(H-282) Evaluating temporal convergence in personalized hemodynamic simulations of multiple activity states

Introduction:: Digital twins of patient-specific vasculature are proven to recapitulate physiology accurately [1]. State-of-the-art models resolve cardiac flow over single heartbeats and only track for specific conditions like rest or medically-induced exercise states under clinical settings [2]. Recently, consumer-grade wearables have become ubiquitous and offer the capability to monitor physical states over time continuously [3]. Driving blood flow simulations from wearables would present a new shift towards a longitudinal evaluation of hemodynamic biomarkers beyond single heartbeat analyses.

Simulating hemodynamics over multiple physical states would present scenarios of rapidly changing heart rate, such as when a patient abruptly starts running from resting conditions. Hemodynamic simulations can only be accurate when solutions are temporally converged, where a sufficient number of preceding heartbeats is simulated before evaluating biomarkers on the heartbeat of interest. Literature standard models have only evaluated temporal convergence for single activity states, but discerning temporal convergence requirements in a simulation of multiple activity states remains an open question [2]. A naive approach would simulate excessive preceding heartbeats to ensure temporal convergence but at the expense of computational cost. Clinically accurate digital twins require high-resolution, and simulating an exorbitant number of heartbeats could become intractable, thereby necessitating the evaluation of temporal convergence to determine the minimum required number of preceding heartbeats.

This work aims to evaluate temporal convergence in simulations with multiple physical states, specifically at the interface of different activities. To assess temporal convergence comprehensively, we focus on 5 patient-specific coronary arteries with varying hemodynamic biomarkers and anatomic locations.

Materials and Methods::
Computational simulations were conducted on the left coronary arteries of 5 patient-specific 3D geometries using HARVEY, an in-house 3D fluid simulator [4]. Throughout the study, we referred to the number of preceding cardiac cycles as ’pre-flow’, confirming the temporal convergence for the heartbeat of interest. The hemodynamic parameters of pressure, velocity, and wall shear stress (WSS) were calculated across 4 different arterial locations of the proximal, stenosis, post-stenosis, and near-outlet regions. The WSS magnitude was computed at the neighboring fluid points adjacent to walls [2]. We focused on the extremes including both transitions of high-to-low and low-to-high heart rates to consider the worst-case scenario. These extreme ranges were selected using the heart rates from 53 patients recorded during rest and different activities given by the electrocardiogram (ECG) [5]. From this data sample, the maximum and minimum heart rates observed were 137 (activity) and 44 (resting) beats per minute (BPM), respectively. Since the asymptotical error measurement of calculating the difference between simulation results and their ideal periodic state is not feasible for aperiodic simulations, we assumed the simulations were temporally converged after 5 pre-flow cycles using it as the ground truth based on the existing literature [6, 2]. Percentage differences for the region of interest in each time step were calculated between the ground truth and the preceding cardiac cycle with a threshold of 1% error [7] (Fig. 1).




Results, Conclusions, and Discussions::
Our analysis revealed that the pressure and velocity averaged across 5 patients tend to converge within 1 pre-flow for both high-to-low and low-to-high heart rate transitions (Fig. 1B). The average pressure varied differently for the outlet region compared to the other locations implying that the pressure can vary differently near the outlet (< 1% error). The WSS also converged within 1 pre-flow only for the high-to-low shift across all the arterial locations. However, for low-to-high transitions, the patient-average WSS required more than 1 pre-flow to converge in the proximal region (3.05% error).

Another observation was that the WSS had the highest percent error compared to the pressure and velocity for all cases. This observation is in line with findings from previous studies where the WSS increased with increasing heart rates [8]. Since the WSS is closely subjected to the flow changes around the walls of stenosed coronary arteries, it can be sensitive to the temporal convergence for large heart rate shifts as well [9]. A closer look at the arterial locations revealed that on average, the percent errors were higher in the proximal regions compared to the other locations. These results suggest that for the highest possible shift of heart rate, we may need to take the other arterial regions such as - proximal locations into account whereas the general practice for single heartbeat simulations is to determine the temporal convergence in the near-outlet region of the coronary artery [6]. Although the changes in the hemodynamic flow are hugely dependent on individual patient geometry, the necessity of calibrating each patient’s temporal convergence for different locations for long simulations is quite apparent from the findings of the study.





In conclusion, it is evident from the study that capturing the extreme heartbeat shifts in the longitudinal simulations and comprehensively determining the minimum number of pre-flows can potentially save a considerable amount of compute hours, especially when just 1 pre-flow is sufficient for temporal convergence. Thus, the result of this work will have a wide-ranging impact providing necessary guidance for minimizing the computational burden while maintaining accuracy for longer simulations.




Acknowledgements (Optional): : Research reported in this publication was supported by the National Institute On Aging of the National Institutes of Health under Award Number DP1AG082343. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Computing support for this work came from Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) which is supported by NSF grant number ACI-1548562.

References (Optional): :

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