Physiological Modeling of Hemodynamic Responses to Sodium Nitroprusside
Abstract
:1. Introduction
2. Methods
2.1. Base Computational Model
2.2. Addition of SNP to the Model
2.3. Animal Data
2.4. Individual Model Fitting
- First, using the initial starting parameters shown in Table 1, a plasma SNP concentration was calculated from the administration rates, φ1 (half-life), and φ2 (infusion-to-onset delay).
- Cardiac stroke volume was calculated using Equation (12b) above and the initial θ1–4 and φ5 parameters in Table 1.
- The root-mean-squared error (RMSE) was then calculated between the measured SV and the simulated SV. RMSE was used as the minimization criterion as this is the parameter reported by the authors in the original Bighamian model, so it made a useful direct comparator.
- Each of the parameters θ1, θ2, θ3, θ4, and φ5 was individually increased and decreased by 10%, and the cardiac stroke volume and resulting RMSE from the new set was recalculated. The modification that resulted in the largest decrease in RMSE was implemented.
- Step 4 was repeated until no modification of a parameter resulted in at least a 1% reduction in RMSE.
- φ1 and φ2 were then individually increased and decreased by 10% and the stroke volume and RMSE recalculated, and the process returned to step 1, calculating new plasma concentrations using the new values and then repeating the fitting process in steps 2–5. The change resulting in the largest reduction of RMSE for φ1 and φ2 was implemented.
- Step 6 was continued until no change in φ1 and φ2 parameters resulted in at least a 1% reduction in RMSE.
- Finally, once the process above was completed, since φ3 and φ4 affect only MAP, they were calculated last using a grid search process identical to steps 4 and 5 above but using a simulated MAP instead of a simulated SV (with said MAP calculated using the previously calculated simulated SV and the model parameters in Equation (14b)) against recorded MAP to calculate RMSE scores.
2.5. Statistical Analysis and Reporting
3. Results
4. Discussion
4.1. Limitations
4.2. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Model Parameter | Initial Value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Mean | SD | % Var |
---|---|---|---|---|---|---|---|---|---|---|---|
Au (crystalloid) | 1.9 | (fixed) | 1.9 | 0 | 0 | ||||||
Au (colloid) | 0.0 | (fixed) | 0.0 | 0 | 0 | ||||||
Av | 0.13 | (fixed) | 0.13 | 0 | 0 | ||||||
Kp | 0.0031 | (fixed) | 0.0031 | 0 | 0 | ||||||
Ki | 1.09 | (fixed) | 1.09 | 0 | 0 | ||||||
θ1 | 13 | 16 | 12 | 16 | 14 | 13 | 13 | 14 | 14 | 1.4 | 10 |
θ2 | −1.0 | −4.3 | 0.0 | 0.0 | −6.9 | −5.0 | −4.6 | −4.9 | −3.7 | 2.6 | −72 |
θ3 | 0.29 | 0.58 | 0.60 | 0.59 | 0.58 | 0.59 | 0.65 | 0.68 | 0.61 | 0.04 | 6 |
θ4 | −420 | 46 | 0 | 0 | 0 | 101 | 130 | 175 | 65 | 71 | 111 |
φ1 | 120 | 144 | 46 | 187 | 207 | 108 | 120 | 120 | 133.2 | 53.2 | 40 |
φ2 | 60 | 104 | 72 | 179 | 149 | 60 | 60 | 60 | 98 | 49 | 50 |
φ3 | 200 | 1013 | 300 | 675 | 675 | 102 | 200 | 300 | 466.4 | 327.6 | 70 |
φ4 | 1.0 | 0.73 | 1.00 | 0.73 | 0.81 | 1.56 | 1.00 | 1.00 | 0.98 | 0.29 | 29 |
φ5 | 2000 | 2000 | 2208 | 1951 | 1951 | 1951 | 2000 | 2000 | 2009 | 91 | 5 |
φ6 | 5.0 | 21.1 | 1.9 | 7.0 | 63.5 | 19.2 | 14.7 | 17.3 | 20.7 | 20.1 | 97 |
Individually Fit Models | Population Models | Partially Fit Models | |||||||
---|---|---|---|---|---|---|---|---|---|
Subject | SV | CO | MAP | SV | CO | MAP | SV | CO | MAP |
1 | 9.6 | 0.8 | 5.5 | 13.2 | 1.1 | 9.5 | 10.7 | 0.9 | 5.4 |
2 | 4.7 | 0.4 | 3.7 | 26.9 | 1.9 | 7.8 | 9.3 | 0.7 | 4.4 |
3 | 7.5 | 0.6 | 5.2 | 13.3 | 0.9 | 9.3 | 7.9 | 0.6 | 4.3 |
4 | 7.4 | 0.6 | 4.5 | 8.6 | 0.7 | 8.4 | 7.4 | 0.6 | 4.6 |
5 | 12.1 | 1.0 | 8.6 | 15.0 | 1.3 | 20.4 | 13.7 | 1.2 | 9.4 |
6 | 15.1 | 1.3 | 6.5 | 16.3 | 1.3 | 11.9 | 16.8 | 1.3 | 6.5 |
7 | 18.6 | 1.6 | 4.4 | 17.5 | 1.7 | 9.3 | 16.5 | 1.5 | 4.9 |
Mean | 10.7 | 0.9 | 5.5 | 15.8 | 1.3 | 11.0 | 11.8 | 1.0 | 5.7 |
SD | 4.9 | 0.4 | 1.6 | 5.7 | 0.4 | 4.4 | 3.9 | 0.4 | 1.8 |
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Rinehart, J.; Coeckelenbergh, S.; Srivastava, I.; Cannesson, M.; Joosten, A. Physiological Modeling of Hemodynamic Responses to Sodium Nitroprusside. J. Pers. Med. 2023, 13, 1101. https://doi.org/10.3390/jpm13071101
Rinehart J, Coeckelenbergh S, Srivastava I, Cannesson M, Joosten A. Physiological Modeling of Hemodynamic Responses to Sodium Nitroprusside. Journal of Personalized Medicine. 2023; 13(7):1101. https://doi.org/10.3390/jpm13071101
Chicago/Turabian StyleRinehart, Joseph, Sean Coeckelenbergh, Ishita Srivastava, Maxime Cannesson, and Alexandre Joosten. 2023. "Physiological Modeling of Hemodynamic Responses to Sodium Nitroprusside" Journal of Personalized Medicine 13, no. 7: 1101. https://doi.org/10.3390/jpm13071101