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D H van Campen

Publications and source records attributed to D H van Campen.

14 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↗
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↗
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↗
PubMed1992

Experimental and numerical analyses of the steady flow field around an aortic Björk-Shiley standard valve prosthesis.

To develop a numerical method for the description of the flow field around a Björk-Shiley (BS) standard valve prosthesis in aortic position, detailed experimental measurements and numerical calculations are performed under steady flow conditions. The experiment was conducted at Reynolds numbers up to 800. In order to perform LDA measurement of velocity in the vicinity of the valve with a curved sinus boundary, a mixture of oil and kerosine was used as the fluid which exactly matches the refractive index of the perspex aortic model. The velocity profiles at six positions in the vicinity and downstream of the valve were measured, including both axial and radial velocity components. The results show very clearly the existence of two nearly symmetric spiral vortex streams downstream of the valve. There is no recirculation area in the aorta downstream and also no obvious stagnation area in the minor orifice region near the valve when Re less than or equal to 800. Theoretically, the flow field of a BS valve is simulated by the flow pattern around a circular plate with an angle of incidence to the approaching stream. The numerical calculations were carried out by means of a 2-D model using the FEM together with the penalty function method. The maximum Reynolds number is 700. The results agree with the experimental results in the plane of symmetry when the Reynolds number is small. However, as the Reynolds number increases, the difference becomes evident. Our conclusion is that the steady flow field of a BS valve is completely 3-dimensional, featured by two spiral vortices. It cannot be simulated exactly by 2-D numerical calculations. To get more detailed and complete information about the flow field of this valve, 3-D numerical calculations are needed.

Aorta↗
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↗
PubMed1992

Porous medium finite element model of the beating left ventricle.

The axisymmetric model described represents myocardial tissue as a spongy anisotropic viscoelastic material. It includes torsion around the axis of symmetry of the ventricle, transmural variation of fiber angle, and redistribution of intracoronary blood in the myocardial wall. In simulations, end-systolic principal strains were equal to 0.45, -0.01, and -0.24 at two-thirds of the wall thickness from the epicardium and 0.26, 0.00, and -0.19 at one-third of the wall thickness from the epicardium. The direction of maximal shortening varied by less than 30 degrees from epicardium to endocardium, whereas fiber direction varied by greater than 100 degrees from epicardium to endocardium. During a normal cardiac cycle peak, equatorial intramyocardial pressure differed by less than 5% from peak intraventricular pressure. When redistribution of intracoronary blood in the ventricular wall was suppressed, peak equatorial intramyocardial pressure was found to exceed peak intraventricular pressure by greater than 30%. Simulated contraction of an unloaded left ventricle (left ventricular pressure = 0 kPa) produced similar magnitude for systolic intramyocardial pressures as the normal cardiac cycle. Transmural systolic fiber stress distribution was very sensitive to the chosen transmural fiber angle distribution.

Animals↗
PubMed1991

A two-phase finite element model of the diastolic left ventricle.

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.

Animals↗
PubMed1991

The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation.

A quasi-linear viscoelastic law with a continuous relaxation spectrum describing triaxial constitutive behaviour of heart muscle tissue is presented. The elastic response of the viscoelastic law is anisotropic, while the relaxation behaviour is assumed isotropic. The law is designed for a biphasic description (fluid-solid) of the myocardial tissue. Biaxial and uniaxial stress-strain curves from the literature are used to evaluate the parameters of the model. The non-linear elastic response, the difference between fibre and cross-fibre stiffness, the phenomenon of stress relaxation, the stiffening of the stress-strain relationship with increasing strain rate and the weak frequency dependency of the dissipated energy during cyclic loading are fairly well described by the proposed law. However, it is found that the model produces realistic values for the dissipated energy during cyclic loading only when relaxation parameter values are chosen which result in an overestimation of the stress relaxation data by more than 100%. This finding may indicate non-quasi-linearity of viscoelasticity of passive heart muscle tissue.

Biomechanical Phenomena↗
PubMed1989

Low Reynolds number steady state flow through a branching network of rigid vessels II. A finite element mixture model.

This research aims at formulating and verifying a finite element mixture formulation for blood perfusion. The equations derived in a companion paper [3] are discretized according to the Galerkin method. A flow experiment in a rigid model of a vascular tree of about 500 vessels is performed in order to verify the finite element mixture formulation. Although the comparison of numerical results and experimental measurements is not conclusive as far as the validity of the theory is concerned, the results do suggest that the finite element model has predictive power in the case of low Reynolds number steady-state flow of a Newtonian fluid in a rigid vascular tree.

Animals↗
PubMed1987

A mixture approach to the mechanics of skin.

Skin can be considered to be a mixture of a solid and a fluid. A general theory for the description of the behaviour of mixtures is presented and applied to a mixture of a solid and a fluid. A numerical procedure is presented to solve the non-linear field equations describing such a mixture. The abilities of the procedure are demonstrated by means of a confined compression test.

Biomechanical Phenomena↗
PubMed1987

In vitro compression of a soft tissue layer on a rigid foundation.

In vitro compression studies have been performed on layers of porcine skin and fat. The tissue layers have been loaded by means of various indentors. Indentor displacements and interstitial fluid pressures have been measured. The results have been compared to finite element calculations with mixture elements. A qualitative agreement between calculations and measurements is found. The results support the hypothesis that skin and fat behave like solid/fluid mixtures.

Adipose Tissue↗
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↗