Comparison of models used to calculate left ventricular wall force

Quantifying myocardial active strain energy density: A comparative analysis of analytic and finite element methods for estimating left ventricular wall stress and strain

AIMS

This study compared commonly used methods for calculating left ventricular wall stress with the finite element analysis and evaluated different approaches to strain estimation. We sought to improve the accuracy of contractance estimation by developing a novel stress equation.

BACKGROUND

Multiple methods for calculating LV contractile stress and strain exist. Contractance is derived from stress and strain information and is a measure of myocardial work per unit volume of muscle. Precise stress and strain information are essential for its accurate evaluation.

METHODS AND RESULTS

We compared widely used methods for stress and strain calculations across diverse clinical scenarios representing distinct types of left ventricular myocardial disease. Our analysis revealed significant discrepancies in both the stress and strain values obtained with different methods. However, a newly developed modified version of the Mirsky equation demonstrated close agreement with the finite element analysis results for circumferential stress, while the Lamé method produced results close to those of finite element analysis for longitudinal stress and improved contractance accuracy.

CONCLUSION

This study highlights significant inconsistencies in stress and strain values calculated using different methods, emphasising the potential impact on contractance calculations and subsequent clinical interpretation. We recommend adopting the Lamé method for longitudinal stress assessment and the modified Mirsky equation for circumferential stress analysis. These methods offer a balance between accuracy and feasibility, making them advantageous for clinical practice. By adopting these recommendations, we can improve the accuracy of LV wall stress and strain estimates, leading to more dependable contractance calculations, better prognostication and improved clinical decisions.

CLINICAL AND TRANSLATIONAL IMPACT STATEMENT

Accurately estimating myocardial stress and strain is of paramount significance in clinical practice because the calculation of the contractance, defined and quantified by myocardial active strain energy density, necessitates correct stress and strain data. Contractance, which assesses myocardial work per unit muscle volume, has emerged as a promising indicator of contractile function and a predictor of future risk. The new recommendations for calculating myocardial stress improve the reliability of calculating contractance and enhance the understanding of myocardial diseases.

Comparison of two ellipsoidal models for the estimation of left ventricular end-systolic stress in patients with significant coronary artery disease

Background

The shape of the left ventricle (LV) is an important index to explore cardiac pathophysiology. A comparison was provided to estimate circumferential, longitudinal, and radial wall stress in LV based on the thick-walled ellipsoidal models of Mirsky and Ghista-Sandler for discriminating significant coronary artery disease (CAD) patients from no CAD patients.

Materials and Methods

According to the angiography findings, 82 patients with CAD were divided into two groups: 25 patients without significant CAD and 57 patients with significant CAD of single vessel and multivessel. An ellipsoidal LV geometry was used to calculate end-systolic passive stress as the mechanical behavior of LV. Echocardiographic views-based measurements of LV diameters used to estimate the end-systolic wall stress.

Results

Circumferential wall stress between the control group and significant CAD groups was significantly elevated for the Ghista model (P = 0.008); also, radial and longitudinal stress of the multi-vessel CAD group was significantly higher than the control group (P = 0.01 and P = 0.005, respectively). All stress parameters of the multi-vessel CAD group were statistically significant compared to the control group for the Mirsky model. Receiver operating characteristics curve analysis was shown the circumferential stress of multi-vessel CAD with an area under the curve (AUC) of 0.736 for the Ghista model and an AUC of 0.742 for the Mirsky model.

Conclusion

These results indicated that Ghista and Mirsky model estimates of circumferential passive stress were the potential biomechanical markers to predict patients with multi-vessel CAD. It could be a noninvasive and helpful tool to quantify the contractility of LV.

Scaling of cardiac morphology is interrupted by birth in the developing sheep Ovis aries

Scaling of the heart across development can reveal the degree to which variation in cardiac morphology depends on body mass. In this study, we assessed the scaling of heart mass, left and right ventricular masses, and ventricular mass ratio, as a function of eviscerated body mass across fetal and postnatal development in Horro sheep Ovis aries (~50-fold body mass range; N = 21). Whole hearts were extracted from carcasses, cleaned, dissected into chambers and weighed. We found a biphasic relationship when heart mass was scaled against body mass, with a conspicuous 'breakpoint' around the time of birth, manifest not by a change in the scaling exponent (slope), but rather a jump in the elevation. Fetal heart mass (g) increased with eviscerated body mass (M_b , kg) according to the power equation 4.90 M_b ^{0.88 ± 0.26 (± 95% CI )} , whereas postnatal heart mass increased according to 10.0 M_b ^{0.88 ± 0.10} . While the fetal and postnatal scaling exponents are identical (0.88) and reveal a clear dependence of heart mass on body mass, only the postnatal exponent is significantly less than 1.0, indicating the postnatal heart becomes a smaller component of body mass as the body grows, which is a pattern found frequently with postnatal cardiac development among mammals. The rapid doubling in heart mass around the time of birth is independent of any increase in body mass and is consistent with the normalization of wall stress in response to abrupt changes in volume loading and pressure loading at parturition. We discuss variation in scaling patterns of heart mass across development among mammals, and suggest that the variation results from a complex interplay between hard-wired genetics and epigenetic influences.

Novel Index of Maladaptive Myocardial Remodeling in Hypertension

BACKGROUND

Hypertensive left ventricular hypertrophy (HTN-LVH) is a leading cause of heart failure. Conventional patterns of cardiac geometry do not adequately risk-stratify patients with HTN-LVH. Using cardiovascular magnetic resonance, we developed a novel Remodeling Index (RI) that was designed to detect an exaggerated hypertrophic response to hypertension and tested its potential to risk-stratify hypertensive patients.

METHODS AND RESULTS

The RI was derived using LaPlace's Law (), and normal RI ranges were established in 180 healthy volunteers. The utility of the RI was examined in 256 asymptomatic hypertensive patients and 10 patients with heart failure with preserved ejection fraction. Hypertensive patients underwent multimodal cardiac assessment: contrast-enhanced cardiovascular magnetic resonance, echocardiograms, 24-hour blood pressure monitoring, and cardiac biomarkers (high-sensitivity cardiac troponins, NT-proBNP [N-terminal pro-B-type natriuretic peptide], and galectin-3). Blood pressure accounted for only 20% of the variance observed in LV mass. Although there was no association between blood pressure and myocardial fibrosis, LV mass was independently associated with fibrosis. Compared with hypertensive patients without LVH (n=191; 74.6%) and those with HTN-LVH and normal RI (n=50; 19.5%), patients with HTN-LVH and low RI (HTN-LVH/low RI; n=15, 5.9%) had an amplified myocardial response: elevated indexed LV masses (83±24 g/m2), more fibrosis (73%), and higher biomarkers of myocardial injury and dysfunction (P<0.05 for all). RI was similar in HTN-LVH/low RI and heart failure with preserved ejection fraction (4.1 [3.4-4.5] versus 3.7 [3.4-4.0], respectively; P=0.15).

CONCLUSIONS

We suggest that RI provides an approach for stratifying hypertensive patients and is suitable for testing in other disease cohorts to assess its clinical utility.

CLINICAL TRIAL REGISTRATION

URL: https://clinicaltrials.gov. Unique identifier: NCT02670031.

Hypertrophic and dilated cardiomyopathy: four decades of basic research on muscle lead to potential therapeutic approaches to these devastating genetic diseases

With the advent of technologies to obtain the complete sequence of the human genome in a cost-effective manner, this decade and those to come will see an exponential increase in our understanding of the underlying genetics that lead to human disease. And where we have a deep understanding of the biochemical and biophysical basis of the machineries and pathways involved in those genetic changes, there are great hopes for the development of modern therapeutics that specifically target the actual machinery and pathways altered by individual mutations. Prime examples of such a genetic disease are those classes of hypertrophic and dilated cardiomyopathy that result from single amino-acid substitutions in one of several of the proteins that make up the cardiac sarcomere or from the truncation of myosin binding protein C. Hypertrophic cardiomyopathy alone affects ∼1 in 500 individuals, and it is the leading cause of sudden cardiac death in young adults. Here I describe approaches to understand the molecular basis of the alterations in power output that result from these mutations. Small molecules binding to the mutant sarcomeric protein complex should be able to mitigate the effects of hypertrophic and dilated cardiomyopathy mutations at their sources, leading to possible new therapeutic approaches for these genetic diseases.

Distribution of normal human left ventricular myofiber stress at end diastole and end systole: a target for in silico design of heart failure treatments

Ventricular wall stress is believed to be responsible for many physical mechanisms taking place in the human heart, including ventricular remodeling, which is frequently associated with heart failure. Therefore, normalization of ventricular wall stress is the cornerstone of many existing and new treatments for heart failure. In this paper, we sought to construct reference maps of normal ventricular wall stress in humans that could be used as a target for in silico optimization studies of existing and potential new treatments for heart failure. To do so, we constructed personalized computational models of the left ventricles of five normal human subjects using magnetic resonance images and the finite-element method. These models were calibrated using left ventricular volume data extracted from magnetic resonance imaging (MRI) and validated through comparison with strain measurements from tagged MRI (950 ± 170 strain comparisons/subject). The calibrated passive material parameter values were C0 = 0.115 ± 0.008 kPa and B0 = 14.4 ± 3.18; the active material parameter value was Tmax = 143 ± 11.1 kPa. These values could serve as a reference for future construction of normal human left ventricular computational models. The differences between the predicted and the measured circumferential and longitudinal strains in each subject were 3.4 ± 6.3 and 0.5 ± 5.9%, respectively. The predicted end-diastolic and end-systolic myofiber stress fields for the five subjects were 2.21 ± 0.58 and 16.54 ± 4.73 kPa, respectively. Thus these stresses could serve as targets for in silico design of heart failure treatments.

B-type natriuretic peptide and wall stress in dilated human heart

Background Although B-type natriuretic peptide (BNP) is used as complimentary diagnostic tool in patients with unknown thoracic disorders, many other factors appear to trigger its release. In particular, it remains unresolved to what extent cellular stretch or wall stress of the whole heart contributes to enhanced serum BNP concentration. Wall stress cannot be determined directly, but has to be calculated from wall volume, cavity volume and intraventricular pressure of the heart. The hypothesis was, therefore, addressed that wall stress as determined by cardiac magnetic resonance imaging (CMR) is the major determinant of serum BNP in patients with a varying degree of left ventricular dilatation or dysfunction (LVD). Methods A thick-walled sphere model based on volumetric analysis of the LV using CMR was compared with an echocardiography-based approach to calculate LV wall stress in 39 patients with LVD and 21 controls. Serum BNP was used as in vivo marker of a putatively raised wall stress. Nomograms of isostress lines were established to assess the extent of load reduction that is necessary to restore normal wall stress and related biochemical events. Results Both enddiastolic and endsystolic LV wall stress were correlated with the enddiastolic LV volume (r = 0.54, P < 0.001; r = 0.81, P < 0.001). LV enddiastolic wall stress was related to pulmonary pressure (capillary: r = 0.69, P < 0.001; artery: r = 0.67, P < 0.001). Although LV growth was correlated with the enddiastolic and endsystolic volume (r = 0.73, P < 0.001; r = 0.70, P < 0.001), patients with LVD exhibited increased LV wall stress indicating an inadequately enhanced LV growth. Both enddiastolic (P < 0.05) and endsystolic (P < 0.01) wall stress were increased in patients with increased BNP. In turn, BNP concentration was elevated in individuals with increased enddiastolic wall stress (>8 kPa: 587 +/- 648 pg/ml, P < 0.05; >12 kPa: 715 +/- 661 pg/ml, P < 0.001; normal < or =4 kPa: 124 +/- 203 pg/ml). Analysis of variance revealed LV enddiastolic wall stress as the only independent hemodynamic parameter influencing BNP (P < 0.01). Using nomograms with "isostress" curves, the extent of load reduction required for restoring normal LV wall stress was assessed. Compared with the CMR-based volumetric analysis for wall stress calculation, the echocardiography based approach underestimated LV wall stress particularly of dilated hearts. Conclusions In patients with LVD, serum BNP was increased over the whole range of stress values which were the only hemodynamic predictors. Cellular stretch appears to be a major trigger for BNP release. Biochemical mechanisms need to be explored which appear to operate over this wide range of wall stress values. It is concluded that the diagnostic use of BNP should primarily be directed to assess ventricular wall stress rather than the extent of functional ventricular impairment in LVD.

Relation of B-type natriuretic peptide to left ventricular wall stress as assessed by cardiac magnetic resonance imaging in patients with dilated cardiomyopathy

Ventricular loading conditions are crucial determinants of cardiac function and prognosis in heart failure. B-type natriuretic peptide (BNP) is mainly stored in the ventricular myocardium and is released in response to an increased ventricular filling pressure. We examined, therefore, the hypothesis that BNP serum concentrations are related to ventricular wall stress. Cardiac magnetic resonance imaging (MRI) was used to assess left ventricular (LV) mass and cardiac function of 29 patients with dilated cardiomyopathy and 5 controls. Left ventricular wall stress was calculated by using a thick-walled sphere model, and BNP was assessed by immunoassay. LV mass (r = 0.73, p < 0.001) and both LV end-diastolic (r = 0.54, p = 0.001) and end-systolic wall stress (r = 0.66, p < 0.001) were positively correlated with end-diastolic volume. LV end-systolic wall stress was negatively related to LV ejection fraction (EF), whereas end-diastolic wall stress was not related to LVEF. BNP concentration correlated positively with LV end-diastolic wall stress (r = 0.50, p = 0.002). Analysis of variance revealed LV end-diastolic wall stress as the only independent hemodynamic parameter influencing BNP (p < 0.001). The present approach using a thick-walled sphere model permits determination of mechanical wall stress in a clinical routine setting using standard cardiac MRI protocols. A correlation of BNP concentration with calculated LV stress was observed in vivo. Measurement of BNP seems to be sufficient to assess cardiac loading conditions. Other relations of BNP with various hemodynamic parameters (e.g., EF) appear to be secondary. Since an increased wall stress is associated with cardiac dilatation, early diagnosis and treatment could potentially prevent worsening of the outcome.

A new methodological approach to assess cardiac work by pressure-volume and stress-length relations in patients with aortic valve stenosis and dilated cardiomyopathy

In experimental animals, cardiac work is derived from pressure-volume area and analyzed further using stress-length relations. Lack of methods for determining accurately myocardial mass has until now prevented the use of stress-length relations in patients. We hypothesized, therefore, that not only pressure-volume loops but also stress-length diagrams can be derived from cardiac volume and cardiac mass as assessed by cardiac magnetic resonance imaging (CMR) and invasively measured pressure. Left ventricular (LV) volume and myocardial mass were assessed in seven patients with aortic valve stenosis (AS), eight with dilated cardiomyopathy (DCM), and eight controls using electrocardiogram (ECG)-gated CMR. LV pressure was measured invasively. Pressure-volume curves were calculated based on ECG triggering. Stroke work was assessed as area within the pressure-volume loop. LV wall stress was calculated using a thick-wall sphere model. Similarly, stress-length loops were calculated to quantify stress-length-based work. Taking the LV geometry into account, the normalization with regard to ventricular circumference resulted in "myocardial work." Patients with AS (valve area 0.73+/-0.18 cm(2)) exhibited an increased LV myocardial mass when compared with controls (P<0.05). LV wall stress was increased in DCM but not in AS. Stroke work of AS was unchanged when compared with controls (0.539+/-0.272 vs 0.621+/-0.138 Nm, not significant), whereas DCM exhibited a significant depression (0.367+/-0.157 Nm, P<0.05). Myocardial work was significantly reduced in both AS and DCM when compared with controls (129.8+/-69.6, 200.6+/-80.1, 332.2+/-89.6 Nm/m(2), P<0.05), also after normalization (7.40+/-5.07, 6.27+/-3.20, 14.6+/-4.07 Nm/m(2), P<0.001). It is feasible to obtain LV pressure-volume and stress-length diagrams in patients based on the present novel methodological approach of using CMR and invasive pressure measurement. Myocardial work was reduced in patients with DCM and noteworthy also in AS, while stroke work was reduced in DCM only. Most likely, deterioration of myocardial work is crucial for the prognosis. It is suggested to include these basic physiological procedures in the clinical assessment of the pump function of the heart.

Cross-Talk Between Cardiac Muscle and Coronary Vasculature

The cardiac muscle and the coronary vasculature are in close proximity to each other, and a two-way interaction, called cross-talk, exists. Here we focus on the mechanical aspects of cross-talk including the role of the extracellular matrix. Cardiac muscle affects the coronary vasculature. In diastole, the effect of the cardiac muscle on the coronary vasculature depends on the (changes in) muscle length but appears to be small. In systole, coronary artery inflow is impeded, or even reversed, and venous outflow is augmented. These systolic effects are explained by two mechanisms. The waterfall model and the intramyocardial pump model are based on an intramyocardial pressure, assumed to be proportional to ventricular pressure. They explain the global effects of contraction on coronary flow and the effects of contraction in the layers of the heart wall. The varying elastance model, the muscle shortening and thickening model, and the vascular deformation model are based on direct contact between muscles and vessels. They predict global effects as well as differences on flow in layers and flow heterogeneity due to contraction. The relative contributions of these two mechanisms depend on the wall layer (epi- or endocardial) and type of contraction (isovolumic or shortening). Intramyocardial pressure results from (local) muscle contraction and to what extent the interstitial cavity contracts isovolumically. This explains why small arterioles and venules do not collapse in systole. Coronary vasculature affects the cardiac muscle. In diastole, at physiological ventricular volumes, an increase in coronary perfusion pressure increases ventricular stiffness, but the effect is small. In systole, there are two mechanisms by which coronary perfusion affects cardiac contractility. Increased perfusion pressure increases microvascular volume, thereby opening stretch-activated ion channels, resulting in an increased intracellular Ca2+transient, which is followed by an increase in Ca2+sensitivity and higher muscle contractility (Gregg effect). Thickening of the shortening cardiac muscle takes place at the expense of the vascular volume, which causes build-up of intracellular pressure. The intracellular pressure counteracts the tension generated by the contractile apparatus, leading to lower net force. Therefore, cardiac muscle contraction is augmented when vascular emptying is facilitated. During autoregulation, the microvasculature is protected against volume changes, and the Gregg effect is negligible. However, the effect is present in the right ventricle, as well as in pathological conditions with ineffective autoregulation. The beneficial effect of vascular emptying may be reduced in the presence of a stenosis. Thus cardiac contraction affects vascular diameters thereby reducing coronary inflow and enhancing venous outflow. Emptying of the vasculature, however, enhances muscle contraction. The extracellular matrix exerts its effect mainly on cardiac properties rather than on the cross-talk between cardiac muscle and coronary circulation.

Assessment of systolic and diastolic ventricular properties via pressure-volume analysis: a guide for clinical, translational, and basic researchers

Assessment of left ventricular systolic and diastolic pump properties is fundamental to advancing the understanding of cardiovascular pathophysiology and therapeutics, especially for heart failure. The use of end-systolic and end-diastolic pressure-volume relationships derived from measurements of instantaneous left ventricular pressure-volume loops emerged in the 1970s as a comprehensive approach for this purpose. As invasive and noninvasive techniques for measuring ventricular volume improved over the past decades, these relations have become commonly used by basic, translational, and clinical researchers. This review summarizes 1) the basic concepts underlying pressure-volume analysis of ventricular and myocardial systolic and diastolic properties, 2) deviations from ideal conditions typically encountered in real-life applications, 3) how these relationships are appropriately analyzed, including statistical analyses, and 4) the most common problems encountered by investigators and the appropriate remedies. The goal is to provide practical information and simple guidelines for accurate application and interpretation of pressure-volume data as they pertain to characterization of ventricular and myocardial properties in health and disease.

Advances in electrical and mechanical cardiac mapping

Cardiac mapping--recording cardiac activity during electrophysiological testing--has evolved into an indispensable tool in studying the cardiac excitation process, analysing activation patterns, and identifying arrhythmogenic tissue. Cardiac mapping is a broad term that is used here to encompass applications that record electrical or mechanical activity of the heart or both. In recent years, simultaneous and sequential electrical mapping methods have been combined with direct mechanical measurements or imaging techniques to acquire information regarding both the electrical and mechanical activity of the heart (electromechanical mapping) during normal and irregular cardiac behavior. This paper reviews the emerging area of electromechanical mapping from the point of view of the applicable technology, including its history and application.

Design of an integrated sensor for in vivo simultaneous electrocontractile cardiac mapping

While there is extensive mapping of the spread of electrical activity in the heart, there have been no measurements of electrical and localized mechanical, or contractile, activity. Yet the development of effective treatments for diseases like chronic heart failure and cardiac hypertrophy depend on the ability to quantify improvements in electrocontractile function. In this paper, we present a sensor that is capable of making simultaneous, electrocontractile measurements. Its small size facilitates placement in multiple myocardial sites for multichannel studies. Semiconductor strain gages are used for force sensing, and Ag/AgCl-plated tungsten electrodes act as electrogram sensors. The sensor contains electronics on-board, including instrumentation amplifiers and a microprocessor for data sampling and analog-to-digital conversion. Each sensor can accurately detect 0-245+/-5 mV in two electrogram channels with a sensitivity of 0.96+/-0.2 mV/step and less than 2% error, and 0-144+/-29 g of contractile force with a sensitivity of 0.56+/-0.11 g/step in the analog-to-digital conversion and less than 6% error. The sensor has been tested in vivo in open-chest rabbit and pig mapping studies. These studies indicated that the average peak-to-peak contractile force at the apex is smaller in the rabbit than the pig (13.3 versus 40.3 g), that the average peak-to-peak contractile force in the pig is smaller near the base than near the apex (31.3 versus 40.3 g), and that contractile force is visibly decreased during ventricular fibrillation compared to normal sinus rhythm.

Simulation and prediction of cardiotherapeutical phenomena from a pulsatile model coupled to the Guyton circulatory model

In order to use simulation prediction for cardiotherapeutical purposes, the well-documented and physiologically validated circulatory Guyton model was coupled to a cardiac pulsatile model which comprises the hemodynamics of the four chambers including valvular effects, as well as the Hill, Frank-Starling, Laplace, and autonomic nervous system (ANS) effects. The program is written in the "C" language and available for everybody. The program system was submitted to validation and plausibility tests both as to the steady-state and the dynamic properties. Pressures, volumes and flows and other variables turned out to be compatible with published experimental and clinical recordings both under physiological and pathophysiological conditions. The results from the application to cardiac electrotherapy emphasize the importance of atrial contraction to ventricular filling, the adequate atrio-ventricular delay, the effect of impaired ventricular relaxation, and the significance of the choice of the adequate cardiac pacemaker, both with respect to the stimulation site and the adequate sensor controlling pacing rate. The simulation will be further developed, tested and applied for cardiological purposes.

Active and passive stresses in the myocardium

A mathematical approach that can be used to calculate the passive stress in the ventricular wall is presented. The active fiber stress (force/unit area) generated by the muscular fibers in the ventricular wall is expressed by means of body force (force/unit volume of the myocardium). It is shown that the total intramyocardial passive stress induced in the passive medium of the myocardium can be expressed as the sum of a passive stress induced by the left ventricular pressure and a passive stress induced by the active fiber stress. Applications to experimental data published in the literature are given. New results are presented that show the relation among those two components of the intramyocardial passive stress. New relations between the intramyocardial passive stress, the slope (elastance) of the pressure-volume relation, and the residual volume are also derived. The results obtained give a better understanding of some aspects of the mechanics of cardiac contraction and can provide a more detailed interpretation of clinical conditions.

Estimates of regional work in the canine left ventricle

Assessment of the magnitude of regional myocardial work requires knowledge of regional fiber stress and fiber shortening. The theoretical development and experimental validation of a method is presented which used values of estimated active and passive fiber stress according to a fluid-fiber model, and measured fiber strain values. This enables the construction of regional stress-strain diagrams, a regional analog of the pressure-volume area model by Suga and co-investigators, which can be linked to regional oxygen consumption. In the left ventricle, either normally or asynchronously activated, the method yields reliable data on strain and active and passive fiber stress. The relation between estimated regional work and myocardial oxygen demand is in quantitative agreement with previously reported relations between global oxygen demand and measured pressure-volume area. During coronary artery occlusion, however, these values were less reliable, which might be due to inaqdequate knowledge of the (passive) material properties of the myocardium.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: II--Prolate spheroidal coordinates

A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

Intramuscular pressures for monitoring different tasks and muscle conditions

Intramuscular fluid pressure (IMP) can easily be measured in man and animals. It follows the law of Laplace which means that it is determined by the tension of the muscle fibers, the recording depth and by fiber geometry (fiber curvature or pennation angle). Thick, bulging muscles create high IMPs (up to 1000 mmHg) and force transmission to tendons becomes inefficient. High resting or postexercise IMPs are indicative of a compartment syndrome due to muscle swelling within a low-compliance osseofascial boundary. IMP increases linearly with force (torque) independent of the mode or speed of contraction (isometric, eccentric, concentric). IMP is also a much better predictor of muscle force than the EMG signal. During prolonged low-force isometric contractions, cyclic variations in IMP are seen. Since IMP influences muscle blood flow through the muscle pump, autoregulating vascular elements, and compression of the intramuscular vasculature, alterations in IMP have important implications for muscle function.

Post-ischemic diastolic dysfunction

Though a sustained post-ischemic decrease in contractile function has been clearly established, post-ischemic diastolic function has not been thoroughly investigated. Accordingly, 11 anesthetized (isoflurane 1%) open-chest beagles were instrumented to measure left ventricular pressure and dimensions (circumferential length and wall thickness) in an apicoanterior area supplied by the left anterior descending coronary artery (LAD). Pressure-dimension relations were modified by stepwise infusion and withdrawal of 200 mL of the animals' own blood during baseline, 45 minutes partial occlusion of the LAD (systolic bulging), and 60 minutes after the onset of reperfusion. Stiffness constants were derived from the end-diastolic pressure-length and stress-strain relations, respectively. Myocardial ischemia was associated with significant (P < 0.05) alterations of the following parameters of diastolic function: (1) 47% increase in end-diastolic pressure; (2) 22% decrease in peak negative dP/dt; (3) 9% increase in the time constant of isovolumic relaxation (tau); (4) postcystolic contraction; (5) 6% increase in end-diastolic length and 10% decrease in end-diastolic thickness; (6) 12% increase in unstressed length (creep) and 13% decrease in unstressed thickness; (7) 51% increase in chamber stiffness and a 63% increase in myocardial stiffness; and (8) 40% decrease in the peak lengthening rate. After 60 minutes of reperfusion, only end-diastolic pressure and tau had returned to baseline values whereas systolic shortening fraction, postsystolic contraction, and end-diastolic and unstressed dimensions had only partially recovered. No recovery occurred in peak negative dP/dt, chamber stiffness, myocardial stiffness, and peak lengthening rate. Thus, both myocardial ischemia and reperfusion are associated with complex changes in global and regional left ventricular diastolic function.

Regional mechanical properties of passive myocardium

There is considerable interest in calculating regional stresses in the heart. This, in turn, requires complete information on regional material properties which, surprisingly, is not available. The specific aim of this work, therefore, was to determine if transmural differences exist in the mechanical behavior of passive myocardium in the equatorial region of the heart. Thus, we performed in vitro biaxial experiments on 28 thin, rectangular slabs of noncontracting myocardium excised from four regions within canine hearts: the middle portion of the interventricular septum (n = 8), and the inner (n = 5), middle (n = 9) and outer (n = 6) layers of the lateral left ventricular (LV) free wall. There were three major findings. First, an existing three-dimensional constitutive relation described the nonlinear and anisotropic behavior exhibited in the four regions equally well. Second, the anisotropy was similar in each region. Third, there were, however, regional differences in the strain-energy stored by specimens during identical finite deformations. In particular, specimens from inner and outer portions of the LV free wall tended to be stiffer than those from the middle of the LV free wall and septum. These findings, together with previous results on excised epicardium, suggest that the mechanical properties of the heart are qualitatively similar from region to region, but quantitatively different.

Graded myocardial ischemia is associated with a decrease in diastolic distensibility of the remote nonischemic myocardium in the anesthetized dog

OBJECTIVES

This study was designed to investigate the changes in regional distensibility of the ischemic segment and of a remote nonischemic segment brought about by graded myocardial ischemia.

BACKGROUND

Ventricular distensibility is a major determinant of left ventricular end-diastolic pressure. The effects of graded myocardial ischemia on the regional distensibility of the ischemic area have not been studied. Moreover, there are few data on the effects of myocardial ischemia on the regional distensibility of the nonischemic myocardium.

METHODS

Nine anesthetized open chest mongrel dogs were fitted with instruments to measure left ventricular pressure and circumferential length (sonomicrometry) in the ischemic segment and in a nonischemic segment. The pressure-length relation was modified by stepwise infusion and withdrawal of 200 ml of each dog's own blood over 30 min in five consecutive stages of regional ischemia. Unstressed dimensions were obtained by repeated inferior vena cava occlusions. In both segments, regional distensibility was assessed at end-diastole by means of the constants of the pressure-length (chamber stiffness), the pressure-strain and the force-strain (myocardial stiffness) relations.

RESULTS

In the ischemic segment, partial and complete coronary occlusions were associated with a twofold increase in the chamber stiffness constant, the pressure-strain constant and the myocardial stiffness constant, whereas in the nonischemic segment the chamber stiffness constant, the pressure-strain constant and the myocardial stiffness constant increased by 50%.

CONCLUSIONS

Regional myocardial ischemia is associated with a decrease in distensibility of both the ischemic and the remote nonischemic myocardium.

Variation in left ventricular regional wall stress with cine magnetic resonance imaging: normal subjects versus dilated cardiomyopathy

We measured the variation of end-systolic wall stress and its relation to regional ejection fraction in short-axis planes through the left ventricle in normal subjects and in patients with dilated cardiomyopathy (DCM) by cine magnetic resonance imaging. There was a gradual increase in end-systolic wall stress but a gradual decrease in ejection fraction from apex to base in normal subjects (14 +/- 6 to 52 +/- 15 kdyne/cm2, 78% +/- 12% to 62% +/- 8%) and in patients with DCM (49 +/- 28 to 130 +/- 30 kdyne/cm2, 40 +/- 18 to 23% +/- 9%). The end-systolic wall stress in patients with DCM was higher than in normal subjects at every level (p < 0.01). We conclude that there is a variation in end-systolic wall stress in both normal subjects and patients with DCM with regional ejection fraction inversely related to regional end-systolic wall stress.

Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study

The dependence of local left ventricular (LV) mechanics on myocardial muscle fiber orientation was investigated using a finite element model. In the model we have considered anisotropy of the active and passive components of myocardial tissue, dependence of active stress on time, strain and strain rate, activation sequence of the LV wall and aortic afterload. Muscle fiber orientation in the LV wall is quantified by the helix fiber angle, defined as the angle between the muscle fiber direction and the local circumferential direction. In a first simulation, a transmural variation of the helix fiber angle from +60 degrees at the endocardium through 0 degrees in the midwall layers to -60 degrees at the epicardium was assumed. In this simulation, at the equatorial level maximum active muscle fiber stress was found to vary from about 110 kPa in the subendocardial layers through about 30 kPa in the midwall layers to about 40 kPa in the subepicardial layers. Next, in a series of simulations, muscle fiber orientation was iteratively adapted until the spatial distribution of active muscle fiber stress was fairly homogeneous. Using a transmural course of the helix fiber angle of +60 degrees at the endocardium, +15 degrees in the midwall layers and -60 degrees at the epicardium, at the equatorial level maximum active muscle fiber stress varied from 52 kPa to 55 kPa, indicating a remarkable reduction of the stress range. Moreover, the change of muscle fiber strain with time was more similar in different parts of the LV wall than in the first simulation. It is concluded that (1) the distribution of active muscle fiber stress and muscle fiber strain across the LV wall is very sensitive to the transmural distribution of the helix fiber angle and (2) a physiological transmural distribution of the helix fiber angle can be found, at which active muscle fiber stress and muscle fiber strain are distributed approximately homogeneously across the LV wall.

Ultrafast computed tomography analysis of regional radius-to-wall thickness ratios in normal and volume-overloaded human left ventricle

BACKGROUND

This study tested two hypotheses: 1) regional left ventricular radius-to-wall thickness ratios (R/T) are uniform in normal subjects, and 2) patients with left ventricular hypertrophy secondary to compensated volume overload normalize global and regional R/T.

METHODS AND RESULTS

Ultrafast computed tomography was used to measure regional short-axis ventricular R/T in 11 normal subjects and 13 patients with compensated aortic insufficiency (AI) of moderate severity (regurgitant fraction, greater than or equal to 25%). Radius and wall thickness dimensions were calculated by two different methods. In method 1, the average radius and wall thickness were determined for each planimetric transaxial tomographic image. In method 2, the left ventricle was three-dimensionally reconstructed; then, new radii and wall thickness were recalculated as if all the images were acquired orthogonal to the endocardial surface at each tomographic level. In normals, the mean R/T ratio was 1.75 +/- 0.11 (SEM) with method 1 and 1.80 +/- 0.07 with method 2. The R/T ratios varied as a function of the relative apex-to-base position. R/T ratios at the basal four levels were relatively uniform, whereas R/T at the lower three tomographic levels were significantly less than those at the base (p less than 0.01). Patients with AI had a mean regurgitant fraction of 44 +/- 3.8% (range, 25-63%). The mean R/T ratio was 2.18 +/- 0.16 with method 1 and 2.55 +/- 0.18 with method 2. Similar to the pattern observed in normals, the regional R/T ratios at the lower three or four levels were significantly less than the basal R/T ratios (p less than 0.01). Regional comparison of the normal to the volume-overloaded ventricles demonstrated that R/T ratios in the AI patients were significantly greater at the upper five levels with method 1 and at all eight levels with method 2 (p less than 0.01-0.001, AI versus normal).

CONCLUSIONS

These findings demonstrate that regional R/T ratios are heterogeneous in both normals and patients with left ventricular hypertrophy secondary to compensated aortic insufficiency. Furthermore, these findings challenge the accepted hypothesis that global and regional R/T ratios normalize in patients with compensated volume-overload hypertrophy.

Developmental modulation of myocardial mechanics: age- and growth-related alterations in afterload and contractility

Somatic growth is associated with alterations in myocardial mechanics in children with heart disease and in most animal models of congenital heart disease. However, the effect of age and body size on myocardial contractility and loading conditions in normal infants and children is not known. Therefore, 256 normal children aged 7 days to 19 years (34% less than 3 years old) were evaluated with noninvasive indexes of left ventricular contractility and loading conditions. Two-dimensional and M-mode echocardiographic recordings of the left ventricle were obtained with a phonocardiogram, indirect pulse tracing and blood pressure recordings. Left ventricular dimensions, wall thickness and pressure measurements obtained from these data were used to calculate peak and end-systolic circumferential and meridional wall stress and mean and integrated meridional wall stress. Velocity of shortening adjusted for heart rate was compared with end-systolic stress to assess contractility independently of loading status. The subjects were stratified for gender and each of the derived variables was related to age and body surface area. Ventricular shape, assessed as the major/minor axis ratio, and the circumferential/meridional stress ratio were found to be invariant with growth. The ratio of posterior wall thickness to minor axis dimension did not change with age, despite the normal age-related increase in blood pressure. The increase in pressure despite unvarying ventricular shape and wall thickness/dimension ratio resulted in a substantial increase in wall stress that was most dramatic during the first few years of life. In association with the increase in afterload, systolic function decreased with age. However, the age-related decrease in the velocity of shortening was greater than that expected from the increase in afterload alone, indicating a higher level of contractility in infants and children during the first years of life than in older subjects. The process of normal growth and development, similar to that in children with heart disease, is associated with a rapid decrease in the trophic response to hemodynamic loads, resulting in an age-associated increase in wall stress. There is a similar but somewhat more rapid decrease in contractility, with the highest values seen in the youngest patients.

Regional three-dimensional geometry and function of left ventricles with fibrous aneurysms. A cine-computed tomography study

BACKGROUND

To assess the extent and nature of the dysfunction surrounding aneurysms of the left ventricle (LV), we examined the parameters of local and global three-dimensional shape, size, and function of LVs of eight patients with histologically confirmed anterior fibrous aneurysms.

METHODS AND RESULTS

Three-dimensional reconstructions of each LV were made from 10-12 short-axis fast cine-angiographic computed tomography (cine-CT) slices encompassing the entire heart at end diastole and end systole. Regional three-dimensional wall thickness, thickening, motion, curvature, and stress index were calculated for 84 elements encompassing the entire LV. The aneurysmal border was defined by a sharp decrease in end-diastolic wall thickness and separated the LV into an aneurysmal zone and a normal zone that was further divided into adjacent normal (AN) and remote normal (RN) zones. As expected, thickening was negligible in both the aneurysmal and the border zones. Although both the AN and the RN zones had normal wall thickness (1.05 +/- 0.20 and 1.09 +/- 0.20 cm, respectively), thickening was depressed in the AN (0.22 +/- 0.08 cm) but not the RN (0.44 +/- 0.19 cm) zones. The size of the dysfunction zone (defined as less than 2 mm thickening) was found to be considerably greater than the anatomic size of the aneurysm (60.9 +/- 13.7% versus 33.6 +/- 7.6% of the left ventricular endocardial area, respectively; p less than 0.001). In addition, the AN zone had a smaller curvature and a higher stress index than the RN zone.

CONCLUSIONS

LVs with fibrous aneurysms are characterized by a relatively large region of nonfunction that encompasses the thin aneurysmal area and its transitional border zone, a normally functioning remote zone, and an intermediate region of normal wall thickness but with reduced function, which may be attributed to its low curvature and high stress index.

Matching between ventricle and arterial load. An evolutionary process

The hemodynamic properties of the ventricle are related to those of the arterial load. However, the precise nature of this relation is not known. At least three different matching criteria have been described in the literature: optimization of heart rate, of power output, and of external efficiency. Although these suggestions are based on experimental findings, there is little understanding of the underlying principles. We now suggest that the balance between the ventricle and its load is a result of the evolutionary process. To support our view, three simple assumptions are proposed regarding the evolutionary determinants underlying the relation between ventricle and arterial load: 1) Arterial pressure and flow to be generated by the ventricular pump under normal (control) conditions are set by the demands of the body. 2) Mechanical properties of contractile machinery and arterial wall material are given. 3) The heart and arterial system should have minimum size. On the basis thereof, we argue that heart rate is related to maintenance of diastolic pressure and show that the ventricle operates close to optimum power and efficiency to attain minimum size.

Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall

Pumping power as delivered by the heart is generated by the cells in the myocardial wall. In the present model study global left-ventricular pump function as expressed in terms of cavity pressure and volume is related to local wall tissue function as expressed in terms of myocardial fiber stress and strain. On the basis of earlier studies in our laboratory, it may be concluded that in the normal left ventricle muscle fiber stress and strain are homogeneously distributed. So, fiber stress and strain may be approximated by single values, being valid for the whole wall. When assuming rotational symmetry and homogeneity of mechanical load in the wall, the dimensionless ratio of muscle fiber stress (sigma f) to left-ventricular pressure (Plv) appears to depend mainly on the dimensionless ratio of cavity volume (Vlv) to wall volume (Vw) and is quite independent of other geometric parameters. A good (+/- 10%) and simple approximation of this relation is sigma f/Plv = 1 + 3 Vlv/Vw. Natural fiber strain is defined by ef = In (lf/lf,ref), where lf,ref indicates fiber length (lf) in a reference situation. Using the principle of conservation of energy for a change in ef, it holds delta ef = (1/3)delta In (1 + 3Vlv/Vw).

Regional metabolic rate of exogenous glucose in the isoprenaline and dobutamine stimulated canine myocardium as estimated by the 2-deoxy-D[1-14C]glucose method

The effect of beta-adrenoceptor stimulation by isoprenaline and dobutamine on the transmural distribution pattern of regional myocardial metabolic rate of exogenous glucose (RMMRGlc) was studied in the anesthetized closed chest dog using the 2-deoxy-D[1-14C]glucose method. In a previous series a lumped constant (LC) value of 0.93 +/- 0.47 (1 SD) was measured for [14C]2-deoxyglucose in the canine myocardium. In the control group (N = 12) RMMRGlc was significantly higher in the subendocardial layer of the left ventricular free wall than in both the middle and subepicardial layer, where it was quite evenly distributed (P less than or equal to 0.05). With i.v. dobutamine (N = 8) RMMRGlc was significantly lower in the midportion of left ventricular free wall than in the subepicardial layer (P less than or equal to 0.05), but it was not different from the inner wall section. Significant differences between the subepicardial and subendocardial portions of the left ventricular free wall could not be found, either. In the isoprenaline group (N = 9) no transmural gradients of RMMRGlc were observed in the left ventricular myocardium. In all groups, both the interventricular septum and the right ventricular free wall exhibited homogeneous distribution patterns of RMMRGlc. It is concluded that transmural distribution patterns of exogenous glucose utilization probably reflect corresponding gradients in energy demands of the left ventricular wall. Redistribution of RMMRGlc in the isoprenaline and dobutamine groups may result from altered working conditions, a change in local inotropic state of the left ventricular myocardium, or from regional differences in the proportions of substrate utilization, and from regional differences in adrenoceptor density.

Left ventricular regional wall stress in dilated cardiomyopathy

Left ventriculography with simultaneous pressure micromanometry was performed in 11 normal control subjects and 17 patients with dilated cardiomyopathy (DCM). Left ventricular silhouettes in the right anterior oblique projection were divided into eight areas, and regional wall stress was computed by Janz's method in each area excluding the two most basal areas. Wall stress was higher in DCM patients than in control subjects (p less than 0.01). The percent area changes from end diastole to end systole in each area were lower in DCM patients than in control subjects (mean for six areas, 22 +/- 14% versus 54 +/- 9%, respectively, p less than 0.01), but the coefficient of variation for the percent area changes in the six areas of the left ventricle in DCM patients was greater than that in control subjects (32 +/- 17% versus 15 +/- 4%, respectively, p less than 0.01), indicating regional differences in hypokinesis. There was a significant negative correlation between end-systolic regional wall stress and percent area change (r = -0.60 to -0.86, p less than 0.05) in each area. Thus, excessive regional afterload may play an important role in causing regional hypokinesis in DCM.

Regional differences of substrate oxidation capacity in rat hearts: effects of extra load and endurance training

Male rats, aged 17 weeks at the end of experiments, were divided into four groups. Two groups lived in normal cage conditions with or without extra load (20% of the body weight) and two groups were trained by running with or without extra load for 8 weeks. Oxidation rates of succinate, glutamate + malate, palmitoylcarnitine, and pyruvate, and the activities of lactate dehydrogenase, citrate synthase, isocitrate dehydrogenase and cytochrome oxidase were measured in homogenates of the right ventricle and in those of the subendocardial and subepicardial layers of the left ventricle. Oxidation rates of succinate and palmitoylcarnitine tended to be higher in the subendocardium than in the subepicardium of sedentary control animals (p less than 0.1 and p less than 0.05, respectively). Transmural differences of succinate and palmitoylcarnitine oxidation rates were even more clear after running training (p less than 0.01 and p less than 0.05, respectively), after carrying extra load (p less than 0.001 and p less than 0.001, respectively) and after training carrying extra load (p less than 0.001 and p less than 0.05, respectively). Training also enhanced pyruvate oxidation rate in the subendocardium. Oxidation rates of all substrates were lower in the right ventricle than in the left ventricle. In control animals there were no regional differences in the myocardial enzyme activities and the training- or extra-load-induced changes were modest compared with the changes in the oxidation rates. The most significant change was the training-induced enhancement in the lactate dehydrogenase activity of the subendocardium (p less than 0.001 vs subepicardium). These results show greater subendocardial than subepicardial oxidation rates of certain substrates in the normal heart. These results also suggest that the myocardium adapts to increased work by increasing the subendocardial oxidation rate of some but not all substrates, indicating further that there may be qualitative mitochondrial differences in the different regions of the heart.

Calcium metabolism and depressed contractility in isolated human and porcine heart muscle

Contractility is often depressed in isolated heart muscle. To analyze this phenomenon, we measured the derivative of left ventricular pressure (dP/dt) in intact and in isolated, blood perfused pig hearts, and peak force (F) or stress (F/mm2) in ventricular trabeculae of man and pig. When the heart was in the steady state at a priming frequency of 2 Hz an extrasystolic interval of 0.3 s was interposed, followed by four postextrasystolic intervals of 0.8 s. In the case of isolated trabeculae the priming frequency was 0.2 Hz, the extra interval 0.4 s, and the post-extrasystolic intervals were 5 s. The exponential decay of potentiation is characterized by the constant D: a low value of D indicates a rapid decay of potentiation. DP/dt was about 1000 mm Hg/s in the intact hearts, but within 1 h after isolation dP/dt decreased to about 700 mm Hg/s, and this was associated with a decrease in D from 0.63 to 0.40. Developed stress in the isolated trabeculae was about 2 mN/mm2 and D was about 0.20 under standard, in vitro conditions (a.o. 1.5 mM Ca2+. 0.2 Hz stimulus frequency). This stress is only 10% of the calculated stress in the intact heart. An increase of priming frequency, or of [Ca2+], or addition of 30 nM isoproterenol to the perfusate caused a marked increase in F and D. Properties of human and porcine trabeculae were quantitatively similar. The strong correlation between dP/dt, or F, and D suggests a causal relationship. This is consistent with the current model of e-c coupling in heart muscle, in which the activity of the Ca2+ pump of the sarcoplasmic reticulum determines the decay of potentiation and the amount of releasable Ca2+ in the reticulum determines force of contraction. Since isoproterenol stimulates the Ca2+ pump in the reticulum, the increase in D and F induced by this drug is consistent with the model. We conclude, that the decreased dP/dt, F, and D in isolated preparations was due to impaired sarcoplasmic reticulum function. The role of this phenomenon in the stunned heart syndrome, species differences and possible causes are discussed.

Left ventricular wall stress distribution in chronic pressure and volume overload: effect of normal and depressed contractility on regional stress-velocity relations

Regional stress-velocity relations were determined in a first group of patients (n = 15) with normal (five controls, five patients with aortic stenosis, and five patients with aortic insufficiency) and a second group of patients (n = 10) with depressed contractility (five patients with aortic stenosis and five with aortic insufficiency). LV circumferential wall stress was calculated from high-fidelity pressure and frame-by-frame angiocardiographic data using the Wong thick-wall model. Regional wall stress and shortening velocity were calculated from the endo- to the epicardium, and from the equator to the apex at 35 points. Regional LV wall stress was in all patients lower at the epi- than the endocardium, and lower at the apex than the equator. Regional stress-velocity relations were downward shifted from the endo- to the epicardium and from the equator to the apex (family of curves) in both groups. At corresponding LV regions stress-velocity relations showed significantly smaller slopes and intercepts (downward depression) in group 2 than in group 1. Thus, wall stress distribution is inhomogeneous in the normal, as well as in the pressure and volume overloaded left ventricle. Regional differences in stress-velocity relations within groups (family of curves) are probably related to changes in preload rather than to changes in regional contractility. Downward depression of the regional stress-velocity relations in group 2 is caused by depressed myocardial contractility.

Residual strain in rat left ventricle

Residual stress in an organ is defined as the stress that remains when all external loads are removed. Residual stress has generally been ignored in published papers on left ventricular wall stress. To take residual stress into account in the analysis of stress distributions in a beating heart, one must first measure the residual strain in the no-load state of the heart. Residual strains in equatorial cross-sectional rings (2-3 mm thick) of five potassium-arrested rat left ventricles were measured. The effects of friction and external loading were reduced by submersing the specimen in fluid, and a hypothermic, hyperkalemic arresting solution containing nifedipine and EGTA was used to delay the onset of ischemic contracture. Stainless steel microspheres (60-100 microns) were lightly imbedded on the surface of the slices, and the coordinates of the microspheres were digitized from photographs taken before and after a radial cut was made through the left ventricular free wall. Two-dimensional strains computed from the deformation of a slice after one radial cut were defined as the residual strains in that slice. It was found that the distributions of the principal residual stretch ratios were asymmetric with respect to the radial cut: in areas where substantial transmural strain gradients existed, the distributions of strain components were different on the two sides of the radial cut. A second radial cut produced deformations significantly smaller than those produced from the first radial cut. Hence, a slice with one radial cut may be considered stress free.(ABSTRACT TRUNCATED AT 250 WORDS)

Constitutive relations and finite deformations of passive cardiac tissue II: stress analysis in the left ventricle

We present a new approach for estimation of transmural distributions of stress and strain in the equatorial region of a passive left ventricle. We employ a thick-walled cylindrical geometry, assume that myocardium is incompressible, and use a three-dimensional constitutive relation that yields a material symmetry consistent with observed transmural variations in muscle fiber orientations. Moreover, we consider finite deformations including inflation, extension, twist, and transmural shearing and suggest a new method for determination of the requisite deformation parameters directly from experimental strain data. We show representative transmural distributions of stress and strain, and perform a parametric study to illustrate differing predictions of stress induced by varying boundary conditions, muscle fiber orientations, or modes of deformation. Our analysis can be used to guide and check future predictions of cardiac stresses, and to guide experimentalists by suggesting the accuracy of measurements essential for stress analysis in the heart.

Nonhomogeneous left ventricular regional shortening during acute right ventricular pressure overload

Acute right ventricular pressure overload shifts the interventricular septum leftward and decreases systolic shortening of the left ventricular (LV) septal-lateral diameter. These changes should alter regional shortening in the LV minor axis. To test this hypothesis, LV minor axis circumferential segment lengths of the septum and anterior, lateral, and posterior walls were measured during pulmonary artery or venae caval constriction in seven open-chest dogs with intact pericardia. Starting at an end-diastolic pressure of 10 mm Hg, venae caval constriction decreased LV end-systolic pressure by 19 +/- 6% and stroke volume by 40 +/- 15% and produced uniform decreases in systolic shortening and end-diastolic length around the minor axis. However, during pulmonary artery constriction resulting in similar decreases in end-systolic pressure (22 +/- 7%) and stroke volume (39 +/- 11%), decreases in systolic shortening were significantly larger in the anterior (-34 +/- 10%) and posterior (-33 +/- 21%) walls than in the septum (-10 +/- 9%) or lateral wall (-8 +/- 13%). The mechanisms of these large anterior and posterior shortening decreases differed: anterior end-diastolic length decreased more than posterior and lateral end-diastolic lengths, while posterior end-systolic length decreased less than anterior and lateral end-systolic lengths. Similar changes were seen at starting end-diastolic pressures of 5 and 15 mm Hg. Propranolol did not alter this nonuniform response, while pericardiectomy attenuated the regional variations. Thus, changes in LV geometry during acute right ventricular pressure overload are associated with nonuniform regional changes in systolic shortening in the LV minor axis that are enhanced by the pericardium.

Regional stress in a noncircular cylinder

Several mathematical formulas are presented for estimating regional average circumferential stress and shear stress in a thick-wall, noncircular cylinder with a plane of symmetry. The formulas require images of exterior and interior chamber silhouettes plus surface pressures. The formulas are primarily intended for application to the left ventricle in the short axis plane near the base (where the meridional radius of curvature is normally much larger than the circumferential radius of curvature) and to blood vessels. The formulas predict stresses in a variety of chambers to within 3% of finite element values determined from a large-scale structural analysis computer program called ANSYS.

Functional significance of ventricular dilatation. Reconsideration of Linzbach's concept of chronic heart failure

On the basis of theoretical considerations and experimental data this study deals with the functional consequences of structural dilatation, particularly in view of Linzbach's concept of chronic heart failure (34-38). After a short review of the literature, a theoretical analysis of the relationship between stroke volume and ventricular inner radius is presented assuming a thick-walled sphere. Presupposing constant contractility, end-diastolic sarcomere length, end-diastolic wall thickness and end-systolic pressure, only a considerable increase of ventricular radius could be the direct cause of ventricular pumping failure - despite increasing wall stress and reduced ejection fraction. Impaired contractility, as well as insufficient hypertrophy and increased systemic pressure, would intensify the adverse consequences of ventricular enlargement to a predictable extent. Thus, hemodynamic and energetic consequences of dilation, although mutually interacting, should in principle be distinguished. Despite considerable simplifications involved in model calculations, the relative significance of contractility, ventricular size, wall thickness, and extracardiac factors (mechanical overload; neuroendocrine reactions) can be estimated in various animal models with congestive failure. Hence, this theoretical and experimental approach permits the modification and deepening of previous concepts of structural dilatation and also has implications for interpreting the effects of therapeutical interventions.

Transverse stiffness: a method for estimation of myocardial wall stress

Determination of regional ventricular wall stress would allow quantification of both regional contractile state and its interplay with global function. Current methods for quantifying regional stress include mathematical modelling and measurements with strain gauges. Both methods are difficult to validate. We hypothesized that transverse stiffness (i.e., the ratio of indentation stress to strain as the ventricular wall is indented in the direction perpendicular to the wall) would be proportional to the stresses in the plane of the wall and could be used to estimate the latter. To test this hypothesis, 6 arterially perfused canine ventricular septa were mounted in an apparatus that could exert biaxial load in the plane of the wall. A servo system maintained the central third of the septa isometric during active contractions while the septa were paced at 30-60 pulses/min. In the center of the isometric region, a probe of 7 mm diameter indented the septa while the transverse indentation stress and strain were measured. For values of peak systolic in-plane stress from 0.56 to 2.6 g/mm2, the transverse stiffness varied from 1.2 to 11.7 g/mm2 and was linearly related to the in-plane wall stress in each septum (p less than 0.001, ANOVA). After cardioplegia, the transverse stiffness also correlated with passively applied wall stress for each dog (p less than 0.001). The slopes of the individual relations between transverse stiffness and wall stress from active contractions were similar to those from passively applied stress (mean +/- SEM; 1.82 +/- 0.36 versus 1.45 +/- 0.31, NS).(ABSTRACT TRUNCATED AT 250 WORDS)

Regional comparison of midwall segment and area shortening in the canine left ventricle

We used ultrasonic segment length gauges to examine the regional behavior of midwall fibers at different sites around the left ventricular minor axis in 12 anesthetized dogs. In six dogs (group I) with circumferentially oriented midwall gauges, significantly greater shortening of anterior than lateral or posterior wall segments was demonstrated over a range of left ventricular end-diastolic pressures from 2 to 18 mm Hg. Normalized end-diastolic segment lengths increased more in the anterior wall as end-diastolic pressure increased, suggesting that regional differences in diastolic distensibility may in part account for the observed shortening differences. To examine the extent to which shortening of longitudinally oriented fibers of the subendocardium and subepicardium might influence the behavior of the midwall circumferential fibers, we implanted mutually perpendicular midwall gauges circumferentially and longitudinally in the anterior and posterior walls in six dogs (group II). Longitudinal shortening of midwall fibers was negligible at low end-diastolic pressures, but increased significantly at higher end-diastolic pressures. In the anterior wall, there was greater circumferential than longitudinal shortening, whereas, in the posterior wall, shortening was similar in the two directions. Finally, we calculated the midwall area subtended by the mutually perpendicular gauges and found the systolic change in midwall area to be similar for the anterior and posterior walls at all end-diastolic pressures. We conclude that midwall fibers demonstrate considerable nonuniformity of contraction at different sites around the minor axis. This finding may be related in part to regional differences in diastolic distensibility or in functional interactions between fiber layers. Despite these complex regional, directional, and volume dependent differences in midwall segment function, the systolic changes in midwall area did not vary regionally. Thus, different midwall sites around the minor axis circumference appear to have similar overall contributions to the ejection of blood.

Mechanisms of improving regional and global ventricular function by preload alterations during acute ischemia in the canine left ventricle

We examined the influence of left ventricular end-diastolic pressure (LVEDP) on the mechanical interaction between ischemic and nonischemic areas during acute myocardial ischemia. Circumferentially oriented ultrasonic segment gauges were implanted in the midwall of the anterior apex and posterior apex of the left ventricle in seven anesthetized dogs. Stroke volume was measured with a flow probe around the ascending aorta in five of these animals. We varied LVEDP with vena caval occlusion and dextran infusions to three matched levels (7, 12, and 19 mm Hg) before and 30 min after complete occlusion of the mid left anterior descending coronary artery. With acute ischemia, the anterior apex or ischemic zone demonstrated marked segmental lengthening during isovolumetric systole (end-diastole to aortic valve opening) and akinesis during the ejection phase (aortic valve opening to closure). In the posterior apex or nonischemic area, isovolumetric shortening increased and ejection phase shortening decreased during acute ischemia when compared with those under control conditions at the same LVEDP. Thus, a portion of the shortening generated by the nonischemic area was expended in stretching the ischemic zone during isovolumetric systole, thereby reducing the amount of ejection phase shortening. As LVEDP was increased, there was a parallel decrease in both the amount of isovolumetric lengthening in the ischemic zone and the isovolumetric shortening in the nonischemic area. As a result, acute ischemia produced less of a reduction in ejection phase shortening in the nonischemic area and in stroke volume at high as compared with low LVEDP. We conclude that the ischemic zone imposes a mechanical disadvantage on the nonischemic area, the magnitude of which is directly proportional to the amount of isovolumetric lengthening or bulge in the ischemic zone. An increase in LVEDP during acute ischemia improves regional and global ventricular function by both the Frank-Starling mechanism in the nonischemic (but not the ischemic) area and by reducing the mechanical disadvantage that the ischemic zone imposes on the nonischemic area.

Regional work of the ventricle: wall tension--area relation

We clarified that the set of the isotropic component (T) of wall tension and the area (A) of a selected region of the left ventricular wall expresses the regional work with sufficient accuracy. The area surrounded by the locus of the T-A relation in the T-A plane is approximately equal to the real work done by that region. The behavior of the T-A loop was studied in nine anesthetized dogs under various conditions. The regional area and diameter of the left ventricle were measured with ultrasonic crystal pairs. The wall tension was calculated from measured left ventricular pressure and diameter by a generalized Laplace's equation for a thick-walled model. During volume loading, administration of methoxamine, and aortic constriction, the regional work per stroke increased with the increase in end-diastolic regional area, which is considered to be the regional Frank-Starling mechanism. With the development of ischemia, the T-A loop for the ischemic region shifted to the right and the work done by that region decreased. After a certain stage in the development of ischemia, the work done by the ischemic region became negative. When only one of the segmental lengths, rather than the area, is measured, difficulty arises in the physical interpretation of pressure-length or tension-length data in some cases. The T-A loop diagram resolves such difficulty by defining the regional work correctly. We conclude that the T-A loop diagram is a useful tool for analyzing the regional ventricular function.