Left ventricular wall stress compendium.

Left ventricular (LV) wall stress has intrigued scientists and cardiologists since the time of Lame and Laplace in 1800s. The left ventricle is an intriguing organ structure, whose intrinsic design enables it to fill and contract. The development of wall stress is intriguing to cardiologists and biomedical engineers. The role of left ventricle wall stress in cardiac perfusion and pumping as well as in cardiac pathophysiology is a relatively unexplored phenomenon. But even for us to assess this role, we first need accurate determination of in vivo wall stress. However, at this point, 150 years after Lame estimated left ventricle wall stress using the elasticity theory, we are still in the exploratory stage of (i) developing left ventricle models that properly represent left ventricle anatomy and physiology and (ii) obtaining data on left ventricle dynamics. In this paper, we are responding to the need for a comprehensive survey of left ventricle wall stress models, their mechanics, stress computation and results. We have provided herein a compendium of major type of wall stress models: thin-wall models based on the Laplace law, thick-wall shell models, elasticity theory model, thick-wall large deformation models and finite element models. We have compared the mean stress values of these models as well as the variation of stress across the wall. All of the thin-wall and thick-wall shell models are based on idealised ellipsoidal and spherical geometries. However, the elasticity model's shape can vary through the cycle, to simulate the more ellipsoidal shape of the left ventricle in the systolic phase. The finite element models have more representative geometries, but are generally based on animal data, which limits their medical relevance. This paper can enable readers to obtain a comprehensive perspective of left ventricle wall stress models, of how to employ them to determine wall stresses, and be cognizant of the assumptions involved in the use of specific models.

Impact of surgical ventricular restoration on ventricular shape, wall stress, and function in heart failure patients.

Surgical ventricular restoration (SVR) was designed to treat patients with aneurysms or large akinetic walls and dilated ventricles. Yet, crucial aspects essential to the efficacy of this procedure like optimal shape and size of the left ventricle (LV) are still debatable. The objective of this study is to quantify the efficacy of SVR based on LV regional shape in terms of curvedness, wall stress, and ventricular systolic function. A total of 40 patients underwent magnetic resonance imaging (MRI) before and after SVR. Both short-axis and long-axis MRI were used to reconstruct end-diastolic and end-systolic three-dimensional LV geometry. The regional shape in terms of surface curvedness, wall thickness, and wall stress indexes were determined for the entire LV. The infarct, border, and remote zones were defined in terms of end-diastolic wall thickness. The LV global systolic function in terms of global ejection fraction, the ratio between stroke work (SW) and end-diastolic volume (SW/EDV), the maximal rate of change of pressure-normalized stress (dσ*/dt(max)), and the regional function in terms of surface area change were examined. The LV end-diastolic and end-systolic volumes were significantly reduced, and global systolic function was improved in ejection fraction, SW/EDV, and dσ*/dt(max). In addition, the end-diastolic and end-systolic stresses in all zones were reduced. Although there was a slight increase in regional curvedness and surface area change in each zone, the change was not significant. Also, while SVR reduced LV wall stress with increased global LV systolic function, regional LV shape and function did not significantly improve.

Effect of left ventricular shape alteration on contractility and function.

We have investigated the effect of left ventricular (LV) shape on contractility and ejection function. In this study, a new contractility index is developed in terms of the wall stress (sigma*, normalized with respect to LV pressure) by means of an LV ellipsoidal model. Using cine-ventriculography data, the LV ellipsoidal model (LVEM) major (B) and minor axes (A) are derived for the entire cardiac cycle. Thereafter, a new contractility index (CONT1) is derived as dsigma*/dt, incorporating the LV ellipsoidal shape factor. Also, another contractility index (CONT2) was developed in terms of the generated sigma* at the start of ejection phase, and maximized with respect to B/Ashape parameter, to obtain the optimal value of B/Aover the physiological ranges of the ratio of myocardial volume and LV volume. The in vivovalue of B/Aat the start of ejection is compared with this optimal value, and the LV contractility is evaluated in terms of the proximity of the in vivo B/Ato the optimal B/A. The results indicate that a non-optimal less-ellipsoidal shape (or more spherical) is associated with decreased contractility (and poor systolic function) of the LV, associated with a failing heart.

Flow studies in three-dimensional aorto-right coronary bypass graft system.

This paper presents the fluid dynamics of blood flow in a coronary bypass model of the aorto-right coronary bypass system. Three-dimensional computational fluid dynamic simulations are developed of the blood flow in coronary artery-bypass systems, using the computational fluid dynamics software (FLUENT 6.0.1). These blood flow simulations are performed within small intervals of the cardiac cycle, using input data consisting of physiological measurements of flow rates in the aorta, obtained from earlier studies. We have calculated the flow-field distributions of the velocity and the wall shear stress at four typical instants of the cardiac cycle, two during systole and two during the diastole phase. Plots of velocity vector and the wall shear stress are displayed in the aorto-graft-coronary arterial flow-field domain, providing an insight into the link between fluid dynamics and arterial diseases. The prime regions of disturbed flow patterns are at the entrance into the graft from the aorta and at the exit from the graft into the right coronary artery. Our objective is to obtain an understanding of how the coronary artery is perfused by the graft, and thereby into the factors affecting graft patency.

Numerical study on the pulsatile flow characteristics of proximal anastomotic models.

Haemodynamics was widely believed to correlate with anastomosis restenosis. Utilizing the haemodynamic parameters as indicator functions, distal anastomosis was redesigned by some researchers so as to improve the long-term graft patency rate. However, there were few studies upon the proximal anastomosis. Therefore, in this study, flow characteristics and distributions of the haemodynamic parameters in proximal anastomosis under physiological flow condition have been investigated numerically for three different grafting angles: namely, 45 degrees forward facing, 45 degrees backward facing, and 90 degrees anastomotic joints. The simulation results showed a flow separation region along the graft inner wall immediately after the heel at peak flow phase and it decreased in size with the grafting angle shifting from 45 degrees forward facing to 45 degrees backward facing. At the same time, a pair of vortex was found in the cross-sectional planes of the 45 degrees backward facing and 90 degrees grafts. In addition, stagnation point was found along the graft outer wall with small shifting during the physiological cycle. High spatial and temporal wall shear stresses gradients (WSSG) were observed around the anastomotic joint. Low time-averaged wall shear stress (WSS) with elevated oscillation shear index (OSI) was found near the middle of anastomosis at the aorta wall and along the graft inner wall respectively, while high time-averaged WSS with low OSI was found at the heel, the toe, and the region downstream of the toe. These regions correlated to early lesion growth. Elevated time-averaged WSSG was found at the same region, where the elevated low-density lipoprotein (LDL) permeability was observed as reported in the literature. The existence of nearly fixed stagnating location, flow separation, vortex, high time-averaged WSS with low OSI, low time-averaged WSS with elevated OSI, and high time-averaged WSSG may lead to graft stenosis. Moreover, the simulation results obtained were consistent with those of experimental measurements. Based on the validated simulation results, the 45 degrees backward-facing graft was found to have the lowest variation range of time-averaged WSS and the lowest segmental average of WSSG among the three models investigated. The 45 degrees backward-facing graft is thus recommended for the bypass operation with expected higher patency rate.

Biomechanics of the intrinsically optimal design of the intervertebral disc.

The spinal shock-absorbing disc needs to have the flexibility to enable the spine to bend and twist. At the same time under loading, its lateral and axial deformations have to be contained, so that it does not herniate and impinge on the spinal-chord. The disc is composed of a fluid-like nucleus pulposus (NP) contained within an annulus. Hence when the disc is loaded, the NP gets pressurized and stresses the surrounding annulus. Now, because its elastic modulus is stress-dependent (i.e. E-E 0 = ksigma, where k is a constitutive parameter ), the annulus stiffens under loading. In this way, the flexible disc is able to sustain its loading with minimal deformation and thereby contain its deformation. In this paper, we have carried out a stress and deformation analysis of the spinal disc, and demonstrated that its deformations are invariant with the load intensity and only dependent on its dimensions and its constitutive property parameter k. Thus, we demonstrate that the intrinsic design of the spinal disc makes it an optimal structure.

Cost-effectiveness index modeling for a hospital unit.

The healthcare expenditures around the world are claiming bigger and bigger share of a country GDP each year. However, the effectiveness of the healthcare system compared to the ever-rising healthcare expenditures is not clearly defined and compared. A generic model of cost-effectiveness index is developed for a hospital unit (department). The cost-effectiveness index (CEI) consists of the total operating costs (TOC) and total effect index (TEI). TEI consists of healthcare productivity index (HcPI), health status index (HSI), healthcare quality index (HcQI) and healthcare efficiency index (HcEI). All of the effect measures are in different dimensions, thus index number method was applied to convert the effect measures into non-dimensional numbers that can be summed or subtracted. The CEIs obtained are relative among a few different hospitals. The CEIs can be a performance assessment tool to compare the operation of different hospital, and subsequently act as a motivation tool to drive for improvement.

Biomechanics of lumbar vertebrae as a functionally optimal structure.

In this paper, we demonstrate that the spinal vertebral body (VB) remodels (as per Wolf's law) such that its shape and dimensions enable it to be a light-weight high-strength structure. The VB is modeled as a hyperboloid shell, whose generators are shown to sustain (and transmit) all the loadings on the VB as axial forces. Upon minimizing the sum of the forces in the hyperboloid VB generators with respect to its shape parameters theta (the angle between pairs of generators), we obtain the optimal shape-dimensions of the VB which corresponds to its measured shape-dimensions. This parameter theta is deemed to be the prime shape parameter of the hyperboloid VB.

A non-invasive system for assessment of aortic stiffness in clinical practice.

Previously aortic stiffness is frequently assessed through pulse pressure and pulse wave velocity (PWV) measurements. However, these methods need aortic pressure obtained by catheterization. A new model has been developed to rapidly determine the aortic pressure profile and simultaneously calculate aortic stiffness. Comparison between the aortic pressure result obtained from this and catheterization data demonstrates good agreement, while this method is non-invasive. This totally non-invasive method should be useful in assessing arteriosclerotic disease in clinical setting.

Perfusion studies of steady flow in poroelastic myocardium tissue.

The behaviour of the heart has always elicited interest and particularly the study of its myocardium, as 5-10% of the blood pumped by the heart is passed through the coronary arteries to the myocardium itself. An in-depth investigation of the myocardium behaviour is useful. The present work aims to investigate how myocardium perfusion is influenced by myocardial stress and diseased states, and in general by LV pumping abnormalities. LV myocardial perfusion can then serve as a possible index of the capacity of the LV to respond to its work demand, and thus of the risk of heart failure. The poroelastic analysis of the myocardium based on finite element method (FEM) for regional perfusion through a rectangular element with various physiological ranges of loading conditions was studied.

Characterization of autonomic dysfunction in patients with irritable bowel syndrome by means of heart rate variability studies.

OBJECTIVE: Our aim was to characterize autonomic dysfunction in patients with irritable bowel syndrome (IBS) using heart rate variability (HRV) studies. METHODS: EKG signals were obtained from 35 patients (mean age, 39.1 +/- 9.5 yr, M:F ratio = 2.9:1) and 18 healthy controls (mean age, 38.2 +/- 6.5 yr, M:F ratio = 2:1) in supine, standing, and deep-breathing modes. Fast Fourier transformation and autoregressive techniques were used to analyze the HRV power spectra in very low (VLF, 0.0078-0.04 Hz), low (LF, 0.04-0.14 Hz), and high (HF, 0.14-0.4 Hz) frequency bands. RESULTS: In the supine position, the VLF power spectral density (PSD) in IBS was significantly higher than normal (3 vs 1.3 beats per minute [bpm]2/Hz, p < 0.01). On changing from the supine to standing position, the normals (NC) had raised median PSDs in the VLF (1.3 vs 12.8 bpm2/Hz, p < 0.01) and LF (1.6 vs 6.1 bpm2/Hz, p < 0.01) bands, as a sign of increased sympathetic tone, whereas the median HF PSDs (parasympathetic tone) remained unchanged (1.8 bpm2/Hz each, p = 0.8). Similarly, the IBS patients had increased VLF (3.04 vs 14.93 bpm2/Hz, p < 0.01) and LF (2.8 vs 8.7 bpm2/Hz, p < 0.01) PSDs on standing up, but the HF PSD was also raised (from 2.4 to 5.7 bpm2/Hz, p = 0.04). On changing from standing to the deep-breathing mode, the normals had a significant increase in the HF (from 1.8 to 10.3 bpm2/Hz, p < 0.001) and a significant reduction of the VLF (from 12.8 to 2.2 bpm2/Hz, p < 0.01) PSDs. The reduction of the LF PSD was not significant (from 6.1 to 5.6 bpm2/Hz, p = 0.6). In IBS, HF PSD remained constant (5.7 bpm2/Hz each, p = 0.6), whereas the LF PSD increased from 8.7 to 24.2 bpm2/Hz (p < 0.0001). The VLF PSD was reduced (from 14.9 to 4.1 bpm2/Hz, p < 0.0001). In IBS, the median sympathovagal outflow ratio was significantly lower in the standing position (1.4 vs 2.8, p < 0.02) and higher in the deep-breathing mode (7.33 vs 0.42, p < 0.0001) than normal. CONCLUSIONS: IBS patients have reduced sympathetic influence on the heart period in response to orthostatic stress and diminished parasympathetic modulation during deep breathing.

Asymmetrical loads and lateral bending of the human spine.

The human spine is modelled as a cantilever-type beam column. Under the influence of static asymmetrical loads, muscle and low-back forces are predicted from a hypothetical but revealing model. Such forces produced by asymmetrical loads are much larger than for a corresponding symmetrical load. Asymmetrical loads can encourage, especially in young schoolchildren, lateral bending of the spine by alleviating muscle and low-back forces. This could possibly be a factor contributing to the surprisingly high percentage of schoolchildren with measurable scoliotic curves. The wearing of knapsack-type bags is advocated.

Biomechanical simulations of scoliotic spinal deformity and correction.

A new approach to surgical correction of scoliosis has been advanced by us, in the form of simulation of the surgical correction system and technique. For this purpose, we developed a finite-element model of the spinal column (SFEM), applied tractions to it and determined the model stiffness so as to watch the actual spinal geometry. Having patient-simulated this SFEM, we applied to this SFEM corrective forces and determined the optimal set of forces to gain the best correction of the spinal deformity. We then developed a special instrumentation to measure the applied corrective forces during surgery using a particular fixation system. The SFEM corrected geometry was shown to compare favourably with the post-surgical curve. We have now developed an elastic beam-column model (EBCM) to which muscle activation forces, representing asymmetrical paralysis of the vertebral column muscles, can be applied to generate a given scoliotic curve. In that process the stiffness properties of the patient-simulated EBCM are determined. Now on these patient-simulated EBCM(s), identical corrective force systems are applied as developed by the finite-element model (SFEM) and implemented surgically for these patients. It is shown that the EBCM corrected geometries compare favourably with both SFEM corrected geometries as well as with the post-surgical curves for similar corrective force systems. Thus the EBCM can be employed to presurgically simulate scoliolic correction, specify the optimal corrective system of forces so as to gain the best surgical correction.

Continuous model of the human scoliotic spine.

The human scoliotic spine is mathematically modelled by employing the classical non-linear theory of curved beam-columns. A realistically representative muscle force system is included in the model. Scoliosis due to asymmetrical bi-lateral muscular contractions has been studied and arbitrary large displacements and curvatures are allowed. The two-dimensional model allowing curvature in the frontal plane can show the progression of a scoliotic curve from an initially straight configuration. For various parameter values, particularly muscle asymmetry, the model attempts to simulate the progression of actual scoliotic curves. Once these curves have been simulated, forces corresponding to corrective surgical systems are applied to the scoliotic spine. The corresponding corrected curves are then compared with those produced by a finite element model and also to the actual clinical curve. The comparisons were very favourable, considering the simplicity of the continuous model. The commonly observed phenomenon of the scoliotic curve lying to the weaker side of the back in terms of muscle strength is reproduced and explained by the model. The possible usefulness of continuous spinal models to analyse the overall deformation of the spine under various loading conditions can then be deduced.

Developmental and corrective biomechanics for scoliosis.

The developmental mechanism for scoliosis and its surgical correction are studied by modeling the spinal column as a curved nonlinear (large-deformation-sustaining) beam column to which are applied (a) muscle forces to simulate scoliosis development due to asymmetrical bilateral muscle contractions and (b) corrective forces to simulate the action of surgically implanted corrective systems. The two-dimensional model permits curvature in the frontal plane and can simulate and demonstrate the progression of a scoliotic curve from an initially straight configuration for various model parameter values. The calculation of the bonding moments is treated, and a simple algorithm for solving the model equations is presented. Results for an actual clinical case are given.

Guidelines for treatment of myocardial infarction.

Two interventions for the treatment of myocardial infarction, pharmacological and surgical, are discussed. The biomechanical analysis for the pharmacological intervention entails minimization of the hydraulic load against which the infarcted left ventricle is pumping. The biomechanics of the surgical intervention involves optimization of the coronary-bypass graft's geometrical and material properties in order to maximize its patency. Both of these analyses employ the concept of blood-pressure pulse-wave reflection. The relationship of the pressure-pulse reflection coefficient to blood vessel properties is presented and used to develop guidelines for pharmacological and surgical intervention.

Performance assessment of the Terry Fox jogging prosthesis for above-knee amputees.

The Terry Fox jogging (TFJ) prosthesis was developed at Chedoke-McMaster Hospital to alleviate the asymmetric jogging pattern experienced by above-knee amputees when attempting to jog with conventional walking prostheses. This prosthesis features a spring-loaded, telescoping shank designed to eliminate any vaulting action and control the trunk motion during stance. The spring is intended to attenuate the impact forces and release its stored energy at push-off to provide momentum transfer to the jogger. This prosthesis was comprehensively assessed in the gait laboratory, by evaluating the kinematics, energy and power flow patterns of an above-knee amputee jogger wearing the TFJ prosthesis. Included in the assessment is the ability of the prosthesis to satisfy a set of relevant design criteria that have been established from non-amputee jogging patterns. An increased swing phase time for the prosthetic limb and the need to have the knee hyperextended throughout the stance phase contributed to an asymmetric jogging style. The telescoping action did lower the amputee's centre of mass, thereby reducing the vaulting effect. However, the spring only imparted a lifting action to the jogger and the ground reaction forces were double those of a non-amputee jogger. These findings clearly indicate a need to redesign the TFJ prosthesis and are being incorporated in the design of a new physiological jogging prosthesis.

Presurgical finite element simulation of scoliosis correction.

For surgical correction of scoliotic spinal deformity, internal fixation systems apply lateral and distractive corrective forces. In order to gain maximal correction, a finite--element analysis of the spinal deformity correction technique has been carried out preoperatively, after first employing the spinal deformity correction finite--element model to determine the in vivo spinal stiffness. The presurgical analysis also gives us an appreciation of how the parameters of deformity, stiffness and corrective forces jointly contribute to the value of the correction index. The paper presents the methodology and clinical application. It also summarizes the results for ten patients, whereby the efficacy of presurgical analysis is assessed by comparing the corrective index values by presurgical simulation with the surgical results for equivalent levels of corrective forces.