Estimation of Simulated Left Ventricle Elastance Using Lumped Parameter Modelling and Gradient-Based Optimization With Forward-Mode Automatic Differentiation Based on Synthetically Generated Noninvasive Data.

The present study evaluates a parameter discovery approach based on a lumped parameter model of the cardiovascular system in conjunction with optimization to approximate important cardiac parameters, including simulated left ventricle elastances. Important parameters pertaining to ventricular function were estimated using gradient optimization and synthetically generated measurements. Forward-mode automatic differentiation was used to estimate the cost function-parameter matrices and compared to the common finite differences approach. Synthetic data of healthy and diseased hearts were generated as proxies for noninvasive clinical measurements and used to evaluate the algorithm. Twelve parameters including left ventricle elastances were selected for optimization based on 99% explained variation in mean left ventricle pressure and volume. The hybrid optimization strategy yielded the best overall results compared to 1st order optimization with automatic differentiation and finite difference approaches, with mean absolute percentage errors ranging from 6.67% to 14.14%. Errors in left ventricle elastance estimates for simulated aortic stenosis and mitral regurgitation were smallest when including synthetic measurements for arterial pressure and valvular flow rate at approximately 2% and degraded to roughly 5% when including volume trends as well. However, the latter resulted in better tracking of the left ventricle pressure waveforms and may be considered when the necessary equipment is available.

In-silico modelling of the impact of hypertension on the mean transvalvular gradients in aortic stenosis.

INTRODUCTION: The influence of hypertension on the diagnostic assessment of aortic stenosis (AS) severity is unclear, yet clinically relevant. To clarify the effect of hypertension on transvalvular gradients, requires a better understanding of the impact that blood pressure change has on mean flow rate. Also, the effect of various degrees of AS severity, the valve geometry and intrinsic left ventricular contractile function (elastance) on this interaction, needs to be clarified. The current work aims to assess this interaction and the magnitude of these effects. METHODS: A validated, zero-dimensional electro-hydraulic analogue computer model of the human cardiovascular circulatory system was generated. It was used to assess the impact of blood pressure changes on left ventricular pressure and transvalvular gradients at various flow rates, left ventricular elastances, a range of aortic valve areas and for different aortic valve morphologies. RESULTS AND DISCUSSION: The magnitude of the impact of hypertension induced changes on the mean gradient (MG) is influenced by the mean flow rate, the AS severity, the hydraulic effective valve orifice area and the left ventricular elastance. Generally, for a given change in systemic arterial pressure, the impact on MG will be the most marked for lower flow rate states such as is expected in more severe degrees of AS, for worse intrinsic left ventricular (LV) contractility, shorter ejection times and lower end diastolic LV volumes. Given the above conditions, the magnitude of the effect will be more for a larger aortic sinus diameter, and also for a typical degenerative valve morphology compared to a typical rheumatic valve morphology. CONCLUSION: The interaction between hypertension and mean gradients in AS is complex. The current work places previous recommendations in perspective by quantifying the magnitude of the effect that the changes in blood pressure has on mean gradient in various pathophysiological states. The work creates a framework for the parameters that should be considered in future clinical research on the topic.

Dynamic simulation of aortic valve stenosis using a lumped parameter cardiovascular system model with flow regime dependent valve pressure loss characteristics.

Valvular heart diseases are growing concern in impoverished parts of the world, such as Southern-Africa, claiming more than 31 % of total deaths related to cardiovascular diseases. The ability to model the effects of regurgitant and obstructive lesions on the valve body can assist clinicians in preparing personalised treatments. In the present work, a multi-compartment lumped parameter model of the human cardiovascular system is developed, with a newly proposed valve modelling approach which accounts for geometry and flow regime dependent pressure drops along with the valve cusp motion. The model is applied to study various degrees of aortic stenosis using typical human cardiovascular parameters. The predicted transvalvular pressure drops for the different modelling approaches are compared to typical measured mean and peak gradients found in literature for severely stenosed aortic valves. The comparison between the predicted and measured values show that the previously published valve models under predicts expected severely stenosed peak and mean transvalvular pressure drops by approximately 47% and 25% respectively, whereas the newly proposed model under predicts the peak pressure drop by 25% and over predicts mean pressure drop by 7%.