A novel cardiovascular systems model to quantify drugs effects on the inter-relationship between contractility and other hemodynamic variables

Abstract

The use of systems-based pharmacological modeling approaches to characterize mode-of-action and concentration-effect relationships for drugs on specific hemodynamic variables has been demonstrated. Here, we (i) expand a previously developed hemodynamic system model through integration of cardiac output (CO) with contractility (CTR) using pressure-volume loop theory, and (ii) evaluate the contribution of CO data for identification of system-specific parameters, using atenolol as proof-of-concept drug. Previously collected experimental data was used to develop the systems model, and included measurements for heart rate (HR), CO, mean arterial pressure (MAP), and CTR after administration of atenolol (0.3-30 mg/kg) from three in vivo telemetry studies in conscious Beagle dogs. The developed cardiovascular (CVS)-contractility systems model adequately described the effect of atenolol on HR, CO, dP/dtmax, and MAP dynamics and allowed identification of both system- and drug-specific parameters with good precision. Model parameters were structurally identifiable, and the true mode of action can be identified properly. Omission of CO data did not lead to a significant change in parameter estimates compared to a model that included CO data. The newly developed CVS-contractility systems model characterizes short-term drug effects on CTR, CO, and other hemodynamic variables in an integrated and quantitative manner. When the baseline value of total peripheral resistance is predefined, CO data was not required to identify drug- and system-specific parameters. Confirmation of the consistency of system-specific parameters via inclusion of data for additional drugs and species is warranted. Ultimately, the developed model has the potential to be of relevance to support translational CVS safety studies.

FIGURE 1

Quantitative inter‐relationships in left ventricle (LV) pressure‐volume loop. (1) Red dashed line 1: the afterload relationship. The slope equals the arterial elastance (E_A), which is the product of heart rate (HR) and total peripheral resistance (TPR). Its x‐axis intercept is end diastolic volume (EDV); (2) Blue dashed line 2: the end‐systolic pressure‐volume relationship (ESPVR) with the slope contractility (CTR) and x‐axis intercept of V₀, which is the minimum volume needed to get pressure in left ventricle; P_A: the pressure at the intersection point A of line 1 and line 2, when aortic valve closes in a single cardiac cycle; SV: stroke volume, the difference between EDV and end systolic volume (ESV)

FIGURE 2

CVS‐contractility model structure to characterize drug effects on the cardiovascular systems. HR, heart rate; CTR, contractility; CTRM, contractility measurements variable for dP/dt_max; TPR, total peripheral resistance; MAP, mean arterial pressure; CO, cardiac output; SV, stroke volume; ESV, end‐systolic volume; EDV, end‐diastolic volume; E_A, arterial elastance. HR, TPR, and CTR are regulated by negative feedback through MAP, where FB represents the magnitude of feedback on HR, TPR, and CTR. Effects on HR, CTR, EDV, and TPR are described by four linked turnover equations, in which ${\mathrm{k}}_{\mathrm{inHR}}$, ${\mathrm{k}}_{\mathrm{inEDV}}$, ${\mathrm{k}}_{\mathrm{inTPR}}$, and ${\mathrm{k}}_{\mathrm{inCTR}}$ represent the zero‐order production rate constants, and ${\mathrm{k}}_{\mathrm{outHR}}$, ${\mathrm{k}}_{\mathrm{outEDV}}$, ${\mathrm{k}}_{\mathrm{outTPR}}$, and ${\mathrm{k}}_{\mathrm{outCTR}}$ represent the first‐order degradation rate constants of HR, EDV, TPR, and CTR, respectively. CTRM is the variable for dP/dt_max, which is influenced by CTR and EDV. The inter‐relationships between ESV, EDV, EA, and CTR are illustrated in Figure 1. Potential drug effect cites are indicated in orange. Hemodynamic variables which can be observed are indicated in light blue

FIGURE 3

Visual predictive check for the final model. (a) Study 1 data following administration of placebo, 3 mg/kg, 10 mg/kg, and 30 mg/kg atenolol. (b) Study 2 data following administration of placebo, 1 mg/kg, 3 mg/kg, and 10 mg/kg atenolol. The grey points and grey lines represent the observed data for biomarkers of HR, dP/dt_max, CO, and MAP. The black lines represent the median of the observed data for each biomarker. The shaded blue areas represent the 95% CI of the median of the predictions. CI, confidence interval; CO, cardiac output; HR, heart rate; MAP, mean arterial pressure

FIGURE 4

Identification of the site of action of compounds with effects on HR, CTR, or TPR. The y‐axis shows the delta objective function value of the re‐estimated models compared to a model with no drug effect. The red bars are incorrect alternative models, which do not match the original model, and the green bars are correct alternative models, which match the original model. The SD bars represent the standard error around the mean value. CTR, contractility; HR, heart rate; MAP, mean arterial pressure; TPR, total peripheral resistance

FIGURE 5

Signature profiles following administration of 30 mg of a hypothetical compound with negative effect on HR (panel a), CTR (panel b), and TPR (panel c), respectively. The red lines represent a decrease the biomarkers after pharmacological intervention. The green lines represent an increase in the biomarkers after pharmacological intervention. CO, cardiac output; CTR, contractility; HR, heart rate; MAP, mean arterial pressure; TPR, total peripheral resistance