Monitoring variability in parameter estimates for lumped parameter models of the systemic circulation using longitudinal hemodynamic measurements

Abstract

Background Physics-based cardiovascular models are only recently being considered for disease diagnosis or prognosis in clinical settings. These models depend on parameters representing the physical and physiological properties of the modeled system. Personalizing these parameters may give insight into the specific state of the individual and etiology of disease. We applied a relatively fast model optimization scheme based on common local optimization methods to two model formulations of the left ventricle and systemic circulation. One closed-loop model and one open-loop model were applied. Intermittently collected hemodynamic data from an exercise motivation study were used to personalize these models for data from 25 participants. The hemodynamic data were collected for each participant at the start, middle and end of the trial. We constructed two data sets for the participants, both consisting of systolic and diastolic brachial pressure, stroke volume, and left-ventricular outflow tract velocity traces paired with either the finger arterial pressure waveform or the carotid pressure waveform. Results We examined the feasibility of separating parameter estimates for the individual from population estimates by assessing the variability of estimates using the interquartile range. We found that the estimated parameter values were similar for the two model formulations, but that the systemic arterial compliance was significantly different ($$p < 10^{-6}$$ p < 10 - 6 ) depending on choice of pressure waveform. The estimates of systemic arterial compliance were on average higher when using the finger artery pressure waveform as compared to the carotid waveform. Conclusions We found that for the majority of participants, the variability of parameter estimates for a given participant on any measurement day was lower than the variability both across all measurement days combined for one participant, and for the population. This indicates that it is possible to identify individuals from the population, and that we can distinguish different measurement days for the individual participant by parameter values using the presented optimization method.

Examining temporal changes in model-optimized parameters using longitudinal hemodynamic measurements

“…Results from Bjørdalsbakke et al indicate that the closed-loop model does not have any considerable advantage compared to the open-loop model in terms of resolving parameter changes [ 17 ]. Results from the current study suggest that the open-loop model may be better suited for detecting parameter changes.…”

“…By applying a lumped-parameter model of the systemic circulation to the data from the trial, the mechanical properties of the circulation were estimated for specific individuals as described in previous work [ 17 ]. We continued on to specifically investigate the left-ventricular contractility by way of maximal left-ventricular elastance ( ), arterial stiffness by arterial compliance ( ), and arterial vascular resistance by total peripheral resistance ( ).…”

“…Additionally, the activity levels throughout the study period was monitored using wrist-worn heart rate monitors. Waveform data preprocessing has been described previously by Bjørdalsbakke et al [ 17 ]. The types of measurements are listed in Table 10 .…”

“…This includes the derived quantities of systolic and diastolic blood pressure, as well as ventricular volumes by way of stroke volume. The models used have been presented in detail previously by Bjørdalsbakke et al [ 17 , 23 ]. The closed-loop model is based on previous models by Smith et al, Segers et al, and Bovendeerd et al [ 31 – 33 ].…”

“…PAI score is the output of a mathematical model considering an individual’s heart rate history to compute an easily understandable personalized metric of physical activity [ 15 , 16 ]. Using data from this trial, Bjørdalsbakke et al personalized two simple CV models of the systemic circulation and analyzed the variability in parameter estimates due to personalization method as well as variation in the population [ 17 ]. The chosen personalization method was an ensemble method based on local non-linear optimization producing multiple parameter estimates to find an averaged solution after filtering out the worst estimates.…”