Pulsatility Index in the Basal Ganglia Arteries Increases with Age in Elderly with and without Cerebral Small Vessel Disease.

BACKGROUND AND PURPOSE: Cerebral small vessel disease contributes to stroke and cognitive impairment and interacts with Alzheimer disease pathology. Because of the small dimensions of the affected vessels, in vivo characterization of blood flow properties is challenging but important to unravel the underlying mechanisms of the disease. MATERIALS AND METHODS: A 2D phase-contrast sequence at 7T MR imaging was used to assess blood flow velocity and the pulsatility index of the perforating basal ganglia arteries. We included patients with cerebral amyloid angiopathy (n = 8; identified through the modified Boston criteria), hypertensive arteriopathy (n = 12; identified through the presence of strictly deep or mixed cerebral microbleeds), and age- and sex-matched controls (n = 28; no cerebral microbleeds). RESULTS: Older age was related to a greater pulsatility index, irrespective of cerebral small vessel disease. In hypertensive arteriopathy, there was an association between lower blood flow velocity of the basal ganglia and the presence of peri-basal ganglia WM hyperintensities. CONCLUSIONS: Our results suggest that age might be the driving factor for altered cerebral small vessel hemodynamics. Furthermore, this study puts cerebral small vessel disease downstream pathologies in the basal ganglia region in relation to blood flow characteristics of the basal ganglia microvasculature.

Cardiac resynchronization: insight from experimental and computational models.

Cardiac resynchronization therapy (CRT) is a promising therapy for heart failure patients with a conduction disturbance, such as left bundle branch block. The aim of CRT is to resynchronize contraction between and within ventricles. However, about 30% of patients do not respond to this therapy. Therefore, a better understanding is needed for the relation between electrical and mechanical activation. In this paper, we focus on to what extent animal experiments and mathematical models can help in order to understand the pathophysiology of asynchrony to further improve CRT.

Towards model-based analysis of cardiac MR tagging data: relation between left ventricular shear strain and myofiber orientation.

Many cardiac pathologies are reflected in abnormal myocardial deformation, accessible through magnetic resonance tagging (MRT). Interpretation of the MRT data is difficult, since the relation between pathology and deformation is not straightforward. Mathematical models of cardiac mechanics could be used to translate measured abnormalities into the underlying pathology, but, so far, they even fail to correctly simulate myocardial deformation in the healthy heart. In this study we investigated to what extent (1) our previously published three-dimensional finite element model of cardiac mechanics [Kerckhoffs, R.C.P., Bovendeerd, P.H.M., Kotte, J.C.S., Prinzen, F.W., Smits, K., Arts, T., 2003. Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study. Ann. Biomed. Eng. 31, 536-547] can simulate measured cardiac deformation, and (2) discrepancies between strains in model and experiment are related to the choice of the myofiber orientation in the model. To this end, we measured midwall circumferential strain E(cc) and circumferential-radial shear strain E(cr) in three healthy subjects using MRT. E(cc) as computed in the model agreed well with measured E(cc). Computed E(cr) differed significantly from measured E(cr). The time course of E(cr) was found to be very sensitive to the choice of the myofiber orientation, in particular to the choice of the transverse angle. Discrepancies between circumferential-radial shear strain in model and experiment were reduced strongly by increasing the transverse angle in the original model by 25%.

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.

Torsion of the left ventricle during the ejection phase in the intact dog.

Torsion of the left ventricle (LV) is associated with rotation of the apex with respect to the base around the long axis of the LV. A mathematical model of LV mechanics, which relates torsion to transmural distribution of fibre shortening, was evaluated with two-dimensional echocardiography in nine anaesthetised closed-chest dogs. Torsion was calculated as the difference between the angles of rotation (radians) of echo-derived transverse cross-section projections of the LV obtained at the mitral valve and low papillary level, divided by the axial distance between these projections measured in a long-axis cross-section, and multiplied by the outer radius in a mid-papillary transverse projection of the LV. A shortening to torsion ratio (STR) was defined as the ratio of inner wall shortening to torsion occurring during ejection. In a series of 11 measurements, each based on frame-to-frame analysis of 15 cardiac cycles, STR was found to be 2.31 +/- 0.23 rad-1 (mean +/- SD), whereas the mathematical model predicted a STR value of 2.4 rad-1 over a wide range of preload, afterload and contractility levels. We conclude that two-dimensional echocardiography validates the presence of torsion in the normal canine left ventricle, as predicted by the model of left ventricular mechanics.

Remodeling by ventricular pacing in hypertrophying dog hearts.

OBJECTIVE: Asynchronous electrical activation of the left ventricle (LV), induced by ventricular pacing (VP), reduces mechanical load in early- and enhances it in late-activated regions. Consequently, chronic VP leads to asymmetric hypertrophy. We investigated whether such locally induced myocardial hypertrophy also occurs in the presence of pressure overload hypertrophy (POH). METHODS: POH was induced by aortic banding in puppies. At age 9 months, seven dogs were paced at the right ventricular (RV) apex at physiological heart rate for 6 months (POH-pace group), while four POH dogs served as POH-control group. Changes in volume of the LV cavity and the total LV wall and of five LV wall sectors were measured by means of 2D-echocardiography and X-ray marker detection. RESULTS: During the last 6 months of the protocol the volume of the five LV wall sectors increased in the POH-control group, ranging from 27+/-9 to 30+/-5% (mean+/-S.D.). In POH-pace animals sector wall volume in the four sectors at intermediate to long distance from the pacing site increased to a similar extent (ranging from 31+/-16 to 35+/-17%), but wall volume in the early-activated apical septum increased significantly less (17+/-21%). In these hearts myocyte diameter was significantly smaller in the apical septum than in the lateral LV wall. The regional difference in wall volume changes (19+/-21%) was significantly smaller in the POH-pace group than in chronically paced, non-hypertrophic, canine hearts in a previous study from our laboratory (43+/-14%). CONCLUSIONS: In hypertrophying hearts chronic pacing at the RV apex suppresses the development of hypertrophy in the early-activated apical septum but does not cause additional hypertrophy in late-activated regions, as is the case in non-hypertrophic hearts. The latter suggests that the local growth response is reduced in hypertrophying hearts.

Endoscopic intrauterine fetal therapy: a monkey model.

OBJECTIVES: Prenatal ultrasonographic investigations have led to an increasing number of prenatally detected abnormalities, of which a large number involves the urogenital tract. This study was performed to evaluate if endoscopic intra-amniotic access is possible in primates. METHODS: In 10 midtrimester rhesus monkeys (Macaca mulatta), endoscopic intrauterine fetoscopy was performed with three access cannulas. Using a Seldinger technique, a vascular access system, and a pediatric laparoscopy set, intra-amniotic inspection was attempted. Fetal growth throughout pregnancy was monitored by ultrasonographic measurements of fetal biometry. RESULTS: Intrauterine access could successfully be achieved in 10 rhesus monkeys with three cannulas. After partial amniotic fluid exchange, adequate fetoscopy was always possible. Two monkeys aborted on the second and sixth postoperative days. Serial ultrasonographic investigations for fetal biometry showed no disturbance of the intrauterine growth patterns in the remaining 8 monkeys. CONCLUSIONS: We currently conclude that the rhesus monkey model for experimental intrauterine endoscopic surgery may be suitable for study of the developmental abnormalities of the genitourinary tract.

Maximum likelihood estimation in calibrating a stereo camera setup.

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x-ray cameras simultaneously. Regularly, calibration of the position measurement system is obtained by registration of the images of a calibration object, containing 10-20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measured image positions of stereo pairs can be used for calibration. Thus, a separate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensionless parameters. Maximum Likelihood (ML) estimates of these parameters were obtained in an error analysis. It is shown that the ML estimates can be found by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in more accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction problem appeared well conditioned as long as the object aperture is larger than 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstruction of the 3-D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error in this parameter.

Dynamics of left ventricular wall and mitral valve mechanics--a model study.

The relation between global left ventricular pumping characteristics and local cardiac muscle fiber mechanics is represented by a mathematical model of left ventricular mechanics in which the mitral valve papillary muscle system is incorporated. The wall of the left ventricle is simulated by a thick-walled cylinder. Transmural differences in fiber orientation are incorporated by changing the direction of material anisotropy across the wall. The cylinder is free to twist. The upper end of the cylinder is covered by a thin, flexible sheet, representing the base of the left ventricle. The mitral valve is incorporated in this sheet. The tips of the mitral leaflets are connected by chordae tendineae to the papillary muscles which are attached to the bottom of the cylinder. Canine cardiac cycles were simulated for various end-diastolic values of left ventricular volume (25-120 ml, control 60 ml), left atrial pressure (0-2.7 kPa, control 0.22 kPa) and aortic pressure (5-11 kPa, control 11 kPa). In this wide range of preload and afterload mechanical loading of the muscle fibers appeared to be distributed quite evenly (SD: +/- 5% of control value) over all muscular structures of the left ventricle, including the papillary muscles.

Stresses in the closed mitral valve: a model study.

In the present model study on the closed mitral valve, tensile force in the chordae tendineae is related to transvalvular pressure using a mathematical model of mechanics of the closed mitral valve. Circumferential stress as well as bending stress in the valve leaflets were neglected. Without precisely knowing the mechanical properties of the leaflet material, geometry of the leaflets was estimated by applying Laplace's law, which relates leaflet stress to leaflet curvature. Independent of shape of the mitral valve orifice, under all circumstances tensile force in the chordae tendineae was calculated to be equal or greater than half the force exerted on the mitral valve orifice by the transvalvular pressure.

Modeling the relation between cardiac pump function and myofiber mechanics.

Complexity of the geometry and structure of the heart hampers easy modeling of cardiac mechanics. The modeling can however be simplified considerably when using the hypothesis that in the normal heart myofiber structure and geometry adapt, until load is evenly distributed. A simple and realistic relationship is found between the hemodynamic variables cavity pressure and volume, and myofiber load parameters stress and strain. The most important geometric parameter in the latter relation is the ratio of cavity volume to wall volume, while actual geometry appears practically irrelevant. Applying the found relationship, a realistic maximum is set to left ventricular pressure after chronic pressure load. Pressures exceeding this level are likely to cause decompensation and heart failure. Furthermore, model is presented to simulate left and right ventricular pump function with left-right interaction.

Mapping of epicardial deformation using a video processing technique.

A method has been developed to measure deformation of the canine epicardium during the cardiac cycle simultaneously in a number (eight) of small regions (1 X 1 cm2). Approximately 50 white markers (diameter 1.5 mm) are attached to the epicardium and their motion is recorded on tape by a video camera. Marker positions are detected by computer processing of the digitized images. In each region the three deformation parameters are calculated from the displacements of all markers in that region by means of a least-squares criterium. In the experimental situation in the center of the area of the epicardium analyzed the accuracy of measuring circumferential strain, base-to-apex strain and shear is +/- 0.005, +/- 0.005 and +/- 0.002 rad, respectively. The method has been applied in an experiment in which local ischemia of the left ventricular wall was induced by occluding the anterior descending branch of the left coronary artery. Healthy and ischemic regions could clearly be distinguished by the differences in deformation.

Fiber shortening in the inner layers of the left ventricular wall as assessed from epicardial deformation during normoxia and ischemia.

A mathematical model of left ventricular mechanics predicts that fiber shortening in the inner layers of the left ventricular wall can be estimated (eendo, est) from the magnitude of minimal (emin, o) and maximal shortening (emax, o) of the outer surface (= epicardium) of this wall. To evaluate this prediction, eendo, est and emin, o were compared with the shortening in the inner layers approximately along the fiber direction (eendo) as measured directly, before and during one minute of coronary artery occlusion. Deformation of the epicardium and the inner layers was determined by measuring mutual motion and angulation of three needles pierced into the myocardial wall, using an electromagnetic inductive technique. The proposed linear relations of eendo, est and emin, o with eendo were found to be significant. The needles hardly influenced wall deformation since similar values of epicardial deformation were found in separate, comparable, experiments (n = 13) using a triplet of epicardial coils. So eendo, est and emin, o are useful estimates of fiber shortening in the inner layers during normoxia and ischemia, especially when the time course of events is followed in the same animal.

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.

Description of the deformation of the left ventricle by a kinematic model.

A model of left ventricular (LV) kinematics is essential to identify the fundamental physiological modes of LV deformation during a complete cardiac cycle as observed from the motion of a finite number of markers embedded in the LV wall. Kinematics can be described by a number of modes of motion and deformation in succession. An obvious mode of LV deformation is the ejection of cavity volume while the wall thickens. In the more sophisticated model of LV kinematics developed here, seven time-dependent parameters were used to describe not only volume change but also torsion and shape changes throughout the cardiac cycle. Rigid-body motion required another six parameters. The kinematic model employed a deformation field that had no singularities within the myocardium, and all parameters describing the modes of deformation were dimensionless. Note that torsion, volume and symmetric shape changes all require the definition of a cardiac coordinate system, which has generally been related to the measured cardiac geometry by reference to approximate anatomical landmarks. However, in the present study the coordinate system was positioned objectively by a least-squares fit of the kinematic model to the measured motion of markers. Theoretically, at least five markers are needed to find a unique set of parameters.(ABSTRACT TRUNCATED AT 250 WORDS)

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.

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.

Tracking markers with missing data by lower rank approximation.

Motion and deformation of an object may be quantified by following attached markers in video or cine frame sequences. When recording cardiac motion by video (256 x 256 pixels, 50 Hz), generally no more than approximately 20 markers can be followed due to difficulties in proper identification of marker images. In the present study we developed the lower rank (LR) tracking method which can automatically follow considerably more than 20 markers. The performance of the method was evaluated in computer simulations of naturally moving myocardial markers observed in a sequence of 60 video frames. White noise was added to the marker coordinates. Realistic loss of data due to detection failure was simulated by deleting a generated marker image when the distance to another marker image was below a given minimum value. In a test, realistic values were substituted for the noise level sigma (0.5 pixel) and the minimum marker distance dm (4 pixels). For numbers of markers ranging from 50 to 100, 95-90% of the detected marker images was correctly tracked. Less than 0.7% was part of a false track, i.e. a track containing images of different markers. Under less favourable conditions (sigma = 1 pixel; dm = 8 pixels) the method was robust: for 75 markers with 40% of the marker images missing, still 70% of the detected images was correctly tracked, while the fraction in false tracks did not increase. The LR tracking method appears reliable for automatic tracking of large amounts of moving markers in a sequence of video or cine frames.

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.

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.