded fMRI measurements (also known as "traveling wave" measurements; 1) [3,4,7,[29][30][31][32]. This technique uses two sets of periodic stimuli that each contain a set of stimulus values presented in an orderly sequence across a range of interest at a given frequency per scan (typically 6-8 cycles per scan; Figure 1Aiii, 1Biii), which allows the use of a Fourier analysis to determine the cortical responses [31]. The phase-encoded paradigm only considers activity that is at this signal frequency, excluding low-frequency physiological noise, among other things. The statistical threshold for phase-encoded cortical activity is commonly determined by coherence, which is equal to the amplitude of the bloodoxygenation-dependent (BOLD) signal modulation at the frequency of stimulus presentation (e.g., 6 stimulus cycles per scan), divided by the square root of the power over all other frequencies except the first and second harmonic (e.g., 12 and 18 cycles per scan) [7,12,31].
For measuring CFMs of visual space (known as retinotopic or visual field maps), one stimulus set is designed to elicit each voxel's preferred eccentricity typically by presenting (i) Top diagram shows the components of a single block of one stimulus presentation (striped orange) for one position (i.e., stimulus phase) of an expanding ring stimulus composed of a black and white moving checkerboard pattern. Note that scanner acquisition occurs simultaneously with the stimulus presentation in this case [7,12]. (ii) Middle diagram shows 6 blocks (striped orange) that together compose one stimulus cycle (teal). Each phase of the expanding ring stimulus is displayed above the blocks; one block thus represents one stimulus position in the "phase-encoded" sequence. The term "traveling wave" is also used to describe this type of stimulus presentation, as the stimuli produce a sequential activation of representations across a topographically organized cortical region. (iii) Lower diagram displays how 6 cycles (teal)-each repeating the same blocks-compose a full, single scan. (B) an example phase-encoded fMRI paradigm for auditory field mapping. (i) Top diagram shows the components of a single block of one stimulus presentation (striped orange) followed by an fMRI data acquisition period (solid orange). The sparse-sampling paradigm separates the auditory stimulus presentation from the noise of the scanner acquisition [35]. The timing of the acquisition is set to collect the peak cortical response to the auditory stimulus, in accordance with the approximate hemodynamic delay. (ii) Middle diagram similarly shows 6 blocks (striped orange + solid orange) grouped together into one stimulus cycle (teal). Each block, or stimulus phase, in each cycle now represents a specific frequency. An example of this sequence for tonotopic measurements is displayed in Hz. (iii) Lower diagram again shows a full, single scan comprising 6 cycles. Note legend in inset. a high-contrast, flickering checkerboard stimulus shaped like a ring, which expands or contracts in discrete even steps between the central fovea and the periphery to sequentially activate distinct eccentricity representations of visual space (Figure 1Aii). The second, orthogonal visual stimulus then activates the preferred polar angle of each fMRI voxel by displaying the same checkerboard pattern now shaped as a wedge spanning a small range of polar angles over all eccentricities. The wedge pattern sequentially activates all polar angles around the central fixation point by rotating clockwise or counterclockwise in discrete steps.
The phase-encoded methods are adapted for auditory field map measurements by combining a phase-encoded stimulus with the sparse-sampling paradigm often used in auditory measurements ( Figure 1B) [4,[33][34][35][36]. Sparse-sampling allows the auditory stimulus presentation to avoid contamination from the noise of the MR scanner during data acquisition by separating the two in time (Figure 1Bi) [37][38][39].
The value of the stimulus (e.g., 5° of visual angle for eccentricity; 400 Hz frequency for tonotopy) that most effectively drives each cortical location is then estimated from the pattern of responses (Figure 2). The cortical response at a specific location is said to be "in phase" throughout the scan with the stimulus that most effectively activates it, hence the term "phase-encoded" mapping. The alternative term "traveling wave" arises from the sequential activation of one neighboring cortical location after the other to create a wave-like pattern of activity across the CFM during the stimulus presentation. It is important to note that the phase-encoded methods will not produce a significant BOLD signal in cortex if the stimulus representation in the region is not organized topographically, as there would be no differential activation across the cortical representation [2,7,20].
The analysis of phase-encoded cortical field mapping data must be done within individual subjects. Each CFM in sensory cortex can vary dramatically in size and anatomical location across individuals, leading to shifts in cytoarchitectural and topographic boundaries [40][41][42][43][44][45]. Primary visual cortex, for example, can vary in size by at least a factor of three, independent of brain size [41]. Consequently, when these data are group-averaged across subjects, especially by aligning the data to an average brain through such atlases as Talairach space [46] or Montreal Neurological Institute (MNI) coordinates [47], the measurements are blurred to such an extent that the gradients composing the CFMs are either inaccurate or missing. Relying on wholebrain anatomical co-alignment for cortical averaging will cause different CFMs to be averaged together incorrectly into one measurement, blurring together data from adjacent areas within each subject and making it impossible to differentiate computations in adjacent areas.

Population receptive field modeling has been developed for measuring visual field maps
A model-based method has been developed for visual field mapping that allows for additional information to be collected about visual field maps (VFMs) by modeling the population receptive field (pRF) of each voxel within a VFM (Figure 2A; for complete details, see [48]). Because VFMs are retinotopically organized, the population of RFs in each voxel within a VFM is expected to have similar representations of visual space, allowing for their combined pRF to be estimated as a single, two-dimensional Gaussian. The pRF modeling approach provides an accurate estimate of not only the preferred center for each voxel's pRF (as with phase-encoded mapping alone), but also its size. In addition, this analysis can be done for any visual stimulus that periodically moves through visual space (e.g., moving bar), rather than just expanding rings and rotating wedges. Research is currently underway to develop a similar pRF model for auditory field maps (AFMs).  [8,49]. For a voxel within a CFM, the neurons each have similarly tuned receptive fields (orange circles with black outlines) with preferred centers of maximal response (black dots). Note how the overlapping receptive fields concentrate coverage in one region of sensory space (darker orange) corresponding to the average receptive field of the group. Middle/top: each typical voxel is on the order of 1 × 1 × 3 mm for cortical field mapping experiments, though voxels are often slightly larger (e.g., 3 × 3 × 3 mm) for other types of experiments [7]. Middle/bottom: phaseencoded (i.e., traveling wave) measurements take advantage of the fact that nearby neurons in sensory cortex have similar preferred centers (black dot) in order to estimate an average preferred center for the population of neurons in a given voxel. Bottom: Population receptive field (pRF) modeling in visual field mapping takes advantage of the fact that nearby neurons in retinotopic cortex have similar receptive fields in order to estimate not only a preferred center, but also a pRF for the population of neurons in a given voxel [48]. (B) Schematic of three example phase-encoded time series with different stimulus responses. Each row represents the activity and analysis of a time series of a single 6-cycle scan of one type of experimental stimuli (e.g., expanding rings) for a single voxel. Black dots indicate simulated raw data points of percent blood-oxygen-level-dependent (BOLD) modulation (i.e., response amplitude). The orange dotted lines represent sinusoidal fits of the simulated data points; each orange line characterizes the average BOLD activation in a different example voxel. The red lines indicate the peak activations per cycle for this imaginary set of voxels. Top and middle rows represent time series of voxels with the same % BOLD modulation, but different timing of peak responses. This difference in peaks indicates differences in stimulus selectivity (i.e., responses to different "phases" of a stimulus). Note the offset of the red lines between the two rows. For example, the top row might represent a voxel with a preferred eccentricity tuning of 3° eccentric to fixation, whereas the middle row might have a preferred tuning of 6° eccentric to fixation. Middle and bottom rows represent time series of voxels with the same timing of peak responses, indicating matching stimulus selectivity; for example, both might have a preferred eccentricity tuning of 6° eccentric to fixation. However, the bottom row has much lower % BOLD modulation than the middle row. Such a difference in response amplitude can be due to several factors, such as differences in receptive field tuning or local vasculature [8,11]. (C) Schematic of three example Fourier power spectra corresponding to the schematic time series in (B). In the phase-encoded paradigm, only BOLD responses that match the stimulus frequency of 6 cycles per scan (red peak) are considered as data. The responses must also be above a predetermined statistical threshold, typically measured in coherence or percent variance explained [7,48]. Gray lines denote noise frequencies. (D) Schematic of three example averaged stimulus cycles corresponding to the schematic Fourier spectra in (C) and to averages of the time series in (B). Each orange dotted line represents the sinusoidal fit for the average, while the peak activation is again marked by the red line. The timing of the peak of each averaged cycle is used to calculate the phase of the preferred stimulus independently for each voxel. Typical pseudocolor overlays on 3-D or flattened brain renderings as shown in Figures 7 and 10 use color to denote cortical responses to this peak activation (e.g., [4,12,33,34]). Note how the top measurement has an earlier peak (red line) that corresponds to an earlier phase of the stimulus (i.e., an earlier presentation time in the cycle) while the middle and bottom measurements' peaks are shifted to later in time (e.g., [7]). The bottom example has a lower % BOLD modulation than the other two schematics, but the same peak activation as the middle example. Adapted from [7].

What criteria are used to identify a cortical field map?
The term "map" has often been imprecisely applied to topographical gradients or other similar patterns of cortical organization, but the study of cortical sensory processing requires the explicit definition a "cortical field map" according to very precise criteria (Figures 3 and 4). First, by definition, each CFM must be composed of at least two orthogonal, non-repeating topographical representations of fundamental sensory dimensions (Figure 3) [4,12,13,29,32]. In the visual system, the retinotopic sensory dimensions arise from the orthogonal aspects of visual space: eccentricity (e.g., center to periphery) and polar angle (e.g., "around the clock") [12,31]. In the auditory system, the sensory feature space is composed of two aspects of With only measurements of dimension 1, one cannot determine whether the region within dimension 1 contains one or more CFMs without measuring a second, orthogonal gradient. (ii) Schematic of a single gradient of dimension 2 overlapping the dimension 1 gradient in (i) to form a single CFM like V1 or hA1. Black arrow denotes low-to-high gradient for dimension 2. Note the orthogonal orientation of the two gradients (i vs. ii) composing this CFM. (iii) Schematic of an alternative gradient organization for dimension 2 overlapping the same dimension 1 gradient in (i). Black arrows denote two low-to-high gradients of dimension 2. The dotted gray line denotes the boundary dividing this region into two CFMs. (C) (i) In a properly defined CFM, measurements along the cortical representation of a single value of dimension 1 (e.g., green) span all values of dimension 2 (e.g., orange to cyan to purple), and vice versa.
(ii) Schematic of vectors drawn along a single CFM from centers of low-stimulus-value regions of interest (ROIs) to high-stimulus-value ROIs for dimensions 1 (e.g., red to blue) and 2 (e.g., orange to purple). The offset measured between the low-to-high vectors for each dimension should be approximately 90° to be considered orthogonal and thus allow for each voxel/portion of the map to represent a unique combination of dimension 1 and dimension 2 values [4,7,10,12]. sound: spectral (i.e., tone) and temporal (i.e., period or temporal envelope) information [4,50]. Figure 3B demonstrates the importance of measurements of two orthogonal sensory dimensions for defining CFMs. A region of cortex with a single large gradient for one dimension could denote a single CFM (Figure 3Bi,ii) or many CFMs (Figure 3Bi,iii). As the number of neighboring gradients increases, the determination of the CFM organization grows increasingly complex. Thus, the number of CFMs in any region cannot be determined without checking for gradient reversals in the representation of the second, orthogonal dimension.
Similarly, two overlapping gradients that are parallel rather than orthogonal will not represent all the points in sensory space uniquely. For example, a region of visual cortex with parallel eccentricity and polar angle gradients would represent a narrow spiral of visual space rather than the entire visual field [7,20,51,52]. Orthogonality can be examined by first estimating the direction of each gradient using a vector drawn from low-to-high stimulus values and then measuring the angle between the vectors for each gradient (Figure 3Cii) [4]. In addition, orthogonality can be confirmed by checking that measurements along the cortical The schematic depicts representations of dimension 1 (e.g., eccentricity or tonotopy) along a flattened cortical surface. Note the repeating patterns of gradient values that denote multiple, repeating representations of low-to-high gradients for the same dimension (e.g., red to green to blue; G1: gradient one; G2: gradient two). Black arrows highlight gradient directions (low, L, to medium, M, to high, H). The gradients for this dimension fall in concentric circles that merge at the outer high (H, blue) representations. Dashed yellow lines mark gradient "reversals" at the edges of the concentric gradients. Note that it is not possible to determine how many CFMs exist within these two gradient sets without additional information from a second representation of an orthogonal dimension. (B) The schematic depicts representations of dimension 2 (e.g., polar angle or periodotopy) along the same flattened cortical surface. Again note the multiple, repeating representations of gradient values from low (orange) to medium (cyan) to high (purple) that now run "around the clock" (G3: gradient three; G4: gradient four). Dashed yellow lines mark again mark gradient "reversals," which now are organized like spokes on a wheel. (C) The diagram demonstrates how gradient boundaries for one dimension of a CFM are determined. Black dots denote hypothetical measurement points along the cortical surface shown in (B). Arrows and yellow lines are as in (B). Two gradients that span the full range of dimension 2 measurements can be divided into G1 and G2, with the representations of stimulus values increasing from low to high across the cortical surface in one gradient to the boundary where the representations in the next map then reverse back from high to low along the cortical surface in the next gradient. (D) Schematic shows the four CFMs defined by these sets of gradients representing the two orthogonal dimensions and arranged in a cloverleaf cluster [4,7,9,10]. Black and yellow dotted lines demark boundaries defined by gradient reversals of dimension 1 and 2 representations, respectively (M1: map one; M2: map two; M3: map three; M4: map four; C1: cluster one; C2: cluster two).
representation of a single value of the first dimension will span all values of the second dimension, and vice versa (Figure 3Ci). The orthogonality of each CFM can be determined for individual subjects and can then be compared across the individual subjects.
Second, each of these topographical representations must be organized as an orderly gradient that is generally contiguous (Figures 3, 4AB) [20,52]. For such a gradient to arise, a large number of voxels must be organized such that they span an entire range of sensory space, in order from one boundary to the other (e.g., from upper to lower vertical meridian for visual polar angle). A topographical gradient is therefore one of the most highly organized features of the cortical surface that we can measure using fMRI; the likelihood of two, orthogonal, overlapping, orderly gradients arising as a spurious pattern from noise is extraordinarily low (for a calculation of the probability of spurious gradients arising from noise, see [11]).
Third, each CFM should represent a substantial portion of sensory space. There may be some differences among CFMs based on the cortical magnification of specific subsets of sensory space, such as the relatively increased foveal representation along the ventral visual cortex, but a large portion of sensory space is still expected to be represented (e.g., [19,20]). Obtaining a high quality measurement of topographic responses across sensory space is dependent upon choosing a set of phase-encoded stimuli that is appropriate for the sensory domain of interest. The range of values in the stimulus set and the sampling density of those values across feature space both influence the accuracy and precision of the measurement. In addition, the specificity of the representations may undergo some degree of blurring due to such factors as the inherent spatial spread of the fMRI signal, overlapping broad receptive fields, and measurement noise [30,[53][54][55]. In auditory cortex, in particular, the intensity (or loudness) of the tonotopic stimulus alone can alter the width of the receptive fields of neuron in primary auditory cortex (PAC) and consequently increase the lateral spread of the BOLD signal measured in neuroimaging [56]. Careful consideration should thus be given to the stimulus parameters and how they may affect the cortical responses.
Fourth, the general features of the gradient representations composing the CFMs should be consistent across individuals. It is important to note, however, that even well-accepted CFMs in visual cortex (e.g., V1) can vary dramatically in size and anatomical location [12,20,41,57], as can cytoarchitectural and topographic boundaries in PAC [40,[42][43][44][45]58]. Despite these variations, the general topographical pattern of adjacency among specific CFMs and cloverleaf clusters will be preserved across individuals. The measurement of CFMs provides one of the few in vivo ways to localize the distinct borders of a particular cortical region across individuals reliably.
The boundaries of a CFM are determined by carefully delineating the edges of each of the orthogonal gradients measured in a particular cortical region of interest (ROI) within a single hemisphere of an individual subject (Figures 3 and 4). Representations of one dimension may be repeated across a region of cortex or may exist in isolation. In isolation, the boundary can be drawn where the gradient responses end, although there will likely be some blurring or spreading of the representation along this edge [12,20,31,48]. Two repeating and adjacent gradients that each span the full range of one dimension (e.g., visual field polar angle) can be divided into two sections at the point at which the gradients reverse (Figures 3B, 4). At the gradient reversal, the representations of stimulus values increase from low to high (or vice versa) across the cortical surface in one section to the boundary where the representations in the next CFM then reverse back from high to low (or vice versa) along the cortical surface in the next section ( Figure 4C).

How are cortical field maps distinguished from sensory gradients or cortical areas?
A pervasive mistake in cortical field mapping has been the attempt to define a CFM using only a single cortical gradient (for reviews, see [2,7,8]). As described above, it is vital to understand that the representation of one dimension of sensory space -one topographical gradient along cortex -is not sufficient to define a CFM (Figures 3, 4). A lone gradient simply reveals that this particular feature of sensory space is represented in that region of cortex.
In addition, we describe measurements of "cortical field maps" rather than use the phrase "cortical areas," as the definition of CFMs is specifically coupled to the topographical measurement, while cortical area definitions are based on a different and potentially conflicting set of criteria. Cortical areas have most extensively been identified in visual and auditory cortex using various combinations of the following measurements: 1) cytoarchitecture, 2) patterns of connectivity, 3) topography of sensory representations, and 4) functional responses [6,7,12,20]. Because these separate types of measurements can at times produce conflicting results, the definition of cortical areas has led to many controversies in the naming of sensory areas. Observations of one or two cortical area criteria have often been used to propose the presence of a distinct cortical area; such definitions may then view the topography -the defining feature of CFMs -as secondary. Multiple CFMs may be present within what has been otherwise defined as a single cortical area. For example, cytoarchitecture was used to define Brodmann areas 18 and 19, which compose much of occipital visual cortex beyond primary visual cortex (V1). However, this same region of visual cortex is tiled with numerous VFMs (for additional discussion, see [7,12]). Because of the significant complexity and confusion that such conflicting definitions can produce, our understanding of how to divide up cortex into distinct regions is still evolving and our naming schemes may vary based on the level of processing we are considering (e.g., first-order vision motion computations vs. the entire visual motion processing pathway). For current investigations of human visual and auditory cortex, sensory system researchers primarily rely on the topographical measurement of CFMs, which is the most well-established the measurement of cortical areas in the in vivo human brain at this time [7,12].

Cloverleaf clusters: macrostructural organization of cortical field maps
Groups of adjacent CFMs have now been shown by multiple laboratories to be organized within visual and auditory cortex into a macrostructural pattern called the cloverleaf cluster. These clusters of CFMs have been described as a cloverleaf due to the organization of the individual CFMs within the cluster appearing like the leaves of a clover plant ( Figure 4D). Brewer and associates first described cloverleaf clusters in human visual cortex [2,7,12,20]; subsequent measurements demonstrated the presence of these clusters in other parts of human visual cortex [10,11], in macaque visual cortex [9], and in human auditory cortex [4].

Figure 4
demonstrates how CFMs are arranged in a spatial pattern of clusters at a scale of several centimeters. Cloverleaf clusters are composed of groups of adjacent CFMs; one dimension of sensory topography is represented in concentric, circular bands from center to periphery of the cluster (e.g., vision: eccentricity; audition: tonotopy; Figure 4A), and the second, orthogonal dimension divides this confluent representation into multiple CFMs with radial bands spanning the cluster center to periphery (e.g., vision: polar angle; audition: periodotopy; Figure 4B). This type of macrostructural organization is now referred to as being radially orthogonal [7]. While the namesake clover plant is most commonly seen with a four-leaf organization, cloverleaf clusters may contain any number of CFMs. However, only an even number of CFMs will produce a smooth progression of representations around the cluster from the border of one CFM to the next. Measurements to date have shown that these clusters have consistent locations relative to one another, but that the maps within each cluster may be oriented somewhat differently, as if, in each individual's brain, the clusters themselves each may be positioned at a slightly different rotation about the cluster's central representation. Such inter-subject variability in cloverleaf cluster positions is consistent with our understanding of the variability in molecular gradient expression underlying the development of topographical gradients in cortex [26,[59][60][61][62]. Careful analysis across individual subjects can identify common CFMs by analyzing the pattern of CFMs and cloverleaf clusters across sensory cortex. This variability in cluster rotation and as well anatomical location again highlights the need for individual-subject data analysis.
The cloverleaf cluster organization of the CFMs may be important not only for the definition of CFMs, but may also play a role in coordinating neural computations. Neurons within each cluster are thought to share common computational resources. For example, CFMs within a cluster might have common mechanisms to coordinate neural timing or short-term information storage [2]. Similarly, it is likely that functional specializations for perception are organized by cloverleaf clusters rather than by single CFMs [20,63]. VFMs within a cluster, for example, have very similar total surface areas, and each cluster's total surface area is reliable across subjects [11]. Each cloverleaf cluster can be functionally differentiated by its pattern of coherence measurements (i.e., BOLD response), cortical magnification, and pRF sizes. These distinctions indicate that VFMs within individual cloverleaf clusters are not only anatomically but also functionally related [7,9,17]. The cluster organization is not necessarily thought to be driving the common functions, but rather reflects how multiple stages in a sensory processing pathway might arise during development across individuals and during evolution across species.

Overview
The visual field spatial arrangement is a fundamental physical property of a visual image [2]. While an image may still be identifiable despite alterations of such properties as its color, motion, contrast, or rotation, scrambling its spatial arrangement typically destroys our ability to identify or reconstruct the original image. This visual field spatial arrangement is encoded by the circuitry of the retina and then preserved and repeated through visual cortex to produce a unifying matrix of visuospatial organization throughout the visual processing hierarchy, despite the diverse computations being performed across regions (e.g., [7,12,64]). As cortex interprets different aspects of the visual image-such as its motion or orientationthe cortical circuitry is organized using receptive fields organized within VFMs to preserve the critical spatial image information.
Neurons in lower-level VFMs perform computations on low-level visual features within a specific retinal location; these computations grow increasingly complex as the stimulus features are processed along the cortical hierarchy. Even though they may contain neurons primarily with large receptive fields, higher-order visual regions may still preserve the visuospatial organization of the image on the retina by retaining sufficient dispersion of receptive field centers through slight differences in the preferred tuning of neuronal responses to visual space [65]. Thus the occurrence of retinotopic organization in higher-order areas can still provide the position and stimulus size invariances typically attributed to high-order object-and face-responsive visual regions [7,11,48,66,67]. Current research is demonstrating that the majority of higher-order visual areas are organized according to visual space, maintaining retinotopically organized, dispersed receptive field centers despite increasingly large receptive field sizes [7,11,19,65,[68][69][70][71][72][73].
Whether the spatial organization in visual cortex remains truly retinotopic or changes to a broader spatiotopic organization -one based on external space rather than retinal space -is still under investigation and cannot be determined with typical visual field mapping methods [69,70,74,75]. In any case, this extensive preservation of visuospatial organization produces a common frame of reference for passing information up or down the visual hierarchy. Such visuallocation-based "channels" could explain how higher-order areas subserving visual-attention can simultaneously influence many lower-level visual areas in spatially specific patterns [74,[76][77][78][79][80]. Another option may be that retinotopic organization is preserved across the cortical hierarchy even without a critical role for visual location information in the computations of a higher-order cortical region merely because changing the neuronal arrangement after it is established at the level of the retina and early visual cortex may be too costly or disruptive during development.

Low-level VFMs are arranged within a cloverleaf cluster on the medial occipital surface
Human visual cortex includes the entire occipital lobe and extends significantly into the parietal and temporal lobes (Figure 5), composing about 20% of cortex [12]. The medial wall of occipital cortex in each hemifield contains four hemifield representations of visual space known as V1, V2, V3, and hV4 (Figures 6, 7; for detailed reviews, see [7,12]). V1 consistently occupies the calcarine sulcus, bounded on either side by the split-hemifield representations of V2 and V3 on the lingual gyrus and cuneus. Human V4 (designated hV4 because of the unclear homology to macaque V4) is positioned as a complete hemifield on the ventral occipital surface adjacent to ventral V3 along the posterior fusiform gyrus [20,82]. These four VFMs compose the medial aspect of the occipital pole cluster (m-OP cluster), which supports lowlevel visual computations [2,7,20].
Because it receives direct inputs from the retinogeniculate pathway, V1 is considered to be primary visual cortex, and it is the first place in retina-to-cortex pathway where information from the two eyes is combined to form binocular cells. In addition, V1 is an important site of basic calculations such as orientation, color, and motion. Each computation is performed across the entire visual field, yet V1 appears at the level of fMRI measurements consist of a single, contiguous representation of visual space. In essence, V1 is composed of several VFMs overlaid on one another, each of which performs a single computation (i.e., separated maps for color, orientation, and motion). In this arrangement, a very intricate mosaic of neurons subserving these computations allows for each computation to be performed over each portion of the visual field. These mosaics, including pinwheel orientation columns, blobs/interblobs, and ocular dominance columns, are still being extensively investigated (e.g., [83][84][85]). These computations divide up into more specialized processing of the visual image after V1, with V2 and hV4 supporting low-level color and form processing, respectively, and V3 playing a role in low-level motion computations [12,20,51].  [2,13]; red, hMT+ cluster (human medial temporal complex, V5) [2,4,9,10,12]; yellow, pSTS cluster (posterior superior temporal sulcus) [11]; purple, regions along the dorsal cortex (intraparietal sulcus) and ventral cortex (fusiform and parahippocampal gyri) currently under investigation (for reviews, see [4,12]). V1, V2, V3, and hV4 each contain a foveal representation positioned at the occipital pole, with progressively more peripheral representations extending into more anteromedial cortex, forming complete eccentricity gradients (Figure 7Ai,Bi,Ci; e.g., [12,29,30,32]). The region where the individual foveal representations meet at the occipital pole is commonly termed the "foveal confluence" [86]. Although fMRI measurements of eccentricity gradients depict these foveal representations as merging into one combined foveal region, careful fMRI measurements of polar angle gradients have demonstrated that distinct boundaries exist between even the most central foveal representations of V1, V2, V3, and hV4 [20,86,87].
The boundaries between each map are delineated by reversals in the polar angle gradients along the medial surface (Figure 7 Aii, Bii, Cii; e.g., [12,29,30,32]). V1 has a contiguous polar angle gradient representing a full hemifield, while V2 and V3 have split-hemifield representations (i.e., quarterfields), which are named by their positions ventral or dorsal to V1: V2d, V2v, V3d, V3v. Because of their relatively consistent anatomical locations and unique concentric polar angle gradients, these three VFMs are typically the first landmarks identified in visual field mapping analyses [31,32]. However, as noted above, the surface areas of these three VFMs fluctuate significantly among individuals independent of overall brain size [41]. While V1 is always located along the fundus of the calcarine sulcus in normal individuals, an increase in V1 size will consequently shift the specific positions of V2 and V3 along the neighboring gyri and sulci. VFMs beyond V3, such as the contiguous hV4 hemifield, continue to shift variably along the cortical surface in accordance with variable individual VFM sizes.

VFMs compose several cloverleaf clusters along the ventral stream
Several more VFMs representing extensive, contiguous hemifields of visual space are positioned along the fusiform gyrus anterior to hV4 (Figures 5 BD, 6, 7). These VFMs are named by their anatomical location and number within a cluster: VO-1 and VO-2, for ventral-occipital cortex, and PHC-1 and PHC-2, for parahippocampal cortex. VO-1 and VO-2 partially compose the VO cluster, share a distinct foveal representation, and subserve mid-level color and form processing [20]. Similarly, PHC-1 and PHC-2 partially compose the PHC cluster, share another discrete foveal representation, and display varying degrees of scene selectivity [19]. The eccentricity gradients reverse between clusters along the ventral surface, while the polar angle gradient reversals again divide up the clusters into individual hemifield VFMs.
In contrast to the measurements in posterior medial and VFMs, it has been much more difficult to measure retinotopic organization within the lateral occipital cortex, a region encompassing the object-responsive lateral occipital complex (LOC; Figures 5B, 6). The LOC was originally thought to lack retinotopic organization or have only an "eccentricity bias" [88][89][90]. Recent studies along the dorsal aspect of the LOC, however, have described two VFMs, called LO-1 and LO-2 for "lateral occipital" (Figure 6). LO-1 is positioned just anterior to the lateral aspect of V3d, reversing from the upper vertical meridian representation at the boundary into its representation of a full hemifield of visual space with the hemifield of LO-2 at its inferior edge [81,91]. The foveal representations of these two VFMs join with the confluent foveal representations of V1, V2, V3, and hV4 on the occipital pole to form part of the lateral aspect of the occipital pole cluster (l-OP cluster). In addition, regions just inferior to LO-2 have been shown to be responsive to lateralized visual stimuli, but have not yet been divided into specific VFMs [92][93][94][95]. Emerging data suggest that lateral occipital cortex inferior to LO-2 will also consist of multiple VFMs, which would complete the l-OP cluster subserving mid-to-high level object recognition. As noted above, the responses to object stimuli in this region could remain both invariant to stimulus size and position over a wide field of view while retaining visuospatial information [67].

Lateral occipital-temporal cortex
Just anterior to LOC along the bank of the inferior temporal sulcus, motion-selective cortex comprises a distinct cloverleaf cluster, alternatively known as the TO (temporal-occipital) or MT (medial-temporal) cluster (Figures 5B, 6) [2,10,96,97]. This cloverleaf cluster consists of the four VFMs of the hMT+ (human MT complex) thought to be involved in successive stages of visual motion processing [9,10,96,98,99]. The dorsal two hemifield VFMs are positioned just anterior to the LO maps, merging with that cluster at an eccentricity gradient reversal. These VFMs have been alternatively termed TO-1 and TO-2 or MT and MST, respectively, based on the likely homology to the VFMs of the MT cluster in macaque monkey [9,10,97]. These two VFMs share a distinct foveal representation with two VFM along more ventral lateral occipital cortex that are likely homologous to macaque FST and V4 t.
Anterior, but not adjacent, to the TO cluster, is a recently discovered additional cloverleaf cluster on the posterior superior temporal sulcus (pSTS): the pSTS cluster (Figures 5B, 6) [11]. The pSTS clusters consists of four VFMs labeled pSTS-1, pSTS-2, pSTS-3, pSTS-4 and is located in a region implicated in high-order visual processing dealing with complex aspects of face and motion processing [100,101]. In addition, this cortex has been associated with high-order multisensory processing, including the integration of auditory and visual information about objects [102,103]. Thus, these CFMs may have multimodal tuning.

VFMs, cloverleaf clusters, and polar angle gradients in dorsal parietal and frontal cortex
Beyond the medial half of the dorsal boundary of V3d, a series of hemifield VFMs run from the transverse occipital sulcus (TOS) up along the intraparietal sulcus (IPS) (Figures 5B, 6; e.g., [12,76]). The first VFMs here bordering V3d are V3A and V3B, which share a discrete foveal representation within the TOS (Figure 7) [11,13,104,105]. Measurements of V3A suggest that it has some similarities to macaque V3A and V3d, and it is thought to play a role in motion processing; the computations subserved by V3B are not yet resolved, but the basic parameters of its computations match that of V3A [11,13,104,106,107].
Moving anteriorly along the IPS from V3A and V3B, measurements find that visuospatial responses here are activated by attentionally demanding, phase-encoded stimuli, consistent with the description of this parietal region as subserving spatial attention [70, 74, 77-79, 106, 107]. The first VFM along the IPS is IPS-0 (formerly called V7), which has a foveal representation distinct from the one shared by V3A and V3B and represents a full hemifield of contralateral visual space [77,107]. A series of polar angle representations then runs from IPS-0 along the medial wall of the IPS (Figure 6B). These representations have primarily been described as reversing smoothly through a strip of several hemifield representations from IPS-0 to IPS-5, with another polar angle representation termed SPL-1 (superior parietal lobule) just medial to these maps [70-72, 74, 76, 77, 79, 108]. Also along the medial wall of the parietal cortex and just anterior to V3d in the parieto-occipital sulcus are two additional polar angle gradients involved in particular types of motion processing, such as self-motion and visuomotor integration: V6 and V6A [109,110]. V6 and V6A both contain relatively coarse polar angle representations of the contralateral hemifield and potentially eccentricity representations of the far periphery. It is important to note that, except for V6, these parietal representations are all descriptions of polar angle gradients rather than complete VFMs (Figure 3). Thus the full extent of VFMs and cloverleaf clusters along the IPS remains to be determined [7].
Several polar angle representations of the contralateral hemifield have also been measured in frontal cortex by a few studies using a variety of stimuli including phase-encoded paradigms, memory-guided saccade tasks, and visual spatial attention tasks ( Figure 6B) [69,70,73,76,78,79]. These topographic representations are positioned in precentral cortex (pre-CC), dorsolateral prefrontal cortex (DLPFC), the frontal eye fields (FEF), and the supplementary eye fields (SEF), cortical regions involved in the complex visual processing of spatial attention and eye movement control. Like the polar angle measurements along the IPS, these frontal regions also lack measurements of orthogonal eccentricity representations. As research progresses, we expect overlapping eccentricity gradients will be found, forming VFMs likely organized into cloverleaf clusters.

Overview
The auditory system encodes the complex sound waves we encounter in our daily environments as the intensity of their individual component frequencies, analogous to a Fourier analysis (Figure 8A). Higher frequency variations are transduced near the opening of the cochlea of the inner ear, with decreasing frequencies transduced further down the membrane. This topographic gradient of frequencies, or tones, from low to high is referred to as tonotopy (or, less commonly, cochleotopy -a map of the cochlea). Spectral sound representation in the form of tonotopic gradients is thus one aspect of the fundamental auditory reference frame. This basic auditory information and tonotopic organization is preserved through multiple subcortical areas and at least through low-level auditory cortex (for reviews, see [8,[111][112][113]).
The second, orthogonal aspect of the fundamental auditory reference frame is temporal sound information, termed periodicity ( Figure 8B) [4,114,115]. Periodicity information is thought to be coded in the auditory nerve through neural activity time-locked to the periodicity of the amplitude modulation (i.e., the length of time from peak-to-peak of the temporal envelope) [114,116]. The temporally varying aspects of sound are expected to be encoded by neurons tuned to sounds of certain durations as well as neurons selective for the onset and offset of sounds Periodotopy thus refers to the topographic organization of neurons that respond differentially to sounds of different temporal envelope modulation rates.
Auditory processing in human and non-human primate cortex resides bilaterally within the temporal hemispheres near the lateral sulcus ( Figure 9A) [8,42,[117][118][119][120][121]. In the model system of macaque monkey, the first stage of cortical processing lies along the superior temporal gyrus (STG) and consists of three primary auditory areas: A1, R, and RT [122]. In contrast to visual cortex in which V1 is a single area defined as primary visual cortex, primary auditory cortex is considered to be a core of these three AFMs, as all three contain the dense thalamic inputs from the thalamus, the expanded layer IV, and the high expression of cytochrome oxidase, acetylcholinesterase, and parvalbumin characteristic of primary sensory cortices [117,118,121,[123][124][125][126][127][128]. Secondary levels of cortical processing are then mediated by a set of eight belt regions, situated with four areas along both the lateral (CL, ML, AL, RTL) and medial (CM, RM, MM, RTM) sides of the core [129][130][131]. On the lateral side of the belt, an additional two regions compose the parabelt, which serves as a tertiary level of auditory processing that distributes information to neighboring auditory regions as well as multimodal areas across cortex [123,132].
Due in part to methodological limitations, many studies of human audition over the past few decades have focused on psychoacoustics research of audition at the behavioral level or on neuroimaging investigations of speech production and comprehension in high-order cortex. In contrast, research about the structure and function of lower-level auditory processing in human cortex has been comparatively limited. An understanding of how lower-level auditory cortex is organized is crucial, however, for expanding our understanding of both the cortical pathways supporting basic auditory behavior and the auditory inputs available to speech processing networks.
Recent research has revealed that the cortical organization underlying lower-level human auditory processing resembles that of macaque core, belt, and parabelt structure, but with a rotation of these regions from the STG to Heschl's gyrus (HG), an anatomical structure within the lateral sulcus unique to humans (Figure 9) [4,43,58,121]. The human auditory system also has similarities to the human visual system at several levels, from the fundamental organization of processing lower-level auditory information within AFMs and cloverleaf clusters Light gray indicates gyri; dark gray indicates sulci. The specific location of the hA1 auditory field map for this subject is marked with the black dotted lines. hA1 lies at the tip of HG. Note that HG is a single gyrus in this subject. CG: Circular gyrus (green); PP: planum polare (green); PT: planum temporale (green). Green labels are sections within LS. The three colored ROIs on HG denote the locations of the cloverleaf clusters comprising the core and belt AFMs: Yellow, hCM/hCL cluster; red, HG cluster including hA1, hR, hRM, hMM, hML, hAL; magenta, hRTM/hRT/hRTL cluster [4,8]. Additional cloverleaf clusters are under investigation in the surrounding regions of auditory cortex along LS. [4,8] to the dual-stream model for higher-level speech processing in which ventral pathways support comprehension and dorsal pathways subserve sensorimotor integration [133]. AFMs, like VFMs, comprise two orthogonal representations of dimensions of sensory feature space: tonotopy (maps of tones, the spectral content of sounds) and periodotopy (maps of periods, the temporal content of sounds). Furthermore, these AFMs are organized into several cloverleaf clusters; the discovery of this cross-modal presence of cloverleaf clusters demonstrates that such cluster organization is a fundamental aspect of sensory cortex (Figures 9-11) [4,134].

AFMs compose three cloverleaf clusters overlapping Heschl's gyrus
The history of auditory field mapping was complicated by the long delay between our ability to measure tonotopic gradients in human cortex and the discovery of human and non-human primate orthogonal periodotopic representations. Basing their investigations on only tonotopic responses, neuroimaging researchers futilely attempted to reach a consensus about the organization of human auditory cortex. As expected from schematics in Figure 3, the measurement of only one topographical representation led to a number of variable, conflicting, and ultimately unusable interpretations of the organization of human PAC and surrounding regions (for detailed discussions, see [8,134]).
The relatively recent discoveries of periodotopic gradients in the macaque monkey midbrain brain and human auditory cortex have now allowed for an accurate definition of the first auditory field maps [4,115]. This finding is supported by evidence from human psychoacoustic studies, which show that separable filter banks exist not only for frequency spectra, but also temporal information, signifying the presence of neurons with receptive fields tuned to ranges of frequencies and periods [50,[135][136][137]. Additionally, gradients representing temporal acoustic information have been measured in other animal models, including domestic cat PAC and chinchilla inferior colliculus [82,138].
Eleven AFMs have been defined in human auditory cortex to date and show clear homologies to the eleven core and belt subfields of auditory cortex identified in human cytoarchitectural studies and in non-human primate cytoarchitectural, connectivity, and tonotopic measurements (Figures 10, 11) [4,8,42,118,119,122,123,126,[139][140][141]. The naming of the human AFMs follows that of the suspected homology to macaque, but appends an "h" to indicate human [4].
Three separate sets of concentrically organized tonotopic gradients overlap HG, running from STG to the circular sulcus (CiS; Figure 10A, 11C). The first complete auditory cloverleaf cluster measured in humans -the HG Cluster -is centered on the primary, circular tonotopic gradient on Heschl's Gyrus (HG; Figures 9-11) [8]. The low-tone representation in this cluster is positioned centrally and expands in iso-tone bands out to high-tone representations. A reversal in the anteromedial high-tone region of the HG cluster divides the HG cluster from the CM/CL cluster. Abutting the HG cluster where HG meets STG, there exist another tonotopic reversal into the RT cluster. More research is required to determine the full extent of the CM/CL and RT clusters.
Periodotopic gradient reversals along HG divide the tonotopic representation of the central HG cluster into two AFMs each of core, medial belt, and lateral belt: hA1, hR, hMM, hRM, hML, and hAL (Figures 10B, 11D). HA1 lies within this cluster at the tip of HG and is the largest of the core and belt AFMs. It is thought to subserve the most basic of cortical auditory computations, and this is reflected in its detailed tonotopic and periodotopic gradients [123]. The anterior/medial aspect of hA1 is tuned to high tones, and the posterior/lateral aspect is tuned to low tones. Just past the tip of HG and the high-tone reversal in the circular sulcus (CiS), a high-periodicity gradient reversal divides the tonotopic representation of the CM/ CL cluster into hCM, and hCL, two regions that have been implicated in early language and speech processing as well as audiovisual integration [142]. Similarly, at the base of HG, a set of periodotopic gradients divides the partial third cloverleaf cluster into hRT, hRTM, and hRTL. These AFMs along STG in macaque have been shown to be involved in lower-level processing of stimuli like temporally modulated environmental sounds [129,130]. Now that these AFMs and cloverleaf clusters can be reliably identified in individual subjects, researchers can are shown in gray, as defined by [4]. Schematics were created from individual-subject data drawn from multiple phaseencoded fMRI experiments. Diagrams are oriented along the same global anatomical axes. Darker beige background indicates the plane of the lateral sulcus, while lighter beige overlay indicates gyri. The edges of gyri are also noted with dashed black lines. HG: Heschl's gyrus. a/p STG: anterior/posterior superior temporal gyrus; CiS: circular sulcus; CG: circular gyrus. (A) Diagram depicts the locations of tonotopic representations overlaid along the core (white) and belt (gray) AFMs. The approximate locations of low (L) and high (H) tonotopic representations are shown in red and blue, respectively. Dotted black lines mark the boundaries between AFMs within these three cloverleaf clusters: hCM/hCL cluster (partial cluster defined to date); HG cluster with hA1; hRTM/hRT/hRTL cluster (partial cluster defined to date).
(B) Diagram now shows periodotopic representations overlaid along the same example region of cortex. L and H now refer to the approximate locations of low (orange) or high (purple) periodotopic representations, respectively. (C) Color legends for tonotopy schematic (left), core/belt AFMs (middle left), and periodotopy schematic (right). Inset legend (middle right) shows anatomical directions for both diagrams. M: Medial; L: lateral; A: anterior; P: posterior. For a detailed review, see [8].
begin to investigate the specific functions subserved by each AFM. Based on emerging data, we also expect that neighboring cortex like planum temporale (PT) and STG will also contain AFMs organized into cloverleaf clusters.

Considerations for defining additional CFMs and cloverleaf clusters
To date, cloverleaf clusters have been shown to both be common to multiple sensory systems across human cortex and conserved across some primate species [2,7,9,10,20,134,143]. As we continue to delineate additional CFM clusters and study their functional responses, it is important to consider what homologies may exist across sensory domains and species as well as potential ways CFMs may be altering under evolutionary pressures. Evolution is an ongoing process; CFMs and clusters are not necessarily, and in fact are unlikely to be, at an optimal evolutionary endpoint. Thus it is important to keep in mind that the cortical sensory representations that we are measuring may not be perfectly organized. In addition, with 25 million years of divergent evolution between humans and macaque monkeys, some CFMs and clusters may be unique to one species or the other [144]. Figure 12 depicts several ways in which CFMs may have changed or be in the process of changing across species or sensory domains (for extended discussion, see [5]). The size of a CFM itself (Figure 12B) or the total number of CFMs devoted to a particular sensory processing pathway ( Figure 12D) may increase or decrease, reflecting an expansion or reduction of the Figure 12. Potential cortical field map changes over evolution. Schematic diagrams depict numerous ways CFMs might change over the course of evolution. Consideration of such changes is important for evaluating potential homology of CFMs across sensory cortices and among species (for extended discussion, see [5]). (A) Each schematic shows two pictures of the same CFM, one for each orthogonal dimension (e.g., dimension 1: tonotopy or eccentricity; dimension 2: periodotopy or polar angle). The subsequent schematics depict changes to this CFM. importance of the particular behavior this cortex subserves. The internal structure of a CFM may be altered in the magnification of specific sections of the representations (Figure 12C) or may contain additional, emerging representation subsections (Figure 12E). Similarly, the number of cloverleaf clusters may be modified. Thus the homology of CFMs across species is very important for understanding functional similarities in different model systems, but care must also be taken to recognize what differences may exist.
In addition to the likely role of cloverleaf clusters in efficiently grouping together neurons performing associated computations, the emergence of new cloverleaf clusters during evolution as an organizational unit across cortex could facilitate the development of expanded or even novel cortical computations for an emerging species [8,145]. In other words, once a particular organizational unit such as the cloverleaf cluster has arisen in one sensory modality, the same organizational unit might be duplicated and repeated across the brain as it evolves, following consistent genetic mechanisms during development [145]. Now that CFMs and cloverleaf clusters have been established as fundamental organizational principles in visual and auditory cortex, we can use this knowledge to guide measurements of similar topographic groupings in other sensory domains (e.g., somatosenstaion, pain matrix, olfaction; [3,4,146]).

Conclusion
Human visual and auditory cortex thus interestingly share a common organizational scheme, with each sensory system compartmentalized into CFMs that are themselves arranged on a larger scale into cloverleaf clusters. This fundamental organization provides a basic framework for the complex processing and analysis of input from sensory receptors. Such similarity may be common across many sensory domains, which may aid in the future identification of CFMs in the representation of other senses and in homologous regions in related species. The detailed examination of these CFMs and clusters in individual subjects can also be applied to the careful analysis of the computational stages of sensory processing and to the detailed tracking of cortical changes in a variety of diseases.