Credibility Assessment of a Subject-Specific Mathematical Model of Blood Volume Kinetics for Prediction of Physiological Response to Hemorrhagic Shock and Fluid Resuscitation

Abstract

Subject-specific mathematical models for prediction of physiological parameters such as blood volume, cardiac output, and blood pressure in response to hemorrhage have been developed. In silico studies using these models may provide an effective tool to generate pre-clinical safety evidence for medical devices and help reduce the size and scope of animal studies that are performed prior to initiation of human trials. To achieve such a goal, the credibility of the mathematical model must be established for the purpose of pre-clinical in silico testing. In this work, the credibility of a subject-specific mathematical model of blood volume kinetics intended to predict blood volume response to hemorrhage and fluid resuscitation during fluid therapy was evaluated. A workflow was used in which: (i) the foundational properties of the mathematical model such as structural identifiability were evaluated; (ii) practical identifiability was evaluated both pre- and post-calibration, with the pre-calibration results used to determine an optimal splitting of experimental data into calibration and validation datasets; (iii) uncertainty in model parameters and the experimental uncertainty were quantified for each subject; and (iv) the uncertainty was propagated through the blood volume kinetics model and its predictive capability was evaluated via validation tests. The mathematical model was found to be structurally identifiable. Pre-calibration identifiability analysis led to splitting the 180 min of time series data per subject into 50 and 130 min calibration and validation windows, respectively. The average root mean squared error of the mathematical model was 12.6% using the calibration window of (0 min, 50 min). Practical identifiability was established post-calibration after fixing one of the parameters to a nominal value. In the validation tests, 82 and 75% of the subject-specific mathematical models were able to correctly predict blood volume response when predictive capability was evaluated at 180 min and at the time when amount of infused fluid equals fluid loss.

Keywords: fluid resuscitation; mathematical model; model credibility assessment; model validation; subject-specific; workflow.

FIGURE 1

Model fluid input (A) and change in blood volume (B) for subjects 1 and 2.

FIGURE 2

Entire cohort singular values for $\frac{K_p}{\mathrm{\hspace{0.25em}1}+{\mathrm{\alpha }}_v}$, K_p, and $\frac{K_p}{\mathrm{\hspace{0.25em}1}+{\mathrm{\alpha }}_u}$ as determined by the approximation of the right singular matrix. Plot on the bottom right indicates the experimental protocol used for data collection depicting timing of fluid hemorrhage and infusion. X-axis of the singular value plots relates to the amount of experimental data under consideration, for example T_c = 50 min corresponds to considering all data between 0 and 50 min. The calibration window of 0–50 min was selected because it was the largest time window that would allow for evaluation of model prediction in an independent data segment (i.e., 50–180 min) containing both infusion and hemorrhage while still having relatively large singular values for majority of subjects in the study. Overall, it can be concluded that α_v is more identifiable than α_u.

FIGURE 3

Cost function visualization for the subject 20 for the three parameter model. (A) Cost function as a function of α_u and α_vat fixed K_p. The direction of unbounded ellipses representing cost function contours demonstrates unidentifiability of α_u. (B) Cost function as a function of K_p and α_v at fixed α_u values.

FIGURE 4

Calibration results for the two parameter model.

FIGURE 5

95% confidence regions for the calibrated parameters using the two parameter model. Subjects 3 and 16 were excluded because calibrated parameters were outside physiological range (see section “Discussion”).

FIGURE 6

Subject-specific model calibration and validation. Each figure represents a different animal (subjects 3 and 16 were excluded because parameters were not identifiable for these subjects). Model was calibrated to experimental data between 0 and 50 min (model: green line, experiment: triangles). Model was then simulated from 50 to 180 min (red dashed line) and can be compared against experimental measurements (triangles) (model validation). Shaded regions represent 95% confidence intervals.