Examining temporal changes in model-optimized parameters using longitudinal hemodynamic measurements
Authors: Bjørdalsbakke Nikolai L. , Sturdy Jacob , Wisløff Ulrik , Hellevik Leif R. 
Published: July 2024

Abstract
Background
We previously applied hemodynamic data to personalize a mathematical model of the circulation expressed as physically interpretable parameters. The aim of this study was to identify patterns in the data that could potentially explain the estimated parameter changes. This included investigating whether the parameters could be used to track the effect of physical activity on high blood pressure. Clinical trials have repeatedly detected beneficial changes in blood pressure after physical activity and uncovered changes in lower level phenotypes (such as stiffened or high-resistance blood vessels). These phenotypes can be characterized by parameters describing the mechanical properties of the circulatory system. These parameters can be incorporated in and contextualized by physics-based cardiovascular models of the circulation, which in combination can become tools for monitoring cardiovascular disease progression and management in the future.

Methods
Closed-loop and open-loop models of the left ventricle and systemic circulation were previously optimized to data from a pilot study with a 12-week exercise intervention period. Basal characteristics and hemodynamic data such as blood pressure in the carotid, brachial and finger arteries, as well as left-ventricular outflow tract flow traces were collected in the trial. Model parameters estimated for measurements made on separate days during the trial were used to compute parameter changes for total peripheral resistance, systemic arterial compliance, and maximal left-ventricular elastance. We compared the changes in these cardiovascular model-based estimates to changes from more conventional estimates made without the use of physics-based models by correlation analysis. Additionally, ordinary linear regression and linear mixed-effects models were applied to determine the most informative measurements for the selected parameters. We applied maximal aerobic capacity (measured as $$\text{VO2max}$$
VO2max
) data to examine if exercise had any impact on parameters through regression analysis and case studies.

Results and conclusions
Parameter changes in arterial parameters estimated using the cardiovascular models correlated moderately well with conventional estimates. Estimates based on carotid pressure waveforms gave higher correlations (0.59 and above when p$$<0.05$$

<
0.05

) than those for finger arterial pressure. Parameter changes over the 12-week study duration were of similar magnitude when compared to short-term changes after a bout of intensive exercise in the same parameters. The short-term changes were computed from measurements made immediately before and 24 h after a cardiopulmonary exercise test used to measure $$\text{VO2max}$$
VO2max
. Regression analysis indicated that changes in $$\text{VO2max}$$
VO2max
did not account for any substantial amount of variability in total peripheral resistance, systemic arterial compliance, or maximal left-ventricular elastance. On the contrary, changes in stroke volume contributed to far more explained variability. The results suggest that more research is required to be able to accurately track exercise-induced changes in the vasculature for people with pre-hypertension and hypertension using lumped-parameter models.