Biomedical subjects

P H Bovendeerd

Publications and source records attributed to P H Bovendeerd.

11 recordsLinked to original sources

PubMed2000

Cardiac mechanoenergetics replicated by cross-bridge model.

The aim of this work is to reproduce the experimentally measured linear dependence of cardiac muscle oxygen consumption on stress-strain area using a model, composed of a three-state Huxley-type model for cross-bridge interaction and a phenomenological model of Ca2+-induced activation. By selecting particular cross-bridge cycling rate constants and modifying the cross-bridge activation model, we replicated the linear dependence between oxygen consumption and stress-strain area together with other important mechanical properties of cardiac muscle such as developed stress dependence on the sarcomere length and force-velocity relationship. The model predicts that (1) the amount of the "passenger" cross bridges, i.e., cross bridges that detach without hydrolyzing ATP molecule, is relatively small and (2) ATP consumption rate profile within a beat and the amount of the passenger cross bridges depend on the contraction protocol.

Actomyosin↗

PubMed1999

Diffusion tensor imaging in biomechanical studies of skeletal muscle function.

In numerical simulations of skeletal muscle contractions, geometric information is of major importance. The aim of the present study was to determine whether the diffusion tensor imaging (DTI) technique is suitable to obtain valid input with regard to skeletal muscle fibre direction. The accuracy of the DTI method was therefore studied by comparison of DTI fibre directions in the rat tibialis anterior muscle with fascicle striation patterns visible on high-resolution magnetic resonance imaging (MRI) and with fibre directions in an actual longitudinal section (ALS) through the same muscle. The results showed an excellent qualitative agreement between high-resolution MRI and DTI. Despite less accurate quantitative comparison with ALS, it was concluded that DTI does indeed measure skeletal muscle fibre direction. After the experiment, it was possible to determine an appropriate voxel size (0.9 mm3) that provided enough resolution and acceptable accuracy (5 degrees) to use DTI fibre directions in biomechanical analyses. Muscle deformation during contraction, resulting from a finite element simulation with a mesh that was directly generated from the experimental data, has been presented.

Animals↗

PubMed1997

Optimization of cardiac fiber orientation for homogeneous fiber strain at beginning of ejection.

Mathematical models of left ventricular (LV) wall mechanics show that fiber stress depends heavily on the choice of muscle fiber orientation in the wall. This finding brought us to the hypothesis that fiber orientation may be such that mechanical load in the wall is homogeneous. Aim of this study was to use the hypothesis to compute a distribution of fiber orientation within the wall. In a finite element model of LV wall mechanics, fiber stresses and strains were calculated at beginning of ejection (BE). Local fiber orientation was quantified by helix (HA) and transverse (TA) fiber angles using a coordinate system with local r-, c-, and l-directions perpendicular to the wall, along the circumference and along the meridian, respectively. The angle between the c-direction and the projection of the fiber direction on the cl-plane (HA) varied linearly with transmural position in the wall. The angle between the c-direction and the projection of the fiber direction on the cr-plane (TA) was zero at the epicardial and endocardial surfaces. Midwall TA increased with distance from the equator. Fiber orientation was optimized so that fiber strains at BE were as homogeneous as possible. By optimization with TA = 0 degree, HA was found to vary from 81.0 degrees at the endocardium to -35.8 degrees at the epicardium. Inclusion of TA in the optimization changed these angles to respectively 90.1 degrees and -48.2 degrees while maximum TA was 15.3 degrees. Then the standard deviation of fiber strain (epsilon f) at BE decreased from +/- 12.5% of mean epsilon f to +/- 9.5%. The root mean square (RMS) difference between computed HA and experimental data reported in literature was 15.0 degrees compared to an RMS difference of 11.6 degrees for a linear regression line through the latter data.

Heart↗

PubMed1997

Effect of ventricular contraction, pressure, and wall stretch on vessels at different locations in the wall.

A cylindrical model of the heart was used to calculate the influence of ventricular filling and (isovolumic and isobaric) contraction on the cross-sectional area and resistance of a subendocardial and subepicardial maximally dilated arteriole and venule. Contraction is defined as the difference between static diastole and static systole. Furthermore, a small piece of rectangular myocardium containing the vessel was modeled to distinguish between the individual contributions of contractility (i.e., myocardial elastic properties), ventricular pressure, and local circumferential stretch to the changes in vascular area and resistance during contraction. Calculations were performed assuming the muscle fibers ran in either an apex-to-base or a circumferential direction. The results were similar for the two directions. Assuming constant, physiological arteriolar and venular pressures of 45 and 10 mmHg, respectively, coronary blood vessels were predicted not to collapse during ventricular contraction. Moreover, vascular area reduction was found to be larger for the arteriole (approximately 50%) than for the venule (approximately 30%) during both isovolumic and isobaric contractions. Consequently, arteriolar resistance was found to increase more than venular resistance (approximately 340 and 120%, respectively). Subendocardial area reductions were found to be somewhat smaller than subepicardial area reductions for the venule (by approximately 10%) but not for the arteriole. Contractility was found to be the main contributor to the changes in vascular area and resistance in the subepicardium but to contribute by < 50% to the changes in the subendocardium. Because pressure does, but stretch does not, contribute to the area change during isovolumic contraction and the reverse is true during isobaric contraction, it was concluded that although changes in vascular area and resistance may be similar for different contractions, the causes for these changes are very different.

Arterioles↗

PubMed1996

Determination of muscle fibre orientation using Diffusion-Weighted MRI.

Biomechanical studies have shown that the distribution of stress and strain in biological tissue is strongly dependent on fibre orientation. Therefore, to analyze the local mechanical load, accurate data on muscle fibre orientation are needed. Traditional techniques to determine fibre orientation are inherently invasive. Here we used Diffusion Weighted MRI to non-invasively determine, in each image voxel of 0.23 x 0.23 mm, the diffusion tensor of water in the cat semimembranosus muscle. The direction corresponding to the largest eigenvector of this tensor was calculated. This direction was found to correspond qualitatively to the muscular fibre direction, as determined by visual inspection.

Animals↗

PubMed1996

Regional wall mechanics in the ischemic left ventricle: numerical modeling and dog experiments.

The mechanics of the ischemic left ventricle during a complete cardiac cycle were simulated using a finite-element model accounting for the thick-walled ventricular geometry, the fibrous nature of the myocardial tissue, and the dependency of active muscle fiber stress on time, strain, and strain rate. Ischemia was modeled by disabling the generation of active stress in a region comprising approximately 12% of total wall volume. In the model simulations, the approximately 12% reduction in the amount of normally contracting tissue resulted in an approximately 25% reduction in stroke work compared with the normal situation. The more-than-proportional loss of stroke work may partly be attributed to storage of elastic energy in the bulging ischemic region. Furthermore the mechanical performance in the nonischemic border zone deteriorated because of reduced systolic fiber stress (if fibers were in series with those in the ischemic region) or reduced fiber shortening (if fibers were parallel). The deformation pattern of the ventricle was asymmetric with respect to the ischemic region because of the anisotropy of the myocardial tissue. Epicardial fiber shortening in and around the ischemic region, as predicted from the model simulations, was in qualitative agreement with shortening, as measured in four dogs in which ischemia was induced by occlusion of the distal part of the left anterior interventricular coronary artery.

Animals↗

PubMed1994

Influence of endocardial-epicardial crossover of muscle fibers on left ventricular wall mechanics.

The influence of variations of fiber direction on the distribution of stress and strain in the left ventricular wall was investigated using a finite element model to simulate the mechanics of the left ventricle. The commonly modelled helix fiber angle was defined as the angle between the local circumferential direction and the projection of the fiber path on the plane perpendicular to the local radial direction. In the present study, an additional angle, the transverse fiber angle, was used to model the continuous course of the muscle fibers between the inner and the outer layers of the ventricular wall. This angle was defined as the angle between the circumferential direction and the projection of the fiber path on the plane perpendicular to the local longitudinal direction. First, a reference simulation of left ventricular mechanics during a cardiac cycle was performed, in which the transverse angle was set to zero. Next, we performed two simulations in which the spatial distribution of either the transverse or the helix angle was varied with respect to the reference situation, the spatially averaged variations being about 3 and 14 degrees, respectively. The changes in fiber orientation hardly affected the pressure-volume relation of the ventricle, but significantly affected the spatial distribution of active muscle fiber stress (up to 50% change) and sarcomere length (up to 0.1 micron change). In the basal and apical region of the wall, shear deformation in the circumferential-radial plane was significantly reduced by introduction of a nonzero transverse angle. Thus, the loading of the passive tissue may be reduced by the endocardial-epicardial crossover of the muscle fibers.

Aorta↗

PubMed1993

Subepicardial fiber strain and stress as related to left ventricular pressure and volume.

In a mathematical model of the mechanics of the left ventricle (LV) by Arts et al. (1), assuming uniformity of fiber stress (sigma f) and fiber strain (delta epsilon f) in the wall during the ejection phase, fiber stress and fiber strain were related to LV cavity pressure (Plv), LV cavity volume (Vlv) and wall volume (Vw) by the following pair of equations: sigma f = Plv (1 + 3 Vlv/Vw) and delta epsilon f = 1/3 delta ln (1 + 3 Vlv/Vw). The ratio of Vlv to Vw appeared to be the most important geometric parameter, whereas the actual LV shape was of minor importance. The relationships on fiber strain and stress were evaluated experimentally in six anesthetized open-chest dogs during normal and elevated (volume loading) end-diastolic LV pressure. Subepicardial fiber strain was measured simultaneously in 16 adjacent regions of the LV anterior wall, using optical markers that were attached to the epicardial surface and recorded on video. Changes in Vlv were measured by use of four inductive coils sutured to the LV in a tetrahedric configuration. Vw was measured postmortem. During control as well as hypervolemia the following results were found. At the anterior free wall of the LV, the slope of the estimated linear relationship between measured and calculated fiber strain was 1.017 +/- 0.168 (means +/- SD), which is not significantly different from unity. Calculated fiber stress corresponded qualitatively and quantitatively with experimental results reported on isolated cardiac muscle. Calculated subepicardial contractile work per unit of tissue volume was not significantly different from global pump work as normalized to Vw. These findings support the assumption of homogeneity of muscle fiber strain and stress in the left ventricular wall during the ejection phase. Furthermore, average values of fiber stress and strain can be estimated on the basis of measured left ventricular pressure and volume.

Animals↗

PubMed1992

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.

Computer Simulation↗

PubMed1991

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).

Animals↗

PubMedDate not supplied

Optimization of cardiac fiber orientation for homogeneous fiber strain during ejection.

The strain of muscle fibers in the heart is likely to be distributed uniformly over the cardiac walls during the ejection period of the cardiac cycle. Mathematical models of left ventricular (LV) wall mechanics have shown that the distribution of fiber strain during ejection is sensitive to the orientation of muscle fibers in the wall. In the present study, we tested the hypothesis that fiber orientation in the LV wall is such that fiber strain during ejection is as homogeneous as possible. A finite-element model of LV wall mechanics was set up to compute the distribution of fiber strain at the beginning (BE) and end (EE) of the ejection period of the cardiac cycle, with respect to a middiastolic reference state. The distribution of fiber orientation over the LV wall, quantified by three parameters, was systematically varied to minimize regional differences in fiber shortening during ejection and in the average of fiber strain at BE and EE. A well-defined optimum in the distribution of fiber orientation was found which was not significantly different from anatomical measurements. After optimization, the average of fiber strain at BE and EE was 0.025 +/-0.011 (mean+/-standard deviation) and the difference in fiber strain during ejection was 0.214+/-0.018. The results indicate that the LV structure is designed for maximum homogeneity of fiber strain during ejection.

Animals↗