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A Mathematical Model of the Cardiovascular System Response to Fluid Perturbation

Catalog of Regulatory Science Tools to Help Assess New Medical Devices 

This regulatory science tool is a mathematical model of the cardiovascular system response to fluid perturbations and includes a cohort generation tool to simulate virtual subjects as part of non-clinical testing of physiologic closed-loop control algorithms that automate fluid infusions following blood loss.

Technical Description

The cardiovascular system mathematical model is a low-order lumped parameter model, which is used with a compartment-based virtual cohort generation tool, described in detail here [1]. Software code to implement the model and cohort generation tool are available here [2] built in the MATLAB Simulink environment. Inputs to the model include rate of blood loss (hemorrhage), urinary output, and fluid infusion and time-varying outputs include hematocrit, blood volume, heart rate, stroke volume, cardiac output, and mean arterial blood pressure. The model is organized as four integrated compartments for blood volume, heart rate, stroke volume, and mean arterial blood pressure response and includes a total of 25 parameters. The code implementing the model is currently configured to receive preset input variables over time but can be adapted to interact with a control algorithm for fluid infusion. The mathematical model is developed and evaluated using data collected from animal subjects (sheep and swine) during hemorrhage and fluid infusion experiments [1,3].  A compartment-based virtual cohort generation tool is used to simulate virtual subjects and generate a prediction envelope used for model predictive capability performance evaluation [1,4].  Physiologic virtual subjects with varying responses can be generated using the model and virtual cohort generation tool.

Intended Purpose 

As noted in the FDA Guidance Document “Technical Considerations for Medical Devices with Physiologic Closed-loop Control technology” [6], testing physiologic closed-loop controlled (PCLC) medical devices with computational models can be part of the PCLC development and evaluation process. This tool provides a computational model that can be incorporated into non-clinical test methods as part of the evaluation and performance characterization of physiologic closed-loop control algorithms for automated fluid resuscitation for a range of inter- and intra-subject variability (for example, see [5]).

Testing

The model has been evaluated using two distinct sets of data [1]. The first dataset from 27 experiments performed on non-anesthetized sheep [1,3] was utilized for model development and an initial round of model assessment through a leave-one-out cross-validation procedure. The second dataset from 12 anesthetized swine data served as independent test data for the subsequent evaluation of the model as described in [1]. The model’s predictive capability to generate virtual cohorts for each test subject was evaluated using the normalized interval score, the number of simulations showing a relevant response, and the closest simulated subject to each experimental response [1].  The results indicate that the model can simulate virtual subjects under a broad range of physiologic conditions.

Limitations

The tool is limited to testing physiologic closed-loop control algorithms for automating fluid infusions following blood loss. The model has been tested with crystalloid (Lactated Ringer’s solution) and colloid (for example, 5% Albumin) fluid infusions but has not been evaluated for other fluids such as whole blood. The model has not been studied in patients and is not designed or evaluated during hyperdynamic conditions or other clinical conditions where fluid delivery may be warranted (for example, sepsis). The model has not been designed or tested in other applications or in conjunction with other therapies, such as vasoactive and inotrope administration, or other PCLC applications. The model does not provide waveforms or dynamic measures of hemodynamic variables such as stroke volume variation. In addition, systolic and diastolic blood pressures are not outputs, and, therefore, the model is limited to testing controllers that use mean arterial blood pressure, stroke volume, or cardiac output as the physiologic variable to be controlled. The virtual cohort generator produces a broad spectrum of physiologic and non-physiologic simulations. Among the physiologic scenarios, it can simulate a wide range of responses, including those of fluid responders, non-responders, or less-responsive individuals to fluid infusion, as well as cases with strong baroreflex resulting in a rapid mean arterial blood pressure increase after hemorrhage with minimal infusion. Given this wide range of simulated responses, non-relevant simulations for testing closed-loop control algorithms should be identified in advance. This tool does not include any specific test methods or acceptance criteria using the model for device evaluation. The model’s performance has been tested in conjunction with the proposed cohort generation tool. If a new cohort generation tool is implemented, the model’s predictive capability should be reevaluated accordingly. Additional information on the experimental conditions where the model has been evaluated are available in [1] and summarized in Section 7 of the instructions for use document [2]. 

Supporting Documentation

Software code and instructions to generate a cohort of virtual subjects for a representative test subject are available here.

Reference: 

[1] Y. R. Chalumuri, G. Arabidarrehdor, A. Tivay, C. M. Sampson, M. Khan, G. Kramer, J. O. Hahn, C. G. Scully, R. Bighamian,  "A Lumped-Parameter Model of the Cardiovascular System Response for Evaluating Automated Fluid Resuscitation Systems", IEEE Access, vol. 12, pp. 62511-62525, 2024, doi: 10.1109/ACCESS.2024.3395008.

[2] https://github.com/dbp-osel/Credible-mathematical-model-of-the-cardiovascular-system-response-to-fluid-perturbation

[3] A.D. Rafie, P. A. Rath, M. W. Michell, R. A. Kirschner, D. J. Deyo, D. S. Prough , J. J. Grady, G. C. Kramer, “Hypotensive Resuscitation of Multiple Hemorrhages using Crystalloid and Colloids”, Shock, 2004 Sep;22(3):262-9. doi: 10.1097/01.shk.0000135255.59817.8c.

[4] V. Kanal, P. Pathmanathan, J. O. Hahn, G. Kramer, C. Scully, R. Bighamian, “Development and Validation of a Mathematical Model of Heart Rate Response to Fluid Perturbation”, Sci Rep. 2022 Dec 12;12(1):21463. doi: 10.1038/s41598-022-25891-y.

[5] H. Mirinejad, B. Parvinian, M. Ricks, Y. Zhang, S. Weininger, J. O. Hahn, C. G. Scully, “Evaluation of Fluid Resuscitation Control Algorithms via a Hardware-in-the-Loop Test Bed”, IEEE Trans Biomed Eng. 2020 Feb;67(2):471-481. doi: 10.1109/TBME.2019.2915526. 

[6] https://www.fda.gov/regulatory-information/search-fda-guidance-documents/technical-considerations-medical-devices-physiologic-closed-loop-control-technology

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