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.

Mapping displacement and deformation of the heart with local sine-wave modeling.

The new SinMod method extracts motion from magnetic resonance imaging (MRI)-tagged (MRIT) image sequences. Image intensity in the environment of each pixel is modeled as a moving sine wavefront. Displacement is estimated at subpixel accuracy. Performance is compared with the harmonic-phase analysis (HARP) method, which is currently the most common method used to detect motion in MRIT images. SinMod can handle line tags, as well as speckle patterns. In artificial images (tag distance six pixels), SinMod detects displacements accurately (error < 0.02 pixels). Effects of noise are suppressed effectively. Sharp transitions in motion at the boundary of an object are smeared out over a width of 0.6 tag distance. For MRIT images of the heart, SinMod appears less sensitive to artifacts, especially later in the cardiac cycle when image quality deteriorates. For each pixel, the quality of the sine-wave model in describing local image intensity is quantified objectively. If local quality is low, artifacts are avoided by averaging motion over a larger environment. Summarizing, SinMod is just as fast as HARP, but it performs better with respect to accuracy of displacement detection, noise reduction, and avoidance of artifacts.

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%.

Computer simulations of successful defibrillation in decoupled and non-uniform cardiac tissue.

AIM: The aim of the present study is to investigate the origin and effect of virtual electrode polarization in uniform, decoupled and non-uniform cardiac tissue during field stimulation. METHODS: A discrete bidomain model with active membrane behaviour was used to simulate normal cardiac tissue as well as cardiac tissue that is decoupled due to fibrosis and gap junction remodelling. Various uniform and non-uniform electric fields were applied to the external domain of uniform, decoupled and non-uniform resting cardiac tissue as well as cardiac tissue in which spiral waves were induced. RESULTS: Field stimulation applied on non-uniform tissue results in more virtual electrodes compared with uniform tissue. The spiral waves were terminated in decoupled tissue, but not in uniform, homogeneous tissue. By gradually increasing local differences in intracellular conductivities, the amount and spread of virtual electrodes increased and the spiral waves were terminated. CONCLUSION: Fast depolarization of the tissue after field stimulation may be explained by intracellular decoupling and spatial heterogeneity present in normal and pathological cardiac tissue. We demonstrated that termination of spiral waves by means of field stimulation can be achieved when the tissue is modelled as a non-uniform, anisotropic bidomain with active membrane behaviour.

Electromechanics of paced left ventricle simulated by straightforward mathematical model: comparison with experiments.

Intraventricular synchrony of cardiac activation is important for efficient pump function. Ventricular pacing restores the beating frequency but induces more asynchronous depolarization and more inhomogeneous contraction than in the normal heart. We investigated whether the increased inhomogeneity in the left ventricle can be described by a relatively simple mathematical model of cardiac electromechanics, containing normal mechanical and impulse conduction properties. Simulations of a normal heartbeat and of pacing at the right ventricular apex (RVA) were performed. All properties in the two simulations were equal, except for the depolarization sequence. Simulation results of RVA pacing on local depolarization time and systolic midwall circumferential strain were compared with those measured in dogs, using an epicardial sock electrode and MRI tagging, respectively. We used the same methods for data processing for simulation and experiment. Model and experiment agreed in the following aspects. 1) Ventricular pacing decreased systolic pressure and ejection fraction relative to natural sinus rhythm. 2) Shortening during ejection and stroke work declined in early depolarized regions and increased in late depolarized regions. 3) The relation between epicardial depolarization time and systolic midwall circumferential strain was linear and similar for the simulation (slope = -3.80 +/- 0.28 s(-1), R2 = 0.87) and the experiments [slopes for 3 animals -2.62 +/- 0.43 s(-1) (R2 = 0.59), -2.97 +/- 0.38 s(-1) (R2 = 0.69), and -4.44 +/- 0.51 s(-1) (R2 = 0.76)]. We conclude that our model of electromechanics is suitable to simulate ventricular pacing and that the apparently complex events observed during pacing are caused by well-known basic physiological processes.

End-diastolic myofiber stress and ejection strain increase with ventricular volume overload--Serial in-vivo analyses in dogs with complete atrioventricular block.

BACKGROUND: Myocardial stress and strain are considered primary mechanical stimuli for hypertrophic remodeling. Their values and significance in the intact beating heart during chronic overload remain poorly characterized. METHODS AND RESULTS: Left-ventricular (LV) dimensions (echocardiography) and pressure (invasive) were simultaneously recorded in anesthetized dogs at sinus rhythm (SR), acute and 1, 2, 6, 12 weeks of atrioventricular block (AVB), leading to structural, electrical and contractile remodeling. Mechanical load of the myocardium was quantified as myofiber stress (sigma(f)), being force along myofiber orientation per cross-sectional area, and natural myofiber strain (e(f)), being change in natural logarithm of myofiber length (l) divided by its reference length: e(f) = ln(l/l(ref)). Time courses of sigma(f) and e(f) were calculated from LV pressure and dimensions, using a validated mathematical model of cardiac mechanics. End-diastolic sigmaf increased from 2.0 +/- 0.1 kPa at SR to 3.4 +/- 0.3 kPa at acute AVB, remaining elevated for > 6 weeks. Systolic sigma(f) was not affected by AVB. Ejection strain rose instantly upon AVB, reaching a maximum at 2 weeks: 0.24 +/- 0.02 vs. 0.10 +/- 0.01 at SR. The increase of myofiber stroke work (sigma(f)-e(f) loop area) from 3.1 +/- 0.3 at SR to 6.0 +/- 0.5 kJ/m(3)/beat at 1 week AVB was attributed mainly to an increase of strain during ejection. Stroke work and ejection strain remained elevated up to 12 weeks. The rate of LV-mass increase was maximal (2.2 +/- 0.4 g/day) at 1 week AVB. CONCLUSIONS: Serial mechanical phenotyping is feasible in the intact anesthetized dog with chronic ventricular overload. Our new approach yields values of mechanical load that are comparable to those found in isolated myocardium by others. In chronic AVB, both end-diastolic myofiber stress and ejection strain are increased. Early increases of both parameters coincide with peak hypertrophic growth, suggesting their important role for mechanotransduction. Peak systolic sigmaf is likely not important for hypertrophy in this model, since it does not change throughout the experiment.

Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study.

The use of mathematical models combining wave propagation and wall mechanics may provide new insights in the interpretation of cardiac deformation toward various forms of cardiac pathology. In the present study we investigated whether combining accepted mechanisms on propagation of the depolarization wave, time variant mechanical properties of cardiac tissue after depolarization, and hemodynamic load of the left ventricle (LV) by the aortic impedance in a three-dimensional finite element model results in a physiological pattern of cardiac contraction. We assumed that the delay between depolarization for all myocytes and the onset of crossbridge formation was constant. Two simulations were performed, one in which contraction was initiated according to the regular depolarization pattern (NORM simulation), and another in which contraction was initiated after synchronous depolarization (SYNC simulation). In the NORM simulation propagation of depolarization was physiological, but wall strain was unphysiologically inhomogeneous. When simulating LV mechanics with unphysiological synchronous depolarization (SYNC) myofiber strain was more homogeneous and more physiologic. Apparently, the assumption of a constant delay between depolarization and onset of crossbridge formation results in an unrealistic contraction pattern. The present finding may indicate that electromechanical delay times are heterogeneously distributed, such that a contraction in a normal heart is more synchronous than depolarization.

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.

Transmural gradients of cardiac myofiber shortening in aortic valve stenosis patients using MRI tagging.

Aortic valve stenosis impairs subendocardial perfusion with a risk of irreversible subendocardial tissue damage. A likely precursor of damage is subendocardial contractile dysfunction, expressed by the parameter TransDif, which is defined as epicardial minus endocardial myofiber shortening, normalized to the mean value. With the use of magnetic resonance tagging in two short-axis slices of the left ventricle (LV), TransDif was derived from LV torsion and contraction during ejection. TransDif was determined in healthy volunteers (control, n = 9) and in patients with aortic valve stenosis before (AVSten, n = 9) and 3 mo after valve replacement (AVRepl, n = 7). In the control group, TransDif was 0.00 +/- 0.14 (mean +/- SD). In the AVSten group, TransDif increased to 0.96 +/- 0.62, suggesting impairment of subendocardial myofiber shortening. In the AVRepl group, TransDif decreased to 0.37 +/- 0.20 but was still elevated. In eight of nine AVSten patients, the TransDif value was elevated individually (P < 0.001), suggesting that the noninvasively determined parameter TransDif may provide important information in planning of treatment of aortic valve stenosis.

Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging.

Cardiac myofiber orientation is a crucial determinant of the distribution of myocardial wall stress. Myofiber orientation is commonly quantified by helix and transverse angles. Accuracy of reported helix angles is limited. Reported transverse angle data are incomplete. We measured cardiac myofiber orientation postmortem in five healthy goat hearts using magnetic resonance-diffusion tensor imaging. A novel local wall-bound coordinate system was derived from the characteristics of the fiber field. The transmural course of the helix angle corresponded to data reported in literature. The mean midwall transverse angle ranged from -12 +/- 4 degrees near the apex to +9.0 +/- 4 degrees near the base of the left ventricle, which is in agreement with the course predicted by Rijcken et al. (18) using a uniform load hypothesis. The divergence of the myofiber field was computed, which is a measure for the extent to which wall stress is transmitted through the myofiber alone. It appeared to be <0.07 mm(-1) throughout the myocardial walls except for the fusion sites between the left and right ventricles and the insertion sites of the papillary muscles.

Relating myocardial laminar architecture to shear strain and muscle fiber orientation.

Cardiac myofibers are organized into laminar sheets about four cells thick. Recently, it has been suggested that these layers coincide with the plane of maximum shear during systole. In general, there are two such planes, which are oriented at +/-45 degrees to the main principal strain axes. These planes do not necessarily contain the fiber axis. In the present study, we explicitly added the constraint that the sheet planes should also contain the muscle fiber axis. In a mathematical analysis of previously measured three-dimensional transmural systolic strain distributions in six dogs, we computed the planes of maximum shear, adding the latter constraint by using the also-measured muscle fiber axis. Generally, for such planes two solutions were found, suggesting that two populations of sheet orientation may exist. The angles at which the predicted sheets intersected transmural tissue slices, cut along left ventricular short- or long-axis planes, were strikingly similar to experimentally measured values. In conclusion, sheets coincide with planes of maximum systolic shear subject to the constraint that the muscle fiber axis is contained in this plane. Sheet orientation is not a unique function of the transmural location but occurs in two distinct populations.

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.

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.

Detection of leukocytes in contact with the vessel wall from in vivo microscope recordings using a neural network.

Leukocytes play an important role in the host defense as they may travel from the blood stream into the tissue in reacting to inflammatory stimuli. The leukocyte-vessel wall interactions are studied in post capillary vessels by intravital video microscopy during in vivo animal experiments. Sequences of video images are obtained and digitized with a frame grabber. A method for automatic detection and characterization of leukocytes in the video images is developed. Individual leukocytes are detected using a neural network that is trained with synthetic leukocyte images generated using a novel stochastic model. This model makes it feasible to generate images of leukocytes with different shapes and sizes under various lighting conditions. Experiments indicate that neural networks trained with the synthetic leukocyte images perform better than networks trained with images of manually detected leukocytes. The best performing neural network trained with synthetic leukocyte images resulted in an 18% larger area under the ROC curve than the best performing neural network trained with manually detected leukocytes.

A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction.

The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.

Kinematic analysis of left ventricular deformation in myocardial infarction using magnetic resonance cardiac tagging.

The Magnetic Resonance (MR) tagging technique provides detailed information about 2D motion in the plane of observation. Interpretation of this information as a reflection of the 3D motion of the entire cardiac wall is a major problem. In finite element models of the mechanics of the infarcted heart, an infarcted region causes motional asymmetry, extending far beyond the infarct boundary. Here we present a method to quantify such asymmetry in amplitude and orientation. For this purpose images of a short-axis cross-section of the ejecting left ventricle were acquired from 9 healthy volunteers and 5 patients with myocardial infarction. MR-tags were applied in a 5 mm grid at end-diastole. The tags were tracked by video-image analysis. Tag motion was fitted to a kinematic model of cardiac motion. For the volunteers and the patients the center of the cavity displaced by about the same amount (p = 0.11) during the ejection phase: 3.8 +/- 1.4 and 3.0 +/- 0.9 mm (mean +/- sd), respectively. Cross-sectional rotation and the decrease in cross-sectional area of the cavity were both greater in the volunteers than in the patients: 6.4 +/- 1.5 vs. 3.0 +/- 0.8 degrees (p < 0.001), and 945 +/- 71 vs. 700 +/- 176 mm2 (p = 0.02), respectively. In the patients, asymmetry of wall motion, as expressed by a sine wave dependency of contraction around the circumference, was significantly enlarged (p = 0.02). The proposed method of kinematic analysis can be used to assess cardiac deformation in humans. We expect that by analyzing images of more cross-sections simultaneously, the 3D location and the degree of infarction can be assessed efficiently.

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.