The arterial Windkessel

Frank’s Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload

Non-invasive evaluation of left ventricular afterload, part 2 : arterial pressure-flow and pressure-volume relations in humans

The mechanical load imposed by the systemic circulation to the left ventricle is an important determinant of normal and abnormal cardiovascular function. Left ventricular afterload is determined by complex time-varying phenomena, which affect pressure and flow patterns generated by the pumping ventricle. Left ventricular afterload is best described in terms of pressure-flow relations, allowing for quantification of various components of load using simplified biomechanical models of the circulation, with great potential for mechanistic understanding of the role of central hemodynamics in cardiovascular disease and the effects of therapeutic interventions. In the second part of this tutorial, we review analytic methods used to characterize left ventricular afterload, including analyses of central arterial pressure-flow relations and windkessel modeling (pressure-volume relations). Conceptual descriptions of various models and methods are emphasized over mathematical ones. Our review is aimed at helping researchers and clinicians obtain and interpret results from analyses of left ventricular afterload in clinical and epidemiological settings

Development and characterization of the arterial windkessel and its role during left ventricular assist device assistance

Modeling of the cardiovascular system is challenging, but it has the potential to further advance our understanding of normal and pathological conditions. Morphology and function are closely related. The arterial system provides steady blood flow to each organ and damps out wave fluctuations as a consequence of intermittent ventricular ejection. These actions can be approached separately in terms of mathematical relationships between pressure and flow. Lumped parameter models are helpful for the study of the interactions between the heart and the arterial system. The arterial windkessel model still plays a significant role despite its limitations. This review aims to discuss the model and its modifications and derive the fundamental equations by applying electric circuits theory. In addition, its role during left ventricular assist device assistance is explored and discussed in relation to rotary blood pumps

Role of adenylyl cyclase S674 in central and forearm vasomotor control

This study examined the cardiac and vasomotor responses to submaximal handgrip exercise and beta-adrenergic control in carriers (n = 6) and non-carriers (n = 4) of a genetic variant of adenylyl cyclase 6 (AC S674). Rhythmic handgrip contractions (1 minute bout; 2 second contraction-relaxation period) were performed at three different intensities (20, 40, and 60% of maximal voluntary contraction force) to test the vasodilatory response to exercise. Additionally, two 5 minute infusions of isoproterenol (0.01 and 0.02 µg·kg-1·min-1 diluted in 5% dextrose) and one 10 minute infusion of propranolol (0.1 mg·kg-1 diluted in 0.9% saline) were used to examine beta-adrenergic mediated cardiovascular responses. Ascending aorta and brachial artery mean blood flow velocities (pulsed Doppler ultrasound) and brachial artery blood pressure (Finometer) were continuously measured during handgrip and pharmacological protocols. Vascular mechanics of the forearm were calculated using a three-element lumped windkessel model. At baseline, AC S674 carriers have decreased systemic vascular conductance and forearm vascular bed compliance, as well as increased pulse pressure. However, AC S674 carriers did not exhibit altered cardiac or vasomotor control during handgrip exercise, isoproterenol infusion, or propranolol infusion. These results indicate that expression of the dysfunctional genetic variant AC S674 has profound effects on systemic hemodynamics at rest. Chronic elevation in vascular contractile state may result in vascular stiffening and enhanced pulse pressures with detrimental long-term consequences for cardiovascular health

Anisotropic behaviour of human gallbladder walls

Inverse estimation of biomechanical parameters of soft tissues from non-invasive measurements has clinical significance in patient-specific modelling and disease diagnosis. In this paper, we propose a fully nonlinear approach to estimate the mechanical properties of the human gallbladder wall muscles from in vivo ultrasound images. The iteration method consists of a forward approach, in which the constitutive equation is based on a modified Hozapfel–Gasser–Ogden law initially developed for arteries. Five constitutive parameters describing the two orthogonal families of fibres and the matrix material are determined by comparing the computed displacements with medical images. The optimisation process is carried out using the MATLAB toolbox, a Python code, and the ABAQUS solver. The proposed method is validated with published artery data and subsequently applied to ten human gallbladder samples. Results show that the human gallbladder wall is anisotropic during the passive refilling phase, and that the peak stress is 1.6 times greater than that calculated using linear mechanics. This discrepancy arises because the wall thickness reduces by 1.6 times during the deformation, which is not predicted by conventional linear elasticity. If the change of wall thickness is accounted for, then the linear model can used to predict the gallbladder stress and its correlation with pain. This work provides further understanding of the nonlinear characteristics of human gallbladder