Personalization of electro-mechanical models of the pressure-overloaded left ventricle: fitting of Windkessel-type afterload models

Figures

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  Figure 1.. Overview of model workflow for fitting afterload model (upper panel) and combined EM LV model (lower panel). In a first step, the Wk3 afterload parameters Z, Zv, R and C were identified using measured haemodynamic parameters pop, m, p^m, pcl, m, Δpav, m and q(t) = −dV/dt as inputs. For AS cases, pop, m and p^m were estimated from cuff measurements, whereas pcl, m was estimated from empirical reference data. Subsequently, the EM LV model is fitted. First, the biomechanical bulk modulus CGuc is adjusted to fit the passive behaviour of the LV model to the empirical approximation of the end-diastolic pressure–volume relation (EDPVR) due to Klotz, using {Ved, plv, ed} as inputs. For AS cases plv, ed was estimated from empirical reference data. Using the fitted afterload model coupled to the EM LV model through a resistive valve model, the active stress model is parametrized using fixed-point iterations to adjust the phenomenological active stress model parameters, {τC,S^a,Tdur,τR}, using the discrepancy between measured and simulated p−V metrics during isovolumetric contraction and ejection. In the diagram: EF, ejection fraction; ESV, end-systolic volume; and EDV, end-diastolic…

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  Figure 2.. Results of (a) afterload fitting and (b) EM LV fitting for cases 10-AS and 02-CoA. (a) Fitted and measured pressure traces are drawn as solid grey and dashed-dotted blue traces, respectively. In case 10-AS only discrete pressure values were available (dashed-dotted blue). (b) PV loops simulated with the EM LV are shown over a full cardiac cycle, whereas the resulting LV volume and aortic pressure traces are shown only during ejection. Traces refer to EM LV simulation (solid red), measurements (blue dashed-dotted) and results of the afterload fitting, computed by solving the Wk3 equation (2.1). Gap in IVC phase of measured PV loop for the 02-CoA case can be explained by the low sampling resolution causing Vlv, m to be not completely periodic. End-diastolic (ED, transparent) and end systolic (ES, solid blue) configurations of the LV are also shown. (Online version in colour.)

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  Figure 3.. Input parameters {pop, m,p^m,pcl, m} and associated Wk3 parameters {Z, R, C} for cases 10-AS and 02-CoA. Distributions suggest a continuous mapping. An independent multivariate normal distribution with variance σ2 = 0.2 kPa2 was used to colour the samples. (Online version in colour.)

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  Figure 4.. Effect of Wk3 parameter variability on physiological signal output of EM LV model. Pressure, volume and PV loops resulting from EM simulations with varied input parameters are shown for case 10-AS and case 02-CoA. Deviations due to changes in pop,m (dashed black), p^m (dashed grey) and pcl,m (dashed light grey) are visualized along with initial results in solid red. (Online version in colour.)