Modeling and simulation of blood flow in a sac-type left ventricular assist device

Left ventricular assist devices (LVADs) are among the most important mechanical artificial hearts in medical equipment industry. Since the need for heart transplantation is on the rise, there is a requirement for implantable LVADs, which can be safely used for long-term purposes. One of the most promising kinds of these devices is the sac-type LVAD (ST-LVAD) that has the ability to generate pulsatile flow. In this study and for the first time, three different models of ST-LVAD are analyzed numerically. In the first model, the motion of the elastic membrane wall is simplified, while in the second model, the motion is assumed to be wavy. The pressure boundary conditions are added to the second model to allocate for the effect of pressure on the flow pattern, and hence, form the third model. The simulation results of the analyzed models show that in this particular type of LVAD, the viscous term of the applied stress from the fluid on the moving wall is negligible, compared with the pressure term. Additionally, it can be concluded that the motion pattern of the moving wall does not affect the blood flow pattern in a great deal. Furthermore, the inclusion of the fluid pressure in the boundary conditions does not have a major influence on the blood flow pattern.     

A two phase harmonic model for left ventricular function

A minimal model for mechanical motion of the left ventricle is proposed. The model assumes the left ventricle to be a harmonic oscillator with two distinct phases, simulating the systolic and diastolic phases, at which both the amplitude and the elastic constant of the oscillator are different. Taking into account the pressure within the left ventricle, the model shows qualitative agreement with functional parameters of the left ventricle. The model allows for a natural explanation of heart failure with preserved systolic left ventricular function, also termed diastolic heart failure. Specifically, the rise in left ventricular filling pressures following increased left-ventricular wall stiffness is attributed to a mechanism aimed at preserving heart rate and cardiac output.     

Identification of nonlinear model of ankle joint dynamics during electrical stimulation of soleus

The mechanical impedance of the ankle joint was estimated in two conditions: during submaximal surface electrical stimulation of the soleus muscle, and with no stimulation applied. Both neurologically intact (n=5) and spinal cord injured subjects (n=4) were used. The mechanical impedance was measured by applying angular step and constant velocity (13–100° s⁻¹) perturbations at 10° to the ankle and measuring the resulting changes in torque. A five-element lumped model consisting of an inertial element, a parallel elastic element, and an elastic element in series with a viscous element and a pure tension generator produced a good fit for predicting the compliance characteristics of the ankle for both the relaxed and stimulated conditions. The elastic elements were piecewise linear with different values for the dorsiflexion and plantarflexion directions. The viscous element was velocity-dependent and it decreased in value as the velocity increased. The average torque error between the measured and model's response during soleus stimulation was 10·56% for the dorsiflexed and 11·93% for the plantarflexed perturbations. However, the average error was skewed by several subjects who had excessive error, due to volitional intervention or flexor withdrawal reflex. The average model error for the perturbations without stimulation was 7·12% for dorsiflexed and 5·58% for plantarflexed perturbations.     

Pulsating blood flow in an initially stressed,anisotropic elastic tube: linear approximation of pressure waves

A mathematical model for pulsating flow of a viscous incompressible fluid in an initially stressed elastic tube with anisotropic structure is developed and an analysis of the propagation of pressure waves is presented. The theoretical model can be applied to the study of blood flow in arteries, and its solution leads to a dispersion equation relating wave number with frequency and the rheological parameters of the wall. Determination of fluid velocities and displacement components is obtained.     

Smooth muscle role on pulmonary arterial function during acute pulmonary hypertension in sheep

AIM: We determined the wall mechanical response of the pulmonary artery (PA) to acute pulmonary hypertension induced pharmacologically and by an occlusion maneuver, to study the vascular response of the local segment and its influence in the whole pulmonary circulation. METHODS: Pulmonary pressure and diameter were measured in six anaesthetized sheep under steady-state conditions. Transient hypertension in the PA was induced by phenylephrine (PHE) and a high pressure (HP) mechanical occlusion aimed at producing the same pulse and mean pressure responses. A viscoelastic arterial wall model was applied and the elastic (E(pd)) and viscous (micro) indexes were obtained. The micro/E(pd) ratio was adopted to quantify the damping performance of the arterial wall segment. The diastolic time constant was used as an indicator of the whole pulmonary buffering function. The systemic pressure was always measured. RESULTS: The pulmonary mean, systolic and pulse pressure increases (P < 0.05) were similar during PHE and HP, with respect to control. PHE also induced a systemic pressure rise (P < 0.05). The E(pd) elastic index increased during HP (P < 0.05) and tended to increase during PHE with respect to control. The viscous index micro only increased with PHE (P < 0.05) with respect to control and occlusion. The diastolic time constant increased with PHE with respect to control (P < 0.05). CONCLUSIONS: A pressure rise in the PA, induced by an occlusion maneuver, increased local stiffness. Similar pressure rises with smooth muscle activation (PHE), produced both a stiffness and viscous index increase. In PHE resistance increases more than compliance decreases so that the global net effect is a longer decay time. Smooth-muscle activation enhances the local damping effect (micro/E(pd)), concomitant with the buffering function improvement.     

Analysis of pressure waves as a mean of diagnosing vascular obstructions

A feasibility study was made to examine whether pressure measurements can be used to diagnose vascular obstructions in blood vessels. Distortion of a pressure wave due to an obstruction in an elastic tube was investigated theoretically and experimentally. Linear theory and the method of characteristics were employed in developing mathematical expressions for the distortion of the pressure wave. The quality of the models developed was examined by performing experiments on a latex tube with rigid obstructions. A nonlinear model using the method of characteristics was in good agreement with the experiment data for obstructions with any severity, while a linear model was applicable to small obstructions. The nonlinear model is proposed as a mathematical model for the detection of vascular obstructions by analysing pressure waves.     

Nonlinear and Frequency-Dependent Mechanical Behavior of the Mouse Respiratory System

The assessment of the mechanical properties of the respiratory system is typically done by oscillating flow into the lungs via the trachea, measuring the resulting pressure generated at the trachea, and relating the two signals to each other in terms of some suitable mathematical model. If the perturbing flow signal is broadband and not too large in amplitude, linear behavior is usually assumed and the input impedance calculated. Alternatively, some researchers have used flow signals that are narrow band but large in amplitude, and invoked nonlinear lumped-parameter models to account for the relationship between flow and pressure. There has been little attempt, however, to deal with respiratory data that are both broadband and reflective of system nonlinearities. In the present study, we collected such data from mice. To interpret these data, we first developed a time-domain approximation to a widely used model of respiratory input impedance. We then extended this model to include nonlinear resistive and elastic terms. We found that the nonlinear elastic term fit the data better than the linear model or the nonlinear resistance model when amplitudes were large. This model may be useful for detecting overinflation of the lung during mechanical ventilation. © 2003 Biomedical Engineering Society. PAC2003: 8719Rr, 8719Uv     

Identification of Arterial Wall Dynamics in Conscious Dogs

Viscoelastic properties determine the dynamic behaviour of the arterial wall under pulsatile pressure and flow, suggesting time- or frequency-dependent responses to changes in wall stress and strain. The objectives of the present study were: (i) to develop a simplified model to derive simultaneously the elastic, viscous and inertial wall moduli; (ii) to assess Young's modulus as a function of frequency, in conscious, chronically instrumented dogs. Parametric discrete time models were used to characterise the dynamics of the arterial system based on thoracic aortic pressure (microtransducer) and diameter (sonomicrometry) measurements in control steady state and during activation of smooth muscle with the alpha-adrenoceptor agonist phenylephrine (5 microg kg(-1) min(-1), I.V.), in eight conscious dogs. The linear autoregressive model and a physically motivated non-linear model were fitted to the input-output (stress-strain) relationship. The aortic buffering function (complex Young's modulus) was obtained in vivo from the identified linear model. Elastic, viscous and inertial moduli were significantly increased from control state ((44.5 +/- 7.7) x 10(4) Pa; (12.3 +/- 4.7) x 10(4) Pa s; (0.048 +/- 0.028) x 10(4) Pa s(2) ) to active state ((85.3 +/- 29.5) x 10(4) Pa, P < 0.001; (22.4 +/- 8.3) x 10(4) Pa s, P < 0.05; (0.148 +/- 0.060) x 10(4) Pa s(2), P < 0.05). These moduli, obtained using the linear model, did not present significant differences compared with those derived using the non-linear model. In control conditions, the magnitude of the normalised complex Young's modulus was found to be similar to that reported in previous animal studies ranging from 1 to 10 Hz. During vascular smooth muscle activation, this modulus was found to be increased with regard to control conditions (P < 0.01) in the frequency range used in this study. The frequency-dependent Young's modulus of the aortic wall was obtained for the first time in conscious, unsedated dogs. The parametric modelling approach allows us to verify that vascular smooth muscle activation increases the elastic, viscous and inertial moduli with the advantage of being able to track their time evolution. Furthermore, under activation, the aortic wall remains stiff in the physiological frequency range, suggesting the impairment of the arterial buffering function. Experimental Physiology (2001) 86.4, 519-528.     

An investigation of the hammocking effect associated with interface pressure measurements using pneumatic tourniquet cuffs

A simple experimental arrangement is used to investigate the influence of sensor height on the pressure indicated by an inherently linear sensor sandwiched between a rigid curved surface and a pneumatic tourniquet cuff. The sensor-indicated pressure is monitored for sensor heights in the range 0-3 mm and for cuff inflation pressures of 0-40 kPa ( approximately 0-300 mmHg). The sensor response is found to be non-linear with a saturation tendency at high applied pressures. A model which treats the cuff as an elastic membrane draped over the sensor is shown to be successful in accounting for the general form of the sensor characteristic particularly at cuff pressures greater than about 5 kPa. The model is of use in estimating the errors that are likely to arise in intrusive sensors used to measure interface pressures under tourniquets.     

Assessment of distributed arterial network models

The aim of this study is to evaluate the relative importance of elastic non-linearities, viscoelasticity and resistance vessel modelling on arterial pressure and flow wave contours computed with distributed arterial network models. The computational results of a non-linear (time-domain) and a linear (frequency-domain) mode were compared using the same geometrical configuration and identical upstream and downstream boundary conditions and mechanical properties. Pressures were computed at the ascending aorta, brachial and femoral artery. In spite of the identical problem definition, computational differences were found in input impedance modulus (max. 15–20%), systolic pressure (max. 5%) and pulse pressure (max. 10%). For the brachial artery, the ratio of pulse pressure to aortic pulse pressure was practically identical for both models (3%), whereas for the femoral artery higher values are found for the linear model (+10%). The aortic/brachial pressure transfer function indicates that pressure harmonic amplification is somewhat higher in the linear model for frequencies lower than 6 Hz while the opposite is true for higher frequencies. These computational disparities were attributed to conceptual model differences, such as the treatment of geometric tapering, rather than to elastic or convective non-linearities. Compared to the effect of viscoelasticity, the discrepancy between the linear and non-linear model is of the same importance. At peripheral locations, the correct representation of terminal impedance outweights the computational differences between the linear and non-linear models.     

Experimental and theoretical models of flow during forced expiration: pressure and pressure history dependence of flow rate

Flow characteristics have been studied in elastic mono- and bialveolar lung models made from tubes and balloons in series. Flow rate variation is explained on the basis of two successive limiting factors governed by the mutual interaction of tube mechanical properties and flow characteristics, i.e. wave-speed and viscous limitations induced by the tube collapse. A numerical model of flow in an elastic monoalveolar structure has been developed. It is generally admitted that a remarkable feature of forced expiration is that the flow rate is ‘effort independent’ for approximately the lower 80 per cent of vital capacity. The present results, which describe a continuous process, suggest that the flow rate depends mostly on the external pressure and pressure history. between the 15th August 1987 and the 31st August 1988, and at other periods to him at INSERM U. 296, Faculté de Médecine, 8 av Gl Sarrail, 94010 Creteil Cedex, France.     

Characterization of cellular elastic modulus using structure based double layer model

The mechanical characterization of cells is important for understanding cellular behavior and physiological functions. We used atomic force microscopy (AFM) to obtain a force-displacement curve and estimate the elastic modulus of hepatocellular carcinoma cells (HEP-G2) utilizing both linear Hertz-Sneddon (HS) and non-linear elastic models. In order to overcome the limitations of HS model, which assumes a linear homogeneous cell body, a cell is modeled as a double-layered body with an outer cytoplasmic layer made mostly of interconnected fibers of cytoskeleton proteins and a nucleus. By disrupting all cytoskeletal protein networks, we estimate the elastic modulus of the core nucleus using FEM for a single ellipsoid. Based on the nucleic modulus and cellular dimensions found by 3D confocal imaging, we develop a novel double-layered cellular (DLC) finite element model. The DLC model provides a more reliable estimate of the elastic modulus of the cell than conventionally used HS model and correlates closely with experimental results.     

Viscoelastic behavior of polyurethane vascular prostheses

A method of evaluating the in vitro viscoelastic properties of microfibrous Biomer poly(ether-urethane-urea) vascular prostheses is outlined. Quasi-static and dynamic tests were carried out on Biomer grafts of diameter between 3.4 mm and 3.8 mm and wall thickness between 0.25 mm and 0.55 mm. It is shown that the quasi-static compliance of a Biomer graft may be determined from an equation relating transmural pressure, radius, and longitudinal strains in terms of the graft dimensions and material constants. The dynamic compliance spectra were evaluated as a function of the longitudinal and circumferential strains and temperature. Although the ratio of dynamic compliance to quasi-static compliance was linearly related to the logarithm of frequency it was not significantly affected by strains or temperature over the relevant ranges studied. Employing the usual assumptions of linear isotropic incremental elastic theory the dynamic elastic and viscous moduli were calculated as a function of frequency. Biomer grafts were more viscous than canine carotid and femoral arteries, especially at the higher frequencies. The variation in the ratio of dynamic to static incremental modulus with frequency was similar to that observed in the femoral arteries by Bergel (J. Physiol., 156, 458-469 (1961)).     

The trajectory of human wrist movements

1. To determine the form of human movement trajectories and the factors that determine this form, normal subjects performed wrist flexion movements against various elastic, viscous, and inertial loads. The subjects were instructed with visual and auditory feedback to make a movement of prescribed amplitude in a present period of time, but were free to choose any trajectory that fulfilled these constraints. 2. The trajectories were examined critically to determine if they corresponded to those which would minimize the root mean square (RMS) value of some kinematic variable or of energy consumption. The data agreed better with the trajectory that minimized the RMS value of jerk (the third derivative of length) than that of acceleration. However, systematic deviations from the minimum jerk predictions were consistently observed whenever movements were made against elastic and viscous loads. 3. Improved agreement could generally be obtained by assuming that the velocity profile varied according to a normal (Gaussian) curve. We conclude that minimization of jerk is not a general principle used by the nervous system in organizing voluntary movements, although movements may approach the predicted form, particularly under inertial loading conditions. 4. The EMG of the agonist muscles consisted of relatively simple waveforms containing ramplike increases and approximately exponential decays. The form of the movements could often be predicted quite well by using the EMG as an input to a linear second-order model of the muscle plus load. Rather than rigorously minimizing a kinematic variable or energy consumption, the nervous system may generate simple waveforms and adjust the parameters of these waveforms by trial and error until a trajectory is achieved that meets the requirements for a given load.     

Mechanical impedance of the canine diaphragm

A technique which does not require the measurement of strain has been developed for the investigation of the incremental dynamic properties of soft tissue sheets. Radially prestressed and circularly clamped canine diaphragm samples were exposed to small-amplitude pseudorandom pressure variations. From the measurement of these pressure variations and the volume flow caused by the vibration of the membrane the incremental mechanical impedance spectrum was computed in the 0·25–5 Hz frequency range at three different levels of initial stress. The diaphragm tissue was found to be basically elastic. However, the small viscous component showed a sharp negative frequency dependence between 0·25 and 2 Hz. The quasistatic elastances of the samples were in good, agreement with the elastance values derived from the impedance data. The relationship between the elastance and the initial stress was close to linear. It was concluded that the method is applicable to the study of the incremental dynamic properties of planar soft tissue samples.     

可注射封闭性水凝胶力学性质与其止血性能的相关性

目的探究封闭性水凝胶力学性质与其止血性能之间的关系。方法通过测量透明质酸/明胶水凝胶凝固时间、弹性模量、黏性模量、顶破强度和止血性能,与医用纤维蛋白胶止血剂对比,提出凝固时间和力学参数,用于判断封闭性水凝胶应用于临床止血的可行性。结果凝固时间长以及弹性模量、黏性模量和顶破强度小的水凝胶只可能对小出血量起控制作用,凝固时间短、弹性模量、黏性模量和顶破强度大的水凝胶能有效减少大出血量情况下的血液损失。结论水凝胶的凝固时间、弹性模量、黏性模量以及顶破强度与其止血性能有关,如果水凝胶封闭止血要达到纤维蛋白胶的止血水平,其凝固时间应小于120 s,弹性模量大于600 Pa,黏性模量大于120 Pa;对于直径2 mm的组织模型破损,顶破强度要不低于10.7 kPa,最好高于16.0 kPa。     

A practical guide for analysis of nanoindentation data

Mechanical properties of biological materials are increasingly explored via nanoindentation testing. This paper reviews the modes of deformation found during indentation: elastic, plastic, viscous and fracture. A scheme is provided for ascertaining which deformation modes are active during a particular indentation test based on the load–displacement trace. Two behavior maps for indentation are presented, one in the viscous–elastic–plastic space, concerning homogeneous deformation, and one in the plastic versus brittle space, concerning the transition to fracture behavior when the threshold for cracking is exceeded. Best-practice methods for characterizing materials are presented based on which deformation modes are active; the discussion includes both nanoindentation experimental test options and appropriate methods for analyzing the resulting data.     

The influence of reflection artifacts on apparent phase velocity measurements in the trachea

Models of the pulmonary airway network were analyzed to determine the effect of reflections on apparent phase velocity measurements in the trachea of dogs. A stiffly constrained elastic tube filled with a viscous fluid was used to model each airway segment, and a series resistance-capacitance combination served as a terminal element for each pathway. Reflection, transmission and attenuation coefficients at each branching site and reflection coefficients at each termination were computed. Composite sinusoidal pressure waves at two sites in the trachea where computed for frequencies from 5 to 150 Hz, and crosscorrelograms were used to determine apparent phase velocities. In an asymmetrical model, the randomness of the airway diameters caused phase shifts in the reflection coefficients to vary between approximately 0° and 180° resulting in significant destructive interference between the reflected waves. Calculated apparent phase velocities agreed with the assumed values within 40% at frequencies of 70 Hz and below and within 20% at higher frequencies in this model.     

Changes in Passive But Not Active Mechanical Properties Predict Recovery of Function of Stunned Myocardium

The time course of alterations in active and passive mechanical properties of stunned myocardium during ischemia and throughout reperfusion has not been thoroughly quantified. This investigation tested the hypothesis that the amount of injury as well as the rate and extent of recovery of contractile function in postischemic, reperfused myocardium are directly correlated to changes in regional active and passive elastance and viscosity. A modified viscoelastic Voigt model was employed to quantify myocardial mechanical properties. Left ventricular pressure and segment length (in both ischemic and normal regions) were fit to the model consisting of an active elastic spring in parallel with a viscous damper and a passive elastic spring. The mechanical properties of myocardium from dogs which recovered (50%) baseline regional contractile function as determined by percent segment shortening (n=7) were compared to those from dogs that did not recover function (n=7). Both groups displayed decreased active elastance in the ischemic region during coronary artery occlusion, and this decrease was maintained in the nonrecovery group. Increases in viscosity of ischemic myocardium were observed in both groups during coronary occlusion but returned to control only in the recovery group. The nonrecovery group demonstrated increased passive elastance in the ischemic region during coronary occlusion and throughout the reperfusion period whereas the recovery group remained unchanged. We conclude that functional recovery of stunned myocardium is directly related to alterations in mechanical properties caused by ischemia and that changes in passive elastance during occlusion may predict the ability of ischemic myocardium to recover contractile function. © 1999 Biomedical Engineering Society. PAC99: 8719Rr, 8719Uv, 8710+e     

Model studies of the effects of the thoracic pressure on the circulation

Two models of the cardiovascular system subjected to changes in intrathoracic pressure (ITP) are used to simulate the response to normal and positive pressure ventilation and the Mueller maneuver. The first model, based on our earlier model for cardiopulmonary resuscitation and cardiac assist by ITP variations, is based on lumped parameter representation of the cardiovascular system with two ventricles which function based on the time-varying elastance concept using their transmural pressures as the load. The ITP is assumed to be equally distributed in the thoracic cavity and equally affecting all cardiovascular structures within the chest. The model shows that a decrease in ITP is associated with an initial decrease in aortic pressure and flow and an increase in left ventricular end-diastolic and end-systolic volumes. A transient decrease in left ventricular volume which was suggested to occur by a few studies cannot be predicted based on this model. Such a decrease in left ventricular volume can be only predicted when a pericardial constraint is included, as done in the second model. Positive pressure interventions are associated with decreased heart volumes and cardiac output which is primarily a “preload” effect. In general the model reasonably predicts the hemodynamics as a function of the ITP changes and may be used as a tool to investigate the response of the cardiovascular system to various ITP interventions.