Biomedical Engineering Professional Trail from Anatomy and Physiology to Medicine and Into Hospital Administration: Towards Higher-Order of Translational Medicine and Patient Care

This innovative book integrates the disciplines of biomedical science, biomedical engineering, biotechnology, physiological engineering, and hospital management technology. Herein, Biomedical science covers topics on disease pathways, models and treatment mechanisms, and the roles of red palm oil and phytomedicinal plants in reducing HIV and diabetes complications by enhancing antioxidant activity. Biomedical engineering coves topics of biomaterials (biodegradable polymers and magnetic nanomaterials), coronary stents, contact lenses, modelling of flows through tubes of varying cross-section, heart rate variability analysis of diabetic neuropathy, and EEG analysis in brain function assessment. Biotechnology covers the topics of hydrophobic interaction chromatography, protein scaffolds engineering, liposomes for construction of vaccines, induced pluripotent stem cells to fix genetic diseases by regenerative approaches, polymeric drug conjugates for improving the efficacy of anticancer drugs, and genetic modification of animals for agricultural use. Physiological engineering deals with mathematical modelling of physiological (cardiac, lung ventilation, glucose regulation) systems and formulation of indices for medical assessment (such as cardiac contractility, lung disease status, and diabetes risk). Finally, Hospital management science and technology involves the application of both biomedical engineering and industrial engineering for cost-effective operation of a hospital.


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Treadmill test, for evaluating cardiac fitness; -Lung ventilation modelling, for assessment of status of mechanically ventilated COPD patients; -Derive a Cardiac Contractility index, which can be determined non-invasively (in terms of auscultatory pressures) and applied to assess left ventricular contractile capacity; -Glucose Tolerance tests, to detect diabetic patients and borderline patients at risk of becoming diabetic; -Non-invasive determination of Aortic Pressure profile, systemic resistance and aortic elastance (Eao, to characterize the LV systemic load). Finally, we have also shown the application of this concept and methodology to hospital management. There is a considerable (and hitherto under developed) scope for application of Industrial Engineering discipline for effective hospital administration, in the form of how to determine and allocate hospital budget to optimise the functional performances of all the hospital departments. This leads us to what can be termed as the Hospital Management System. Herein, we have shown how to formulate a performance index (PFI) for ICU. This index divided by the Resource index gives us the cost-effectiveness index (CEI). The Management strategy is to maintain certain acceptable values of both PFI and CEI for all hospital departments, by judicious allocation of staff to the departments. This enables the determination of the Optimal Resource index (RSI) and hospital budget (HOB) to maintain a balance between PFI and CEI for all the hospital departments. This can constitute the basis of Hospital Management. of straight bars placed at equal spacing of (2πa/n) measured at the waist circle, to constitute the generators of the HP surface [3].

Equilibrium of Forces on a Shell Segment under Vertical load P:
At the waist (r o = a), . Equilibrium of Forces on a Shell Segment: Analysis for stresses N φ and N θ due to the vertical force P [3,2].
Then based on the analysis in Fig 5, we obtain the expression for the equivalent resultant compressive forces C in the fibre-generators of the VB HP shell. Thus it is seen that the total axial loading is transmitted into the HP-shell's straight generators as compressive forces. It is to be noted that the value of C is independent of dimensions R and a. Equivalent compressive force C in the generators (corresponding to the stressresultants acting on the shell element) equilibrating the applied axial loading [3,2].
It can be noted that the value of C is independent of dimensions R and a.

Stress analysis under Torsional loading [3]:
Next, we analyse the compressive and tensile forces in the HP shell generators when the VB is subjected to pure torsion (T).In this case (referring to fig. 6), the normal stress resultants are zero, and we and only have the shear stress-resultant , as given by Expressions for tensile forces T and compressive forces C in the generators, indicate that torsion loading is also transmitted as axial compressive and tensile forces through the generators of the VB, which makes it a naturally optimum (high-strength and light-weight) structure [3].

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Biomedical Engineering Professional Trail from Anatomy and Physiology to Medicine and Into Hospital Administration: Towards Higher-Order of Translational Medicine and Patient Care 7 Thus, a torsional loading on the VB HP shell is taken up by one set of generators being in compression and the other set of generators being in tension. Equilibrium of a Shell Element Comprising of Two Intersecting Generators: The equivalent compressive forces (C) and tensile forces (T); in the shell generators (required to equilibrate the applied load), are given by:  Fig 8 illustrates how the mechanism of how the spinal disc bears compression without bulging. It is seen that the nucleus pulposus plays the key role in this mechanism, as will be explained further in this section. Hence the absence of it in a denucleated disc causes the disc to bulge.  We now present the elasticity analysis of the disc to first obtain the radial, circumferential and axial stresses in terms of the disc deformations and annulus modulus E [4]. We next carry out the stress analysis of the disc under vertical loading P (fig 10), to obtain the expressions (equations 10) for the stresses in the disc annulus in terms of the load P , pressure p in the nucleus-pulposus, and the disc dimensions (a and b) [4]. We then derive the expressions for the disc axial and radial deformations u δ and δ h in terms of nucleus pulposus pressure p, the annulus modulus E and the disc dimensions, as given www.intechopen.com Biomedical Science, Engineering and Technology 8 by equations (17) and (18). Now the annulus modulus E is a function of the stress in the annulus (k being the constitutive proportionality constant), and hence of the pressure p and the disc dimensions, as shown by equation (21). As a result of this relationship, we finally show that the disc deformations are only functions of k and the disc dimensions. This implies that irrespective of the increase in the value of load P, the disc deformations remain constant, and only depend on the constitutive property parameter k. This is the novelty of the intrinsic design of the spinal disc! Fig. 9. Geometry and Deformation Variables of the Spinal Disc [4].

Stress Analysis for Vertical Loading [4]:
For a vertically applied force P, where  f is the hydrostatic pressure in the NP fluid, and  z the axial stresses in the annulus.
Because the disc height (h) is small, σ f ≈ constant, and hence fr ra p 22

Physiology: Mechanism of left ventricle twisting and pressure increase during isovolumic contraction (due to the contraction of the myocardial fibres)
Introduction and objective: The left ventricular (LV) myocardial wall is made up of helically oriented fibers. As the bioelectrical wave propagates along these fibers, it causes concomitant contraction wave propagation. Our LV cylindrical model is illustrated in figure  11. The contraction of the helical oriented myocardial fibers causes active twisting and compression of the LV (as illustrated in fig 11), thereby compressing the blood fluid contained in it. Then due to the very high bulk modulus of blood, this fluid compression results in substantial pressure increase in the LV cavity.
Herein we simulate this phenomenon of LV isovolumic contraction, which causes the intra-LV pressure to rise so rapidly during 0.02-0.06 seconds of isovolumic contraction. Our objective is to determine how the pressure generated during isovolumic contraction, due to by active torsion (with LV twisting) and compression (with LV shortening) caused by the contractile stress in the helically wound myocardial fibers [5]. The contraction of the myocardial fibers causes active twisting and compression of the left ventricle, thereby compressing the blood fluid contained in it. Then, due to the very high bulk modulus of blood, this compression results in pressure increase in the ventricular cavity. Hence, we simulate this phenomenon by applying and determining equivalent active torque and compression to the LV-cylindrical model incrementally (as ΔF and ΔT), so as to raise the LV pressure by the monitored amounts.

Modeling approach:
We monitor LV pressure (p), LV volume (V), myocardial volume (V M ), and wall thickness (h) at time intervals during isovolumic contraction. From the monitored V, V M , and h, we determine the LV model radius R and length L and the wall thickness h. We also monitor LV twist angle ϕ.
We then invoke blood compressibility to determine ∆V at subsequent instants , as ∆V = (∆p/K) V, where ∆p is the monitored incremental pressure and K is the bulk modulus of blood. From the volume strain ∆V/V, we then determine the model length and radius strains ∆I/L and ∆r/R, and hence the LV dimensions with respect to LV dimensions at the start of isovolumic contraction. This enables us to determine the stretches (strains) (λ z , λ r , λ θ and ), and thereafter the Lagrange strain tensor components (E rr , E θθ , E zz , E θz ) in terms of these stretches and the hydrostatic pressure. Then, we express the LV wall stresses in terms of the strain energy density function Ψ, of the Lagrange strain tensor components in cylindrical coordinates and the material constitutive parameters (b i ), in which (i) the stretches (λ z , λ r , λ θ and ) have been calculated and are known, (ii) the hydrostatic pressure and the constitutive parameters b i (i = 1, 2, . . . , 9) are the unknowns. So now, we substitute the stress expressions σ rr and σ θθ into the boundary conditions equations (of equilibrium between the internal pressure and the wall stresses σ rr and σ θθ , and between the internal pressure and wall stress σ zz ), and determine the best values of the constitutive parameters (b i ) and the hydrostatic pressure to satisfy these equations. We then go back, and determine the stress expressions. We utilize the stress expressions for σ zz and σ θz , to determine the generated values of torsion (ΔT) and axial compression (ΔF),due to the contraction of the helically wound myocardial fibres. Finally, we determine the principal stresses and principal angle along the radial coordinate of the LV wall thickness, from which we can interpret the fibre orientations, which can be related to the LV contractility index. This procedure is carried out at three instants of time from the start of isovolumic contraction, and at 0.02 s, 0.04 s, 0.06 s into the isovolumic contraction phase. Hence, from the monitored LV ∆p and computed ∆V at these three instants (with respect to the pressure and volume at t = 0 at the start of isovolumic contraction phase, we determine (i) the time variation of the internally generated torque and axial compression during the isovolumic contraction phase (fig 12), as well as (ii) the time variations of the principal (tensile) stress and the principal angle (taken to be equivalent to the fiber angle) during the isovolumic contraction phase (fig 13).

Model Kinematics:
We model the LV as an incompressible thick-walled cylindrical shell subject to active torsion torque and compression as illustrated in fig 11. The upper end of the LV model is constrained in the long-axial direction to represent the suspension of the left ventricle by the aorta at the base. Now, considering the LV at end-diastole to be in the unloaded reference configuration, the cylindrical model in its undeformed state is represented geometrically in terms of cylindrical coordinates (R, Θ, Z) by where R i , R o and L denote the inner and outer radii, and the length of the undeformed cylinder, respectively. In terms of cylindrical polar coordinates (r, θ, z), the geometry of the deformed LV configuration (with respect to its undeformed state at the previous instant) is given by: where r i , r o and l denote the inner and outer radii, and the length of the deformed cylinder, respectively. We further consider the incompressible LV model in its reference state to be subjected to twisting, radial and axial deformations in the radial and long-axis directions during isovolumic contraction, such that (also based on incompressibility criterion), the deformations of incompressible LV cylindrical shell can be expressed as where λ z is the constant axial stretch, r i is the inner radius in the deformed configuration and φ is the measured angle of twist at the apex of the LV (relative to the base). It can be seen that the twist angle (θ) and the axial deformation (z) are zero at the upper end of the LV.

Model Dimensions:
At any instant (t), the geometrical parameters (or dimensions) of the LV cylindrical model (instantaneous radius R and length L, as defined in fig 11) can be determined in terms of the monitored LV volume (V), myocardial volume (V M ) and wall thickness (h), as follows: These equations will be employed to determine the LV dimensions at the start of isovolumic contraction phase (t = 0). The determination of the dimensions of the deformed LV (due to contraction of the myocardial fibers) at the subsequent instants of the isovolumic contraction phase is indicated in the next subsection. We also utilize the information on the LV twist angle ( φ ) during the isovolumic phase, from MRI myocardial tagging. From this information, we can determine the stretches (λ z , λ r , λ θ and ).
www.intechopen.com The strain energy density function suitable for the myocardium material, is given by: wherein Q is a quadratic function of the 3 principal strain-components (to describe 3-d transverse isotropy) in the cylindrical coordinate system, given by: wherein b i are non-dimensional material parameters, and E ij are the components of the modified Green-Lagrange strain tensor in cylindrical coordinates (R, Θ, Z). In order to reduce the mathematical complexity of the problem, we assume negligible shear during isovolumic contraction. Thus E RZ and E θR in equation (6) and their corresponding stress components (σ RZ and σ θR ) are neglected. The stress equilibrium equation (in the cylindrical coordinate system) is given by the following equation: The boundary conditions on the outer and inner surfaces of the LV cylindrical model are given by , where p is the LV pressure acting on the inner surface of the LV model; we employ incremental pressure ∆p with respect to the LV pressure at t = 0, the start of isovolumic contraction.
By integrating eq (7), the Cauchy radial stress σ rr is given by: There from, the boundary condition eq (8) of the internal pressure p = -σ rr (r=r i ) is obtained (by substituting equation 9 into the boundary condition 8), in the form: Since the valves are closed during isovolumic contraction, we impose another set of boundary conditions (at both the top and bottom of the internal LV surface), giving: where σ ZZ denotes the axial component of the Cauchy stresses. In the analysis, we will employ ∆p with respect to the pressure at t = 0, at the start of isovolumic contraction. The blood in the left cavity is assumed compressible, and the change in cavity volume (∆V) due to the monitored incremental pressure (∆p), is given by where K is the bulk modulus of blood.

Analysis and computational procedure:
The following analysis is carried out at the three time instants t (or j) = 0.02 secs, 0.04 secs and 0.06 secs (from the start t = 0 of the isovolumic contraction phase, from the monitored Δp and computed ΔV (eq 12) at the three time instants with respect to p and V at t = 0 ( the start of isovolumic contraction phase). 1. We obtain the increments in LV pressure (Δp) from the monitored pressure data, during isovolumic contraction. By taking K=Δp/ΔV, we compute the corresponding changes in LV volume ΔV. 2. Left ventricular deformation: For this change ΔV in the LV volume, by assuming the ratios of cylindrical-model length and radius strains Δl/L and Δr/R to be equal during isovolumic contraction, we obtain their expressions as: From equation (13), the incremental quantities Δl j and Δr ij can be calculated, and hence: where l j and r ij are the deformed model length and radius at time t (or j) So the wall-thickness h can be obtained from: Let Δφ denote the relative angle of twist measured at the apex, at each of the 3 stages of isovolumic contraction phase, obtained by magnetic resonance imaging (MRI). 3. Next we determine the stretches in the 3 directions (due to deformed dimensions l and r with respect to the undeformed dimensions L and R) as follows We define the twist stretch due to torsion, as wherein φ is zero at the top surface of the LV held by the aorta 4. Next we express the components of the Lagrange Green's strain tensor in terms of the stretches and deformations obtained from equations (8-10), as: 5. Then, by using the strain energy function (eqs 5 and 6), we obtain the expressions of Cauchy stress tensor in terms of the parameters b i : wherein is given by equations (5 & 6), and the to-be-determined unknown parameters are the hydrostatic pressure and the constitutive parameters b i (in equation 6). 6. We now employ the stress expressions into the boundary conditions (10 & 11), and determine the hydrostatic pressure and the parameters b i (i=1,2,…7) and, using a nonlinear least squares algorithm. 7. We next determine (i) the stretches from eqs (16 & 17), and (ii) therefrom, the strains E i,j from eq (18). Then by substituting the computed strains components E i,j and the strain energy density function ψ (eqs 5 & 6) into eq (19), we can determine the LV wall stress components for the LV cylindrical model. 8. From the stress components σ θz , σ θθ , and σ zz , we can computes the principal stresses σ 1 , σ 2 the principal angle φ. 9. Then, we compute the equivalent active axial force ΔF and the torsional couple ΔT as follows: (22)

Results and comments:
1. The computational model results for a sample subject are provided in Tables 1 -5. 2. The variations of the equivalent active torque T and axial compressive force F during the isovolumic phase are calculated and shown in Fig. 12. We hence demonstrate that the big increment of internal pressure in LV cavity is caused by the compression of the blood (due to its high bulk modulus) by the internally generated torque and axial force during the isovolumic phase, due to the contraction of the myocardial fibers. 3. The radial variations of the principal stress and principal angle are found to be almost uniform across the wall thickness [5]. The time variation of the principal stress and angle during isovolumic phase are shown in Fig. 13. At the end of the isovolumic phase, the magnitude of the tensile principal stress is around 1.75x10 5 pa, which is in good agreement with the isometric tension value of 1.40x10 5 pa achieved under maximal activation.  The notable result from Fig. 13 is that both the principle stresses and their orientation angle keep changing during the isovolumic phase. It is seen from Figure 13, that the myocardial fiber was oriented 38 0 at the start and became 33 0 at the end of the isovolumic phase, as the monitored internal pressure increased during isovolumic phase (due to active torsion and compression, corresponding to active contraction of the helically woven fibers from 38 0 to 33 0 ) from 24 to 44 to 62 mmHg during the isovolumic contraction phase. Observing the values of the principle stresses, it is seen that the LV is acted upon by internally generated (i) active torsion (T) causing its twisting, and (ii) compression (F) to cause compression of the blood and develop the LV pressure rise. Fig. 13.Variation of principal stresses as functions of time, during isovolumic phase [5].
In conclusion: we have indirectly shown that the contraction of the myocardial fibers (i) develops active stresses in the LV wall (and corresponding principal stresses), and (ii) causes LV twist and shortening, resulting in the development of substantial pressure increase during isovolumic contraction. The tensile principal stress corresponds to the active contractile stress generated in the myocardial fibers, while the angle of the tensile principal stress corresponds to the fiber helical angle, which is in agreement with the experiment data on the fiber angle.
The computational results are shown in Tables 1 to 5, for a sample subject.  Table 1. Pressure-volume and model parameters for a sample subject with V M =185ml.    Table 1.  Table 5. Results for the sample subject at different instants

Clinical evaluation of Physiological systems in terms of Non-dimensional physiological Indices
Non-dimensional numbers (made up of several phenomenon related terms) are employed to characterise -disturbance phenomena. For example, in a cardiovascular fluid-flow regime, the Reynold'snumber characterizes turbulent flow, which can occur in the ascending aorta when the aortic valve is stenotic (giving rise to murmurs) and accentuated in the case of anaemia (decreased blood viscosity).
Integration of a number of isolated but related events into one non-dimensional physiological index (NDPI) can help to characterise an abnormal state of a particular physiological system [1]. For utilization of an NDPI diagnostically, we evaluate it in a large patient population and develop its distribution into normal and dysfunctional ranges, as illustrated in figure 14.
Then, upon evaluation of the NDPI of a particular subject, we can see if that value falls in the normal or dysfunctional range, and accordingly make the medical diagnosis.

Medical test: Cardiac fitness index based on treadmill HR variation
In this procedure, the cardiac fitness model consists of a first-order differential-equation system model, describing the heart rate (HR) response (y) to exertion (exercise, jogging etc) monitored in terms of the work-load, where y is defined as follows: The subject is exercised on the treadmill for a period of time te (minutes) at a constant work load (W), while the HR(t) (and hence y) is monitored, as displayed in fig 15. Now we develop a model to simulate (i) the y(t) response during exercise, i.e. during t ≤ te, and (ii) thereafter for y(t) decay, after the termination of exercise. In a way, te represents the exercise endurance of the subject [6].
where k 1 and k 2 , are the model parameters, which can serve as cardiac-fitness parameters (in min -1 ).

Non-dimensional Cardiac Fitness Index:
A typical y(t) response is illustrated in Fig 15. The parameters k 1 and k 2 can be continued into a single nondimensional cardiac-fitness index (CFI): According to this formulation of CFI, a healthier subject has (i) greater k 1 (i.e., slower rate-ofincrease of HR during exercise (ii) greater k 2 (i.e., faster rate-of-decrease of HR after exercise) (iii) greater t e (i.e., exercise endurance), and hence (iv) higher value of CFI. Now, we need to evaluate CFI for a big spectrum of patients, and then compute its distribution curve, to determine the efficiency of this index, in order to yield distinct separation of CFI ranges for healthy subjects and unfit patients. This CFI can also be employed to assess improvement in cardiac fitness following cardiac rehabilitation regime. This CFI is non-dimensional, and it can be useful to clinicians as they are able to predict the heart condition or fitness performance of a person by referring to the value of a single index value.
Oral Glucose Tolerance Test (OGTT) is a standard procedure for diagnosing diabetes and risk of becoming diabetic. However, the test data is assessed empirically. So, in order to make this procedure more reliable, we have carried out a biomedical engineering analysis of the OGTT data, to show how to distinguish diabetes subjects and those at risk of becoming diabetic. For Oral-glucose Tolerance Test simulation (entailing digestive & blood-pool chambers), the differential equation is as follows [7,8]: The input to this system is taken to be the impulse function due to the orally ingested glucose bolus [G], while the output of the model is the blood-glucose concentration response y(t). For an impulse glucose-input, a normal patient's blood-glucose concentration data is depicted in Figure 16 by open circles. Based on the nature of this data, we can simulate it by means of the solution of the Oral-glucose regulatory (second-order system) model, as an under-damped glucose-concentration response curve, given by: wherein A is the attenuation constant, is the damped frequency of the system, thenatural frequency   Figure 16 represents the blood-glucose response curve for this potentially diabetic subject. The values of T d , λ and A for both normal and diabetic patients are indicated in the figure, to provide a measure of difference in the parameter values. It was found from these calculations that not all of the normal test subjects' clinical data could be simulated as under-damped response. Similarly, not all the diabetic test subjects' clinical data corresponded to over-damped response. However it was found that the clinical data of these test subjects (both normal and diabetic) could indeed be fitted by means of a critically-damped glucose-response solution of the governing equation.

Non-Dimensional Number for Diagnosis of diabetes:
We decided to develop a unique diabetes index number (DIN) to facilitate differential diagnosis of normal and diabetic states as well as diagnose supposedly normal but high (diabetic) risk patients and diabetic patients in early stages of the disorder [8].  As can be seen from figure 17, normal (i.e., non-diabetic) subjects with no risk of becoming diabetic, will have DIN value less than 0.4, or be in the 1 -2 range. Distinctly diabetic subjects will have DIN value greater than 1.2, or be in the 7 -12 range categories. Supposedly, clinically-identified normal subjects who have DIN values between 0.4 and 1.0, or are in the 3 -5 range, are at risk of becoming diabetic. On the other hand, clinically-identified diabetic subjects with DIN value between 0.4 -1.2, or in the 3 -6 range category are border-line diabetics, who can become normal (with diet control and treatment).

Cardiology: LV contractility index based on normalized wall-stress
The traditional cardiac contractility index (dP/dt) max requires cardiac catheterization. Since LV Pressure is developed by LV wall stress σ θ (based on sarcomere contraction), we have developed a contractility index based on σ θ (normalized with respect to LV pressure) [9]. For a thick walled spherical model of LV, the circumferential wall stress: We define the contractility index as: For the data shown in the figure 18, we have: • .
Now we formulate a non-dimensional cardiac contractility index, * . ≈ 100 Our new contractility indices do not require measurement of LV pressure, and can hence be evaluated noninvasively. In fig 20, we can see how well our contractility index CONT1 (dσ*/dt) max correlates with the traditional contractility index (dP/dt) max . This provides a measure of confidence for clinical usage of this index.

Diagnostics: LV contractility index based on LV shape-factor
Cardiologists have observed shape changes taking place in an impaired LV. We have investigated the effect of ventricular shape on contractility and ejection function. In this study, a new LV contractility index is developed in terms of the wall-stress (σ*, normalized with respect to LV pressure) of a LV ellipsoidal model (Fig. 21) [10,11]. Using cine-ventriculography data of LV volume (V) and myocardial volume MV, the LV ellipsoidal model (LVEM) major (B) and minor axes (A) are derived for the entire cardiac cycle. Thereafter, our new contractility index (dσ*/dt) max is derived in terms of the LV ellipsoidal shape factor (s=B/A). For the LV model (Fig 21) of a prolate spheroid truncated 50% of the distance from the equator to the base, we first put down the for σ* ( = σ θ /P ), and then determine dσ*/dt [2.10]. Thereby, we obtain the following expression for the contractility index: where s is B/A, ś is first-time derivative of s; V and MV are LV volume and myocardial wall volume, Ṽ is the first-time derivative of V. This index is analogous to the traditional employed index (dP/dt) max , but does not involve determination of the intra-LV pressure by catheterization. For patient A (with myocardial infarct and double vessel disease) and B (with double vessel disease and hypertension), the values of CONT1 are obtained to be 3.84 and 6.90 s -1 , whereas the corresponding values of (dP/dt) max are obtained to be 985 and 1475 mmHg/s.   Fig.  24. We can note the good level of correlation with the traditional contractility index of (dP/dt) max . Additionally, our new index can be determined noninvasively, and hence be more conducive for clinical use. From these results, we can also infer that a non-optimal less-ellipsoidal shape (or a more spherical shape, having a greater value of S = B/A) is associated with decreased contractility (and poor systolic function) of the LV, associated with a failing heart. This has an important bearing on a quick assessment of a failing heart based on the values of S and (dσ*/dt) max

ICU Evalution: Indicator for lung-status in mechanically ventilated copd patients (using lung ventilation modelling and assessment)
In chronic-obstructive-pulmonary-disease (COPD), elevated airway resistance and decreased lung compliance (i.e. stiffer lung) make breathing difficult. After these patients are mechanically ventilated, there is a need for accurate predictive indicators of lung-status improvement, for ventilator discontinuation through stepwise reduction in mechanical support, as and when patients are increasingly able to support their own breathing, followed by trials of unassisted breathing preceding extubation, and ending with extubation. So, in this section, we have provided a biomedical engineering analysis of the lung ventilator volume response to mechanical ventilation of COPD patients, and developed an index to assess the lung status as well as the basis of weaning the patient from ventilator support. Figure 25 depicts the model for the lung volume (V) response to the net driving pressure P N =P L -P e (end-expiratory pressure), in which (i) the driving pressureP L = P m (pressure at the mouth) minus P p (the pleural pressure), and (ii) P p is determined by intubating the patient, and assuming that the pressure in the relaxed esophageal tube equals the pressure in the pleural space surrounding it. Fig. 25. Model of the Lung, depicting P m ,P p , P el (lung elastic pressure recoil) = P a (alveolar pressure) -P p (pleural pressure) = 2T/(radius of alveolar chamber), and R (resistance to airflow rate) = (P m -P a ) / (dV/dt ).

V, P a
www.intechopen.com The equation representing the lung model response to the net driving pressure in terms of the model parameters lung compliance (C) and airflow-resistance (R), is given by: wherein: 1. the driving pressure = P L ; Pe = the end-expiratory pressure; net pressure P N = P L -Pe 2. the parameters of the governing equation (1) are lung compliance (C) and airflow-3. resistance(R), with both R & C being instantaneous values 4. V= V(t) -Ve (wherein Ve is the end expiratory lung volume) Fig. 26. Lung ventilatory model data shows air-flow ( o V ) and volume (V) and net pressure (P N ). Pause pressure (P tm ) occurs at t m , at which the volume is maximum (TV = tidal volume). Δt is the phase difference between the time of maximum volume and peak pressure (P k ). It also the time lag between the peak and pause pressures. B is the amplitude of the net pressure waveform P N applied by the ventilator. This P N oscillates about P e with amplitude of B. The difference between peak pressure P k and pause pressureP tm is Δp [12].
We measure Peak pressure (P k ), Pause pressure (P tm ), t m & (or t m ). Then, B is the amplitude of the net pressure wave form applied by the ventilator. Let C a be the average dynamic lung compliance, R a the average dynamic resistance to airflow, the driving pressure P L =P e + B sin (ωt), and the net pressure P N = B sin (ωt). The governing equation (1) then becomes [12]: The volume response to P N, the solution to eqn (2), is given by: wherein: i. ka (=RaCa)is the average time constant, ii. the integration constant H is determined from the initial conditions, iii. the model parameters are Ca and ka(i.e. Ca and Ra), and iv. is the frequency of the oscillating pressure profile applied by the ventilator An essential condition is that the flow-rate is zero at the beginning of inspiration and end of expiration. Hence, applying this initial condition of dV/dt =0 at t=0 to our differential eqn (3), the constant H is obtained as:

Evaluating parameters R a & C a [12,2]:
For evaluating the parameter k a (R a C a ), we will determine the time at which V (t) is maximum and equal to the tidal volume (TV), Hence putting dV/dt =0 in eqn (5), we obtain: , at t = tm (6) From equation (6), we obtain (by neglecting / a tk e − ), the following expression for k a : Hence, from eqns (7 & 13), the average value of airflow-resistance (R a ) is: For our patients, the computed ranges of the parameters are: www.intechopen.com Now, that we have determined the expressions for R a and C a , the next step is to develop an integrated index incorporating these parameters. Formulating a Lung Ventilatory Index (LVI) incorporating Ra and Ca: We now formulate a Lung Ventilatory Index (LVI), incorporating Ra and Ca, as: Let us now obtain order-of-magnitude values of LVI, for a mechanically ventilated COPD patient in acute respiratory failure: Hence, for LVI to reflect lung-status improvement in a mechanically ventilated COPD patient in acute respiratory failure, it has to decrease to the range of LVI for an outpatient COPD patient at the time of discontinuation. In fig. 27, it is shown that for the 6 successfully-discontinued cases, the LVI was (2900) ± (567) (cmH 2 O/L) 3 ; for the 7 failed-discontinuation cases the LVI was (11400) ± (1433) (cmH 2 O/L) 3 . It can be also observed that LVI enables clear separation between failed and successful discontinuation, which again points to the efficacy of LVI.  3 ; for the 7 failed-discontinuation cases the LVI was (11400) ± (1433) (cmH 2 O/L) 3 . It is observed that LVI enables clear separation between failed and successful discontinuation [12].

Monitoring: Noninvasive determination of aortic pressure, aortic modulus (stiffness) and peripheral resistance)
The aortic blood pressure waveform contains a lot of information on how the LV contraction couples with the aortic compliance and peripheral resistance. Since accurate measurement of aortic blood pressure waveform requires catheterization of the aorta, we have developed a noninvasive method to determine the aortic pressure profile along with the aortic volumeelasticity and peripheral resistance. Fig 28 displays such a constructed aortic pressure profile.
The input to the model consists of auscultatory cuff diastolic and systolic pressures, along with the MRI (or echocardiographically) measured ejection volume-time profile (or volume input into the aorta). The governing differential equation for pressure response to LV outflow rate I(t) into the aorta is given by [13]: (1) where (i) m a is the aortic volume elasticity (dP/dV), (ii) R p is the resistance to aortic flow (=P/Q), (iii) λ=m a /R p , (iv) I(t) is the monitored inflow rate into the aorta, and (v) T a is the flow-acceleration period. This governing equation is solved for measured I(t) and dI/dt during the systolic phase from time T 1 to T 3 (Fig. 28). For the diastolic-phase solution from time T 3 to T 4 , the right-hand side is zero. The solutions for diastolic and systolic phases are given below by equations (2) and (3) respectively.

Solutionequations:
• During diastolic phase,  Fig. 28. Model computed cyclic Aortic pressure profile, compared with measured pressure values. The systolic phase from T1 to T3 is when blood is ejected into the aorta. The diastolic phase is from T3 to T4 [13].

•
During systolic phase, where Also, as noted in Fig 28, the boundary values are: At t =T 2 , dP s /dt =0; at t =T 2 , P s (T 2 ) = auscultatory P as = P 2 ; at t = T 3 , P s (t =T 3 ) = P d (t =T 3 ) Hence, based on these boundary values, the following equations are to be solved.
We now solve equations (4, 5 & 6), to determine the unknown parameters m a , R p (and T 2 ).
[ ] We have determined the expressions for the aortic pressure during the systolic and diastolic phases, by solving the governing equation (1), for the monitored LV outflow rate (or input into the aorta) I(t), using (i) the monitored auscultatory diastolic pressures (P ad ), to serve as the boundary condition at the beginning of the systolic-phase solution (at time T 1 ) and at the end of the diastolic-phase solution (at time T 4 ), (ii) the monitored auscultatory systolic pressure (P as =P 2 ) to represent the maximum value of the systolic-phase solution.
Because the pressure solution of equation (1) is a function of m a and R p , we first determine the values of these parameters by making the solution satisfy the above-mentioned boundary conditions, which in turn yields the pressure profile given by P d (t) and P s (t). This noninvasively determinable aortic pressure can provide hitherto unavailable information on vascular compliance and resistance status, as well as on the capacity of the LV to respond to it. Fig. 29. Plot of aortic pressure (of patient B) during one cardiac cycle, t e =0.32s. Herein, T 1 -T 3 represents the systolic phase, and T 3 -T 4 (=0.92s) represents the diastolic phase. At T 2 , the aortic systolic pressure profile has its maximal value (=P s ). The scatter points are the data measured from catheterization. The solid line is the model-computed profile; RMS=2.41 mmHg. Note the excellent correlation between the model-derived aortic pressure profile and the catheter-obtained aortic pressure profile.
In Fig. 29, the model-computed aortic pressure profile patient B (with double vessel disease and hypertension) is shown, along with the actual catheter pressure data. We can note how well the model-computed result matches the actual catheterization data, with RMS 2.41 mmHg. The aortic stiffness (m a ) and peripheral resistance (R p ) are obtained to be 1.03 mmHg/ml and 1.59 mmHg·s/ml, respectively. Let us consider yet another benefit of this analysis. We have determined aortic pressure profile, aortic stiffness (m a ) or aortic elastance (Eao) and peripheral resistance. From the instantaneous aortic pressure and aortic inflow rate, we can determine the instantaneous left ventricular (LV) systolic pressure, in terms of the instantaneous dimensions of the LV outflow tract. We hence determine the LV systolic pressure profile, from which we can evaluate the traditional contractility index (dP/dt max) as well as the LV systolic elastance (Elv). We can then determine the ratio of Elv/Eao, to represent the LV-Aorta Matching Index (VAMI). In ischemic cardiomyopathy patients, this VAMI value is depressed. However, following surgical vascular restoration, this index value is partially restored.

Coronary Bypass surgery: Candidacy
• Interventional candidacy based on computed intra-LV flow-velocity and pressuregradient distributions Fig. 30. Construction of Intra-LV Blood flow velocity and pressure-gradient distributions for a patient with myocardial infarct: (a) Superimposed sequential diastolic and systolic endocardial frames (whose aortic valves centers and the long axis are matched), before (1) and after (2) administration of nitroglycerin; (b) Instantaneous intra-LV distributions of velocity during diastole, before (1) and after (2) administration of nitroglycerin; (c) Instantaneous intra-LV distributions of velocity during ejection phase, before (1) and after (2) administration of nitroglycerin, (d) Instantaneous intra-LV distributions of pressure-differentials during diastole, before (1) and after (2) administration of nitroglycerin; (e) Instantaneous intra-LV distributions of pressure-differential during ejection phase, before (1) and after (2)  A left ventricle with ischemic and infarcted myocardial segments will have lowered ejection fraction and cardiac output, because it will not be able to generate adequate myocardial contraction to raise the intra-LV pressure above aortic pressure for a ling enough duration to generate adequate stroke volume. These patients need coronary bypass surgery, and a presurgical assessment of their candidacy for it, on how much they can from it. For this purpose, we need to determine the intra-LV blood flow velocity and pressure-gradient profiles before and after the administration of nitroglycerin. So, we carry out a CFD analysis of intra-LV blood flow. The data required for the CFD analysis consists of: LV 2-D long-axis frames during LV diastolic and systolic phases; LV pressure vs. time associated with these LV frames; Computation of LV instantaneous wall velocities as well as instantaneous velocity of blood entering the LV during the filling phase and leaving the LV during the ejection phase. From this CFD, we have determined the instantaneous distributions of intra-LV blood-flow velocity and differential-pressure during filling and ejection phases, to intrinsically characterize LV resistance-to-filling (LV-RFT) and contractility (LV-CONT) respectively. The results are summarized in the above Fig. 30. By comparing intra-LV pressure-gradients before and after administration of nitroglycerin (a myocardial perfusing agent, and hence a quasi-simulator of coronary bypass surgery), we can infer how the myocardium is going to respond and how these LV functional indices will improve after coronary by bypass surgery.

Theory of hospital administration: Formulation of hospital units' performance index and cost-effective index
A Hospital has clinical services departments, medical supply and hospital-services departments, financial-management and administrative departments. Each of these five sets of departments has to function in a cost-effective fashion. Let us, for example, consider the Intensive-Care Unit (ICU) department. The human resource to an ICU dept consists of physicians and nurses. Using activity-based costing, we can determine the human-resource strength, based on an assumed reasonable probabilityof-occurrence of (for instance) two patients simultaneously (instead of just one patient) having life-threatening episodes.
Now, let us assume that we raise the PFI (ICU) to (say) 60 by augmenting the nursing staff, so as to have six nurses (R i = 3 units) and 1.5 full-time equivalent physician-on-duty (R i = 3 units), then So while the PFI of ICU has gone up from 40 to 50, the CEI of ICU has gone down from 10 to 8.3. Strategy of Operation: Our strategy would be to operate this Performance-Resource system, in such a way that we can determine the resource index R i for which we can obtain acceptable values of both PFI and CEI. In a way, figure (31) could represent this balance between PFI & CEI, in order to determine optimal Resource Index or resource [15]. With reference to this figure 31, i f w e h a v e a r e s o u r c e v a l u e o f R i = R 1 , then the corresponding PFI (=PFI 1 ) will be unacceptable, as being too low; hence, we will want to increase the value of R i . If we have a resource value of R i = R 2 , then our corresponding CEI (= CEI 2 ) will also be unacceptable, for being too low; hence we will want to decrease R i . In doing so, we can arrive at the optimal value R io , for which both CEI and PFI are acceptable. This procedure, for converging to R i = R i0 , can be formulated computationally. Fig. 31. Optimising the value of R i so to obtain acceptable values of CEI and PFI [15]. Now then, let us formulate how a hospital budget can be optimally distributed. Let us say that a Hospital has 'n' number of departments and a prescribed budget (or budget index, BGI). We would want to distribute the budget among the departments, such that none of the 'n' departments has a PFI below the acceptable value of PFI a and a CEI below the acceptable value of CEI a .

So the Operational research problem is to be formulated as follows:
How to distribute or divide the given Budget (or Budget Index Value) into R i (i= 1,……..,n), such that PFI i ≥ PFI a , for all i; and CEI i ≥ CEI a , for all i This then is the prime task of a Hospital administrator!

Summarizing:
The ICU Operational cost (OPC) is the cost of operating the ICU over this one month period. The ratio of this ICU PFI and the ICU OPC is the Cost-effectiveness index (CEI) of ICU. The Management strategy is to maintain certain acceptable values of both PFI and CEI for all hospital departments, by judicious allocation of staff to the departments. This enables the determination of optimal Resource index (RSI) and hospital budget (HOB) to maintain a balance between PFI and CEI for all the hospital departments. This can constitute the basis of Hospital Management.

How to proceed: For biomedical engineering to become a professional field
So in this chapter, we have talked about: 1. Anatomy: Spine as an optimal structure, 2. Physiology: Mechanism of LV pressure generation 3. Non-dimensional Physiological Index 4. Medical Test: Cardiac Fitness based on Treadmill Heart Rate Variation 5. Medical Physiology: A Non-dimensional Diabetes Index with respect to Oral-Glucose-tolerance Testing 6. Cardiology: LV Contractility based on its normalized wall stress 7. Diagnostics: LV Contractility based on its shape factor 8. ICU Evaluation: Indicator for lung-status in Mechanically ventilated Copd patients, using lung ventilation modeling and assessment 9. Monitoring: Noninvasive determination of Aortic pressure, aortic stiffness and peripheral resistance 10. Coronary Bypass Surgery: candidacy 11. Hospital Operations Management We have shown how biomedical engineering (BME) can open up a new approach to the study of Anatomy, in terms of how anatomical structures are intrinsically designed as optimal structures for their function. We have also seen how BME can be applied to the study of Physiology, by modelling of physiological systems (as bme models), which can enable us to assess their performance for clinical usage by means of our novel NDPIs comprised of the physiological systems' model parameters. The NDPIs can considerably facilitate medical assessment, and lead us to what can be effectively termed as Higher-order Translational Medicine (HOTM), entailing the incorporation of physical and engineering sciences into medical sciences and clinical sciences for more reliable and effective patient care. Even Medical tests can be adroitly modelled as BME systems. These systems are formulated in the form of mathematical models, whose solutions are simulated to the medical tests data, to evaluate the model parameters. The model parameters can be combined into NDPIs, by means of which the test data can be analysed for making more reliable medical assessment and decisions. Finally, we have seen how we can bring to bear the enormous scope of Industrial Engineering (and constrained optimisation theory) to hospital operational management, so as to develop (i) cost-effective performance indices of hospital departments, and (ii) more knowledgeable framework for budget development and allocation to the various department. Putting all of this together is what will justify (i) the incorporation of BME into the MD curriculum, and (ii) its constituting an indispensable patient-care oriented department in tertiary-care hospitals. This verily constitutes the biomedical engineering professional trail, from anatomy and physiology to medicine and into hospital administration. This is what the professional role of biomedical engineering needs to be, to promote a higher order of translational medicine and patient care.