Modeling the hemodynamic response to dopamine in acute heart failure

A Modeling Tool to Study the Combined Effects of Drug Administration and Lvad Assistance in Pathophysiological Circulatory Conditions

The aim of this work is to develop a tool to study the effect of sodium nitroprusside (SNP) on hemodynamics in conjunction with baroreflex and mechanical circulatory assistance. To this aim, a numerical model of the pharmacodynamic effect of SNP was developed and inserted into a cardiovascular circulatory model integrated with baroreflex and LVAD (continuous flow pump with atrio-aortic connection) sub-models.

The experiments were carried out in two steps. In the first step the model was verified comparing simulations with experimental data acquired from mongrel dogs on mean arterial pressure (MAP), cardiac output (CO), heart rate (HR), peripheral resistance, and left ventricular properties.

In the second step, the combined action of SNP and mechanical circulatory assistance was studied. Data were measured at pump off and at pump on (20000 rpm and 24000 rpm). At pump off, with a 2.5 μg/kg per min SNP infusion in heart failure condition, the MAP was reduced by approximately 8%, CO and HR increased by about 16% and 18%, respectively. In contrast, during assistance (24000 rpm) the changes in MAP, CO and HR were around −9%, +12%, and +20%, respectively. Furthermore, the effects of the drug on hemodynamic parameters at different heart conditions were significantly different. Thus, the model provides insight into the complex interactions between baroreflex, drug infusion, and LVAD and could be a support for clinical decision-making in cardiovascular pathologies.

Prediction of Hemodynamic Response to Epinephrine via Model-Based System Identification

In this study, we present a system identification approach to the mathematical modeling of hemodynamic responses to vasopressor-inotrope agents. We developed a hybrid model called the latency-dose-response-cardiovascular (LDC) model that incorporated 1) a low-order lumped latency model to reproduce the delay associated with the transport of vasopressor-inotrope agent and the onset of physiological effect, 2) phenomenological dose-response models to dictate the steady-state inotropic, chronotropic, and vasoactive responses as a function of vasopressor-inotrope dose, and 3) a physiological cardiovascular model to translate the agent's actions into the ultimate response of blood pressure. We assessed the validity of the LDC model to fit vasopressor-inotrope dose-response data using data collected from five piglet subjects during variable epinephrine infusion rates. The results suggested that the LDC model was viable in modeling the subjects' dynamic responses: After tuning the model to each subject, the r (2) values for measured versus model-predicted mean arterial pressure were consistently higher than 0.73. The results also suggested that intersubject variability in the dose-response models, rather than the latency models, had significantly more impact on the model's predictive capability: Fixing the latency model to population-averaged parameter values resulted in r(2) values higher than 0.57 between measured versus model-predicted mean arterial pressure, while fixing the dose-response model to population-averaged parameter values yielded nonphysiological predictions of mean arterial pressure. We conclude that the dose-response relationship must be individualized, whereas a population-averaged latency-model may be acceptable with minimal loss of model fidelity.

An analytic tool for prediction of hemodynamic responses to vasopressors

This paper presents a new analytic tool for automated control of vasopressor infusion, which uses measured changes in blood pressure to infer changes in the underlying cardiovascular system and then estimate dose-response relationships for the underlying cardinal cardiovascular parameters, i.e., those related to cardiac output (CO) and total peripheral resistance (TPR). Ultimately, blood pressure as a function of vasopressor dose is predicted based on the estimated underlying cardiovascular state by extrapolating the dose-response relationship. As well, this tool adapts to individual subjects with a minimum of individualized training data. In this report, proof-of-principle is provided using experimental epinephrine dose-response data from four different sets of subjects. Given two observations from different infusion rates, the analytic tool was able to accurately predict the groups' blood pressure, heart rate, TPR, stroke volume, and CO as a function of vasopressor dose levels: the root-mean-squared prediction error for the mean arterial pressure (MAP) was consistently smaller than 5% of the underlying MAP; the r(2) values for the TPR, stroke volume, and CO were consistently higher than 0.96; and the limits of agreement between actual versus predicted blood pressure (BP), TPR, stroke volume, and CO were consistently smaller than 8% of the respective underlying values. The proposed analytic tool may provide a meaningful step towards automated control of vasopressor therapy.

Model-based estimation of blood pressure response to epinephrine

In this study, we present a model-based approach to estimation of blood pressure (BP) response to epinephrine. The proposed approach estimates systolic (SBP), mean (MAP) and diastolic (DBP) BP based on a 2-parameter windkessel (WK) model with dose-dependent total peripheral resistance (TPR), arterial compliance (AC) and stroke volume (SV) indices that is driven by the epinephrine dose, heart rate (HR). Using the epinephrine dose and hemodynamic response data collected for young/old normotensive and hypertensive subject groups, four group-specific models as well as a generalized model were developed and then were evaluated for BP estimation performance. The results indicated that the group-specific model is superior to its generalized counterpart; on average, the root-mean-squared SBP, MAP and DBP estimation errors associated with the group-specific model were only 34%, 52% and 69%, respectively, compared with the generalized model.

A tool predicting future mean arterial blood pressure values improves the titration of vasoactive drugs

BACKGROUND

Vasoactive drug infusion rates are titrated to achieve a desired effect, e.g., mean arterial blood pressure (MAP), rather than using infusion rates based on body weight. The purpose of this study is to evaluate a method to automatically identify a patient's sensitivity to sodium-nitroprusside, dobutamine or dopamine and to evaluate, whether an advisory system that predicts MAP 5 min in the future enhances a clinician's ability to titrate sodium-nitroprusside infusions.

METHODS

We used published models implemented in MATLAB to simulate the response of 100 individual patients to infusions of sodium-nitroprusside, dopamine and dobutamine. The simulated patient's sensitivity to the three drugs was identified using an adaptive filter approach, where MAP was altered in a binary stepwise fashion. Next, 9 nurses were asked to control the MAP of 6 of the simulated patients. For half of the patients, we used the identified sensitivity to predict and display MAP 5 min into the future.

RESULTS

Identifying each individual patient's sensitivity improved the accuracy of the MAP prediction by 75% for sodium-nitroprusside, 82% for dopamine and 52% for dobutamine over the MAP prediction based on an "average" patient's sensitivity. The advisory system shortened the median time to reach the desired MAP from 10.2 to 4.1 min, decreased the median number of infusion rate changes from 6 to 4, and resulted in a significant reduction of mental workload and effort.

DISCUSSION

Patient-specific drug sensitivity identifi- cation significantly improved the prediction of future MAP. By predicting and displaying the expected MAP 5 min in the future, the advisory system helped nurses titrate faster, reduced their perceived workload and might improve patient safety.

Computationally managed bradycardia improved cardiac energetics while restoring normal hemodynamics in heart failure

In acute heart failure, systemic arterial pressure (AP), cardiac output (CO), and left atrial pressure (P (LA)) have to be controlled within acceptable ranges. Under this condition, cardiac energetic efficiency should also be improved. Theoretically, if heart rate (HR) is reduced while AP, CO, and P (LA) are maintained by preserving the functional slope of left ventricular (LV) Starling's curve (S (L)) with precisely increased LV end-systolic elastance (E (es)), it is possible to improve cardiac energetic efficiency and reduce LV oxygen consumption per minute (MVO (2)). We investigated whether this hemodynamics can be accomplished in acute heart failure using an automated hemodynamic regulator that we developed previously. In seven anesthetized dogs with acute heart failure (CO < 70 mL min(-1) kg(-1), P (LA) > 15 mmHg), the regulator simultaneously controlled S (L) with dobutamine, systemic vascular resistance with nitroprusside and stressed blood volume with dextran or furosemide, thereby controlling AP, CO, and P (LA). Normal hemodynamics were restored and maintained (CO; 88 +/- 3 mL min(-1) kg(-1), P (LA); 10.9 +/- 0.4 mmHg), even when zatebradine significantly reduced HR (-27 +/- 3%). Following HR reduction, E (es) increased (+34 +/- 14%), LV mechanical efficiency (stroke work/oxygen consumption) increased (+22 +/- 6%), and MVO (2) decreased (-17 +/- 4%) significantly. In conclusion, in a canine acute heart failure model, computationally managed bradycardia improved cardiac energetic efficiency while restoring normal hemodynamic conditions.

Automatic regulation of hemodynamic variables in acute heart failure by a multiple adaptive predictive controller based on neural networks

Automated drug-delivery systems that can tolerate various responses to therapeutic agents have been required to control hemodynamic variables with heart failure. This study is intended to evaluate the control performance of a multiple adaptive predictive control based on neural networks (MAPC_NN) to regulate the unexpected responses to therapeutic agents of cardiac output (CO) and mean arterial pressure (MAP) in cases of heart failure. The NN components in the MAPC_NN learned nonlinear responses of CO and MAP determined by hemodynamics of dogs with heart failure. The MAPC_NN performed ideal control against unexpected (1) drug interactions, (2) acute disturbances, and (3) time-variant responses of hemodynamics [average errors between setpoints (+35 ml kg⁻¹ min⁻¹ in CO and ±0 mmHg in MAP) and observed responses; 6.4, 3.7, and 4.2 ml kg⁻¹ min⁻¹ in CO and 1.6, 1.4, and 2.7 mmHg (10.5, 20.8, and 15.3 mmHg without a vasodilator) in MAP] during 120-min closed-loop control. The MAPC_NN could also regulate the hemodynamics in actual heart failure of a dog. Robust regulation of hemodynamics by the MAPC_NN was attributable to the ability of on-line adaptation to adopt various responses and predictive control using the NN. Results demonstrate the feasibility of applying the MAPC_NN using a simple NN to clinical situations.

Hemodynamic management of congestive heart failure by means of a multiple mode rule-based control system using fuzzy logic

A rule-based system was designed to control the mean arterial pressure (MAP) and the cardiac output (CO) of a patient with congestive heart failure (CHF), using two vasoactive drugs: sodium nitroprusside (SNP) and dopamine (DPM). The controller has three different modes, that engage according to the hemodynamic state. The critical conditions control mode (CCC) determines the initial infusion rates, and continues active if the MAP or the CO fall outside of the defined criticality thresholds: an upper and a lower boundary for the MAP and a lower boundary for the CO. Inside the boundaries the control is performed by noncritical conditions control modes (NCC's), which are fuzzy logic controllers. If the CO is within normal range and the MAP is close to the goal range, then the MAP is driven using only SNP, in a single-input-single-output mode (NCC-SISO). Otherwise the NCC multiple-input-multiple-output is active (NCC-MIMO). The goal values for the controlled variables are defined as a band of 5 mmHg for the MAP and 5 mL/kg/min for the CO, but there is little concern for this application if the CO is too high (i.e., in practical terms the CO only needs to achieve a necessary minimum rate). The NCC-MIMO includes a gain adaptation algorithm to cope with the wide variety in sensitivities to SNP. Supervisory capabilities to ensure adequate drug delivery complete the controller scheme. After extensive testing and tuning on a CHF-hemodynamics nonlinear model, the control system was applied in dog experiments, which led to further enhancements. The results show an adequate control, presenting a fast response to setpoint changes with an acceptable overshoot.

Computer-controlled heart rate increase by isoproterenol infusion: mathematical modeling of the system

The purpose of this study was mathematical modeling of the heart rate (HR) response to isoproterenol (Iso) infusion. We developed a computerized system for the controlled increase of HR by Iso, based on a modified proportional-integral controller. HR was measured in conscious, freely moving rats. We found that the steady-state HR can be described as a hyperbolic power function of the steady-state Iso flow rate. This dependence was coupled with a first-order difference equation to form a pharmacodynamic model that reliably describes the relationship between HR and Iso flow for any arbitrary form of Iso flow function. In simulation studies, we showed that the model continued to follow the HR curve from real-time experiments far beyond the initial "learning interval" from which its parameters were calculated. Our results suggest that the predictive ability and the simplicity of calculating the parameters render this pharmacodynamic model appropriate for use within future advanced, model-based, adaptive control systems and as a part of larger cardiovascular models.

A model for the design and evaluation of algorithms for closed-loop cardiovascular therapy

Developing a clinically useful closed-loop drug delivery system can be extremely time consuming and costly. One approach to reducing the time and cost associated with developing closed-loop systems is to reduce the number of animal experiments and perform an extensive set of simulation studies. Through simulations, a closed-loop controller's performance can be evaluated over a complete spectrum of the patient population, including boundary conditions. Simulation studies are repeatable, offering significant advantages in comparing modifications in control algorithms. Finally, simulation studies can be performed in a fraction of the time required for animal studies, at a fraction of the cost. We have developed a simulator, that included a nonlinear pulsatile-flow cardiovascular model, a physiological regulatory mechanism, and the pharmacology of four frequently titrated cardiovascular drugs. This simulator has already been used in the design and evaluation of two closed-loop algorithms-a self-tuning regulator (STR) and a multiple model adaptive controller (MMAC)-for blood pressure control during and after cardiac surgery.

Multiple drug hemodynamic control by means of a supervisory-fuzzy rule-based adaptive control system: validation on a model

A control device that uses an expert system approach for a two input-two output system has been developed and evaluated using a mathematical model of the hemodynamic response of a dog. The two inputs are the infusion rates of two drugs: sodium nitroprusside (SNP) and dopamine (DPM). The two controlled variables are the mean arterial pressure and the cardiac output. The control structure is dual mode, i.e., it has two levels: a critical conditions (coarse) control mode and a noncritical conditions (fine) control mode. The system switches from one to the other when threshold conditions are met. Different "controller parameters sets"-including the values for the threshold conditions-can be given to the system which will lead to different controller outputs. Both control modes are rule-based, and supervisory capabilities are added to ensure adequate drug delivery. The noncritical control mode is a fuzzy logic controller. The system includes heuristic features typically considered by anesthesiologists, like waiting periods and the observance of a "forbidden dosage range" for DPM infusion when used as an inotrope. An adaptation algorithm copes with the wide range of sensitivities to SNP found among different individuals, as well as the time varying sensitivity frequently observed in a single patient. The control device is eventually tested on a nonlinear model, designed to mimic the conditions of congestive heart failure in a dog. The test runs show a highest overshoot of 3 mmHg with nominal SNP sensitivity. When tested with different simulated SNP sensitivities, the controller adaptation produces a faster response to lower sensitivities, and reduced oscillations to higher sensitivities. The simulations seem to show that the system is able to drive and adequately keep the two hemodynamic variables within prescribed limits.

Multiple-model adaptive predictive control of mean arterial pressure and cardiac output

A multiple-model adaptive predictive controller has been designed to simultaneously regulate mean arterial pressure and cardiac output in congestive heart failure subjects by adjusting the infusion rates of nitroprusside and dopamine. The algorithm is based on the multiple-model adaptive controller and utilizes model predictive controllers to provide reliable control in each model subspace. A total of 36 linear small-signal models were needed to span the entire space of anticipated responses. To reduce computation time, only the six models with the highest probabilities were used in the control calculations. The controller was evaluated on laboratory animals that were either surgically or pharmacologically altered to exhibit symptoms of congestive heart failure. During trials, the controller performance was robust with respect to excessive switching between models and nonconvergence to a single dominant model. A comparison is also made with a previous multiple-drug controller design.