Poster T17 - Optimizing Temporal Convergence in Cardiovascular Digital Twins Across Multiple Activity States

Introduction: Digital twins, virtual replicas of physiological systems customized to individual patients, have demonstrated remarkable accuracy in recapitulating physiological conditions [1]. However, they are typically reserved for capture of one particular activity such as rest or medically-induced exercise states within clinical settings [2]. Recently, consumer-grade wearables have enabled continuous monitoring of physical states, leading to a focus on longitudinal evaluations of hemodynamic biomarkers beyond single heartbeat analyses [3, 4]. Simulating hemodynamics across multiple physical states, such as abrupt changes in heart rate during activities such as transitioning from rest to exercise, poses significant challenges. Accurate hemodynamic simulations require temporal convergence, in which a sufficient number of preceding heartbeats are simulated before biomarkers on the heartbeat of interest are evaluated. Although the literature has established standards for temporal convergence in simulations of single activity states, determining convergence requirements in simulations involving multiple activity states remains an open question. An existing standard approach to validating temporal convergence in hemodynamic simulations is to simulate excessive preceding heartbeats to obtain converged solutions [ 2, 5] which incurs substantial computational costs and becomes particularly challenging for clinically accurate digital twins that require high-resolution simulations, making it essential to evaluate the minimum number of preceding heartbeats required for temporal convergence.

This study seeks to assess temporal convergence in simulations that encompass multiple physical states, especially at the juncture of different activities. We develop a method to determine the minimal time required to achieve convergence in patient-specific coronary simulations, optimizing the process by reducing computational time.

Materials and

Methods: For ensuring temporal convergence of single-state simulations in resting or activity states, the literature standard is to simulate excessive beats and consider the last cardiac cycle to be converged (Figure 1(A))[2]. Our proposed method sheds light on longitudinal coronary simulations in which shifting from one activity to another can potentially lengthen the time for temporal convergence for the beats following the shift. To understand the impact, we consider two edge cases namely - (i) active to resting (high-to-low) and (ii) resting to active (low-to-high) and evaluate convergence for the beats after the extreme shift (Figure 1(B)). Throughout the study, we refer to the number of preceding cardiac cycles as ’preflow’, which confirms the temporal convergence for any heartbeat of interest. Within the area of post-extreme shift, the beats that do not match the tenth beat (>1% error) are considered to be impacted by the shift temporally and are defined to be in the ’area of influence (AOI)’ region. Consequently, the following beats that match ( < 1% error) with the tenth beat are considered to be under the non-AOI region (see Figure 1 (C)).

Computational simulations were conducted on the left coronary artery of a patient-specific geometry using HARVEY, a 3D fluid simulator [6]. The hemodynamic parameter of wall shear stress (WSS) was calculated in three different locations in the left anterior descending artery, namely stenosis, post-stenosis, and near-outlet locations (see Figure 1 (D)) where the magnitude of WSS was calculated in the neighboring fluid points adjacent to the walls [2].

Results, Conclusions, and Discussions: To determine the minimum number of pre-flows, we quantified temporal convergence based on average WSS calculated across three slice locations, following significant shifts in physical state. WSS is closely subjected to the changes in flow around the walls of stenosed coronary arteries and can be sensitive to temporal convergence for large changes in heart rate [7, 8, 3]. For case (i) of the high-to-low transition, only two beats after the shift were under AOI and the next three beats were not influenced by the shift, as shown in Figure 2(A). A minimum of 1-2 pre-flows were sufficient to obtain convergent results for beats 6-10 with < 1.5% error across all slices (see Figure 2 (B) & (C)).

We further evaluated temporal convergence for case (ii) of the low-to-high transition (Figure 3). Similarly to case (i), the low-to-high transition also showed that only two beats after the shift were affected and the subsequent three beats (8-10) were outside the AOI region (Figure 3(A)). We confirmed that 1-2 pre-flows were sufficient to obtain convergent results in this scenario achieving < 1.5% error (see Figure 3(B) & (C)).

The convergence results provide insights into the reduction in computation time achieved by employing the minimal number of pre-flows compared to the traditional approach of using five preceding cardiac cycles. Using 1 GPU node with 40 tasks per 3D simulation on Duke Compute Cluster, the setup of 2 pre-flows reduced 6.9 and 21.9 hours worth of compute time for cases (i) to (ii), respectively (shown in Figure 4). This reduction highlights the efficiency of using just two preflows instead of five for simulations spanning only 8-10 seconds. For longer time-domain simulations spanning from hours to days, this method will save significant computational time, making it a highly effective strategy for optimizing computational resources.

In conclusion, our findings suggest that optimal pre-flow determination significantly streamlines computational efforts and ensures temporal accuracy in multibeat simulations, which previously lacked a systematic approach. Thus, the result of this work will have a wide-ranging impact providing the necessary guidance to minimize 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.

References:
[1] F. Viola, G. Del Corso, R. De Paulis, and R. Verzicco, “GPU accelerated digital twins of the human heart open new routes for cardiovascular research,” Scientific Reports, vol. 13, p. 8230, May 2023. Publisher: Nature Publishing Group.

[2] M. Vardhan, J. Gounley, S. J. Chen, E. C. Chi, A. M. Kahn, J. A. Leopold, and A. Randles, “Non-invasive characterization of complex coronary lesions,” Scientific reports, vol. 11, no. 1, pp. 1–15, 2021.

[3] C. Tanade, E. Rakestraw, W. Ladd, E. Draeger, and A. Randles, “Cloud Computing to Enable Wearable-Driven Longitudinal Hemodynamic Maps,” in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’23, (New York, NY, USA), pp. 1–14, Association for Computing Machinery, Nov. 2023.

[4] B. Bent, B. A. Goldstein, W. A. Kibbe, and J. P. Dunn, “Investigating sources of inaccuracy in wearable optical heart rate sensors,” NPJ digital medicine, vol. 3, no. 1, p. 18, 2020.

[5] M. R. Pfaller, J. Pham, N. M. Wilson, D. W. Parker, and A. L. Marsden, “On the Periodicity of Cardiovascular Fluid Dynamics Simulations,” Annals of Biomedical Engineering, vol. 49, pp. 3574–3592, Dec. 2021.

[6] A. P. Randles, V. Kale, J. Hammond, W. Gropp, and E. Kaxiras, “Performance analysis of the lattice boltzmann model beyond navier-stokes,” in 2013 IEEE 27th International Symposium on Parallel and Distributed Processing, pp. 1063–1074, IEEE, 2013.

[7] E. Cecchi, C. Giglioli, S. Valente, C. Lazzeri, G. F. Gensini, R. Abbate, and L. Mannini, “Role of hemodynamic shear stress in cardiovascular disease,” Atherosclerosis, vol. 214, no. 2, pp. 249–256, 2011.

[8] J. Jiang and C. Strother, “Computational Fluid Dynamics Simulations of Intracranial Aneurysms at Varying Heart Rates: A “Patient-Specific” Study,” Journal of Biomechanical Engineering, vol. 131, p. 091001, Sept. 2009.