An analytic method to investigate hemodynamics of the cardiovascular system: Biventricular system.

Previously, we found analytic solutions for single ventricular system based on the lumped parameter model (LPM). In this study, we generalized the method to biventricular system and derived its analytic solutions. LPM is just a set of differential equations, but it is difficult to solve due to time-varying ventricular elastance and high order. Mathematically, there exist no elementary solutions for time-varying equations. It turns out that instead of differential equations, according to volume conservation, a set of algebraic equations can be carried out. The solutions of the set of equations are just physiological states at end of systolic and diastolic phases such as end systolic/diastolic pressure/volume of left ventricle. As a preliminary application, the method is utilized to deduce the hemodynamic effects of VA ECMO. Left ventricular (LV) distension, a serious complication of VA ECMO, is usually attributed to factors such as increased afterload, inadequate LV unloading, reduced myocardial contractility or aortic valve regurgitation (AR), bronchial and Thebesian return in the absence of aortic valve (AoV) opening. Among these, reduced contractility and AR are strongly associated with LV distension. However, in the absence of reduced contractility or AR, it is less clear whether increased afterload or inadequate LV unloading alone can cause LV distension. This leads to the critical question: under what conditions does LV distension occur in the absence of reduced contractility or AR? The analytic formulas derived in this study give conditions for LV distension. Furthermore, the results show that the analytic hemodynamics are coincident with simulated results.

An analytic method to investigate hemodynamics of the cardiovascular system - single ventricular system.

Based on the lumped parameter model (LPM) of the cardiovascular system, an analytic method is developed to derive its hemodynamics theoretically. As soon as the LPM (a series of differential equations) is solved, the hemodynamics would be obtained immediately. However, because of time-varying ventricular elastance and high order, it is difficult to solve analytically. Through simplifying the LPM, the original biventricular system with continuously varying elastance becomes a single ventricular system with discrete elastance which keeps constant during the systolic or diastolic phase. As a consequence, the original time-varying and high-order system becomes a time-invariant and first-order system during each phase. From the analytic solutions of the simplified system, a set of algebraic equations is carried out. Then the hemodynamics are obtained from the solutions of the algebraic equations. The nature of the algebraic equations is an integral form of the differential equations. A connection between the equations and PV loop is established. All of these equations are deduced based on the idealization of replacing the continuous elastance with the discrete elastance. However, there exist algebraic equations, that can be derived directly from volume conservation, still hold for the case of continuous elastance. As a preliminary application, the method is utilized to deduce the hemodynamics of left heart failure (LHF). The results show that the theoretical hemodynamics of LHF are coincident with simulated results. The analytic method can be generalized to investigate biventricular system. A program for developing a more general framework is presented in the last part.

A comprehensive comparison of the in vitro hemocompatibility of extracorporeal centrifugal blood pumps.

Purpose: Blood damage has been associated with patients under temporary continuous-flow mechanical circulatory support. To evaluate the side effects caused by transit blood pumping, in vitro hemocompatibility testing for blood damage in pumps is considered a necessary reference before clinical trials. Methods: The hemocompatibility of five extracorporeal centrifugal blood pumps was investigated comprehensively, including four commercial pumps (the Abbott CentriMag, the Terumo Capiox, the Medos DP3, and the Medtronic BPX-80) and a pump in development (the magAssist MoyoAssist®). In vitro, hemolysis was tested with heparinized porcine blood at nominal operating conditions (5 L/min, 160 mmHg) and extreme operating conditions (1 L/min, 290 mmHg) using a circulation flow loop. Hematology analyses concerning the blood cell counts and the degradation of high-molecular-weight von Willebrand factor (VWF) during 6-h circulation were also evaluated. Results: Comparing the in vitro hemocompatibility of blood pumps at different operations, the blood damage was significantly more severe at extreme operating conditions than that at nominal operating conditions. The performance of the five blood pumps was arranged in different orders at these two operating conditions. The results also demonstrated superior hemocompatibility of CentriMag and MoyoAssist® at two operating conditions, with overall low blood damage at hemolysis level, blood cell counts, and degradation of high-molecular-weight VWF. It suggested that magnetic bearings have an advantage in hemocompatibility compared to the mechanical bearing of blood pumps. Conclusion: Involving multiple operating conditions of blood pumps in in vitro hemocompatibility evaluation will be helpful for clinical application. In addition, the magnetically levitated centrifugal blood pump MoyoAssist® shows great potential in the future as it demonstrated good in vitro hemocompatibility.

Mathematical models for shear-induced blood damage based on vortex platform.

Non-physiological shear stress in Ventricular Assist Device (VAD) is considered to be an important trigger of blood damage, which has become the biggest shackle for clinical application. The researches on blood damage in literature were limited to qualitative but did not make much quantitative analysis. The purpose of this study was to investigate the quantitative influence of two flow-dependent parameters: shear stress (rotational speed) and exposure time on the shear-induced damage of red blood cells and von Willebrand Factor (vWF). A vortex blood-shearing platform was constructed to conduct in vitro experiments. Free hemoglobin assay and vWF molecular weight analysis were then performed on the sheared blood samples. MATLAB was used for regression fitting of original experimental data. The quantitative correlations between the hemolysis index, the degradation of high molecular weight vWF and the two flow-dependent parameters were found both following the power law model. The mathematic models indicated that the sensitivity of blood damage on red blood cells and vWF to exposure time was both greater than that of shear stress. Besides, the damage of vWF was more serious than that of red blood cells at the same flow condition. The models could be used to predict blood damage in blood-contacting medical devices, especially for the slow even stagnant blood flow regions in VAD, thus may provide useful guidance for VAD development and improvement. It also indicated that the vortex platform can be used to study the law of blood damage for the simple structure and easy operation.

The influence of surface roughness on the damage of von Willebrand Factor under shear flow condition.

Despite technological advances in mechanical circulatory support devices to treat end-stage heart failure, blood damage induced by non-physiological shear stress in operation often triggered clinical hemocompatibility complications. The loss of high molecular weight von Willebrand Factor (HMW-VWF) has been considered as an essential cause of gastrointestinal bleeding. In addition to the mechanics factors, interface factors may also affect blood damage, especially the surface characteristics. In this study, the effect of surface roughness on VWF damage under flow condition was investigated. A roller pump circulation experimental platform with a roughness embedded sample chamber was constructed to provide blood shearing flow condition. VWF molecular weight analysis, VWF antigen (VWF-Ag) concentration assay, and VWF ristocetin cofactor activity (VWF-Rico) assay were performed on the sheared blood samples. These variables are the main functional indicators of VWF. It was found that the surface roughness induced VWF damage is mainly caused by the loss of HMW-VWF rather than reducing the total amount of VWF. The threshold value of surface roughness for a rapid increase in the degradation of HMW-VWF under low flow rate was obtained between Ra 0.4 and 0.6 µm, which was smaller than the threshold for hemolysis. Our findings indicated that VWF is more sensitive to the interface factor of surface roughness than red blood cells, thus has a higher requirement for blood pump design. It could provide reference for the material design and processing in developing mechanical circulatory support devices.