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.

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.

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.

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.

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.

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.

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.

Radiological changes in rheumatoid arthritis: measurement of area of juxta-articular bone as outcome event in clinical therapeutic trials of antirheumatic drugs.

A high degree of intra - and inter - rater reproducibility was obtained in measurement of a standardized area of the head of the first right metacarpal using a precision digitizer. This instrument had an accuracy for every point digitized of 0.127 mm. Intra-rater difference between readings at approximately a month's interval showed no significant differences. The method is reasonably simple to perform and is applicable to small joints such as the proximal interphalangeal joints. The method may prove useful in following progression of joint damage in rheumatoid arthritis.

Power spectrum of heart rate variability: a non-invasive test of integrated neurocardiac function.

Under steady state conditions, frequency specific oscillations in the heart rate record reflect beat-to-beat autonomic control of sinus node activity. Using an autoregressive model, samples (2.5 min) of continuous ECG records were analyzed in 36 healthy young adults during supine rest (45 min), orthostatic stress and controlled respiration. In the supine state, constancy of heart rate was achieved (mean HR 62.8 bt/min +/- 4.88 SD). However, the 0.1 Hz peak spectral power varied considerably: average coefficient of variation was 34% compared to only 8% for heart rate. When breathing rates were synchronized to a metronome there was a small insignificant decrease in the peak power at 0.1 Hz compared to spontaneous respiration. Standing produced a significant increase in the peak power at 0.1 Hz especially during synchronized breathing. There was a maximum increase in the low frequency (0.1 Hz) peak power of 40 (bt/min)2. Hz-1 at a controlled breathing frequency of 0.25 Hz in the standing compared to supine position. The data show that reproducibility of the power spectrum heart rate variability is best achieved at controlled but physiologic respiratory rates and, preferably, in the upright position.

Spectral analysis of heart rate variability following human heart transplantation: evidence for functional reinnervation.

To determine the status of innervation in long-term human donor allografts, the power spectrum of heart rate variability was analysed in 9 post-transplant patients and 7 healthy control subjects. The mean post-transplant follow-up was 17.8 months (range: 2-37 months). Continuous ECG signals were recorded throughout a 15-min rest period. An R-R interval tachogram was generated and an autoregressive model using linear predictive coding, was applied to the heart rate variability data. In 8 transplant patients the frequency oscillations were irregular, broad based and widely dispersed from 0 to 1 Hz. The patterns resembled white noise and were consistent with dissociation of the donor allograft from the recipient's central nervous system. In contrast, one patient displayed a heart rate variability spectrum indistinguishable from that of control subjects. This pattern contained two distinct spectral bands; one corresponding to the patient's respiratory rate at 0.2 Hz and a low frequency Mayer wave at 0.1 Hz. Atropine abolished the respiratory (vagal) peak. Except for this patient's post-transplant time (33 months compared to the group mean of 17.6 months), there were no clinical characteristics which distinguished this patient from the others. While the mean heart rate for the remaining 8 allografts was significantly higher than controls (95.3 vs 64.5 bt/min; P less than 0.001) the standard deviation of heart rate variability for the 8 patients was significantly narrower than controls (0.7 vs 4.86; P less than 0.01). The variance of heart rate for the patient with the normal power spectrum was fourfold greater than the mean SD of the other transplant patients.(ABSTRACT TRUNCATED AT 250 WORDS)

Biomechanical basis of optimal scoliosis surgical correction.

For an optimal approach to surgical correction of scoliosis, it was deemed desirable to biomechanically simulate the set of corrective forces applied by alternative internal fixation systems, so as to determine and apply the internal fixation system producing the best correction under safe levels of forces applied by the fixation systems to the spinal structures. To this end, we have developed, and presented here, (1) a spinal finite-element model relating the applied corrective forces to the corrected spinal configurations, (2) a method for determining the stiffness of the patient's spine prior to surgery, (3) computerized finite-element analysis simulation of alternative internal correction-fixation systems, so as to determine the most efficacious system, (4) instrumentations for surgically implementing the recommendations of the surgical simulation analysis and (5) comparisons of the model-simulated and surgically-obtained corrected spinal configurations. These procedures together constitute the biomechanical foundations of scoliosis surgical correction.