A Lumped-Parameter Subject-Specific Model of Blood Volume Response to Fluid Infusion

Dynamic analysis of the individual patterns of intakes, voids, and bladder sensations reported in bladder diaries collected in the LURN study

The goal of this study was to develop the novel analytical approach and to perform an in-depth dynamic analysis of individual bladder diaries to inform which behavioral modifications would best reduce lower urinary tract symptoms, such as frequency and urgency. Three-day bladder diaries containing data on timing, volumes, and types of fluid intake, as well as timing, volumes, and bladder sensation at voids were analyzed for 197 participants with lower urinary tract symptoms. A novel dynamic analytic approach to bladder diary time series data was proposed and developed, including intra-subject correlations between time-varying variables: rates of intake, bladder filling rate, and urge growth rate. Grey-box models of bladder filling rate and multivariable linear regression models of urge growth rate were developed for individual diaries. These models revealed that bladder filling rate, rather than urine volume, was the primary determinant of urinary frequency and urgency growth rate in the majority of participants. Simulations performed with the developed models predicted that the most beneficial behavioral modifications to reduce the number of urgency episodes are those that smooth profiles of bladder filling rate, which might include behaviors such as exclusion of caffeine and alcohol and/or other measures, e.g., increasing number and decreasing volumes of intakes.

Physiological Modeling of Hemodynamic Responses to Sodium Nitroprusside

BACKGROUND

Computational modeling of physiology has become a routine element in the development, evaluation, and safety testing of many types of medical devices. Members of the Food and Drug Administration have recently published a manuscript detailing the development, validation, and sensitivity testing of a computational model for blood volume, cardiac stroke volume, and blood pressure, noting that such a model might be useful in the development of closed-loop fluid administration systems. In the present study, we have expanded on this model to include the pharmacologic effect of sodium nitroprusside and calibrated the model against our previous experimental animal model data.

METHODS

Beginning with the model elements in the original publication, we added six new parameters to control the effect of sodium nitroprusside: two for the onset time and clearance rates, two for the stroke volume effect (which includes venodilation as a "hidden" element), and two for the direct effect on arterial blood pressure. Using this new model, we then calibrated the predictive performance against previously collected animal study data using nitroprusside infusions to simulate shock with the primary emphasis on MAP. Root-mean-squared error (RMSE) was calculated, and the performance was compared to the performance of the model in the original study.

RESULTS

RMSE of model-predicted MAP to actual MAP was lower than that reported in the original model, but higher for SV and CO. The individually fit models showed lower RMSE than using the population average values for parameters, suggesting the fitting process was effective in identifying improved parameters. Use of partially fit models after removal of the lowest variance population parameters showed a very minor decrement in improvement over the fully fit models.

CONCLUSION

The new model added the clinical effects of SNP and was successfully calibrated against experimental data with an RMSE of <10% for mean arterial pressure. Model-predicted MAP showed an error similar to that seen in the original base model when using fluid shifts, heart rate, and drug dose as model inputs.

Dynamic analysis of the individual patterns of intakes, voids, and bladder sensations reported in bladder diaries collected in the LURN study

The goal of this study was to perform an in-depth dynamic analysis of individual bladder diaries to inform which behavioral modifications would best reduce lower urinary tract symptoms, such as frequency and urgency. Three-day bladder diaries containing data on timing, volumes, and types of fluid intake, as well as timing, volumes, and bladder sensation at voids were analyzed for 197 participants with lower urinary tract symptoms. A novel dynamic analytic approach to bladder diary time series data was proposed and developed, including intra-subject correlations between time-varying variables: rates of intake, bladder filling rate, and urge growth rate. Grey-box models of bladder filling rate and multivariable linear regression models of urge growth rate were developed for individual diaries. These models revealed that bladder filling rate, rather than urine volume, was the primary determinant of urinary frequency and urgency growth rate in the majority of participants. Simulations performed with the developed models predicted that the most beneficial behavioral modifications to reduce the number of urgency episodes are those that smooth profiles of bladder filling rate, which might include behaviors such as exclusion of caffeine and alcohol and/or other measures, e.g., increasing number and decreasing volumes of intakes.

Development and validation of a mathematical model of heart rate response to fluid perturbation

Physiological closed-loop controlled (PCLC) medical devices monitor and automatically adjust the patient's condition by using physiological variables as feedback, ideally with minimal human intervention to achieve the target levels set by a clinician. PCLC devices present a challenge when it comes to evaluating their performance, where conducting large clinical trials can be expensive. Virtual physiological patients simulated by validated mathematical models can be utilized to obtain pre-clinical evidence of safety and assess the performance of the PCLC medical device during normal and worst-case conditions that are unlikely to happen in a limited clinical trial. A physiological variable that plays a major role during fluid resuscitation is heart rate (HR). For in silico assessment of PCLC medical devices regarding fluid perturbation, there is currently no mathematical model of HR validated in terms of its predictive capability performance. This paper develops and validates a mathematical model of HR response using data collected from sheep subjects undergoing hemorrhage and fluid infusion. The model proved to be accurate in estimating the HR response to fluid perturbation, where averaged between 21 calibration datasets, the fitting performance showed a normalized root mean square error (NRMSE) of [Formula: see text]. The model was also evaluated in terms of model predictive capability performance via a leave-one-out procedure (21 subjects) and an independent validation dataset (6 subjects). Two different virtual cohort generation tools were used in each validation analysis. The generated envelope of virtual subjects robustly met the defined acceptance criteria, in which [Formula: see text] of the testing datasets presented simulated HR patterns that were within a deviation of 50% from the observed data. In addition, out of 16000 and 18522 simulated subjects for the leave-one-out and independent datasets, the model was able to generate at least one virtual subject that was close to the real subject within an error margin of [Formula: see text] and [Formula: see text] NRMSE, respectively. In conclusion, the model can generate valid virtual HR physiological responses to fluid perturbation and be incorporated into future non-clinical simulated testing setups for assessing PCLC devices intended for fluid resuscitation.

Predicting fluid-response, the heart of hemodynamic management: A model-based solution

BACKGROUND

Intravenous fluid infusions are an important therapy for patients with circulatory shock. However, it is challenging to predict how patients' cardiac stroke volume (SV) will respond, and thus identify how much fluids should be delivered, if any. Model-predicted SV time-profiles of response to fluid infusions could potentially be used to guide fluid therapy.

METHOD

A clinically applicable model-based method predicts SV changes in response to fluid-infusions for a pig trial (N = 6). Validation/calibration SV, SVmea, is from an aortic flow probe. Model parameters are identified in 3 ways: fitting to SVmea from the entire infusion, SVflfit, from the first 200 ml, SVfl200, or from the first 100 ml, SVfl100. RMSE compares error of model-based SV time-profiles for each parameter identification method, and polar plot analysis assesses trending ability. Receiver-operating characteristic (ROC) analysis evaluates ability of model-predicted SVs, SVfl200 and SVfl100, to distinguish non-responsive and responsive infusions, using area-under the curve (AUC), and balanced accuracy as a measure of performance.

RESULTS

RMSE for SVflFit, SVfl200, and SVfl100 was 1.8, 3.2, and 6.5 ml, respectively, and polar plot angular limit of agreement from was 11.6, 28.0, and 68.8°, respectively. For predicting responsive and non-responsive interventions SVfl200, and SVfl100 had ROC AUC of 0.64 and 0.69, respectively, and balanced accuracy was 0.75 in both cases.

CONCLUSIONS

The model-predicted SV time-profiles matched measured SV trends well for SVflFit, SVfl200, but not SVfl100. Thus, the model can fit the observed SV dynamics, and can deliver good SV prediction given a sufficient parameter identification period. This trial is limited by small numbers and provides proof-of-method, with further experimental and clinical investigation needed. Potentially, this method could deliver model-predicted SV time-profiles to guide fluid therapy decisions, or as part of a closed-loop fluid control system.

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

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.

Collective Variational Inference for Personalized and Generative Physiological Modeling: A Case Study on Hemorrhage Resuscitation

OBJECTIVE

Individual physiological experiments typically provide useful but incomplete information about a studied physiological process. As a result, inferring the unknown parameters of a physiological model from experimental data is often challenging. The objective of this paper is to propose and illustrate the efficacy of a collective variational inference (C-VI) method, intended to reconcile low-information and heterogeneous data from a collection of experiments to produce robust personalized and generative physiological models.

METHODS

To derive the C-VI method, we utilize a probabilistic graphical model to impose structure on the available physiological data, and algorithmically characterize the graphical model using variational Bayesian inference techniques. To illustrate the efficacy of the C-VI method, we apply it to a case study on the mathematical modeling of hemorrhage resuscitation.

RESULTS

In the context of hemorrhage resuscitation modeling, the C-VI method could reconcile heterogeneous combinations of hematocrit, cardiac output, and blood pressure data across multiple experiments to obtain (i) robust personalized models along with associated measures of uncertainty and signal quality, and (ii) a generative model capable of reproducing the physiological behavior of the population.

CONCLUSION

The C-VI method facilitates the personalized and generative modeling of physiological processes in the presence of low-information and heterogeneous data.

SIGNIFICANCE

The resulting models provide a solid basis for the development and testing of interpretable physiological monitoring, decision-support, and closed-loop control algorithms.

Accuracy assessment methods for physiological model selection toward evaluation of closed-loop controlled medical devices

Physiological closed-loop controlled (PCLC) medical devices are complex systems integrating one or more medical devices with a patient’s physiology through closed-loop control algorithms; introducing many failure modes and parameters that impact performance. These control algorithms should be tested through safety and efficacy trials to compare their performance to the standard of care and determine whether there is sufficient evidence of safety for their use in real care setting. With this aim, credible mathematical models have been constructed and used throughout the development and evaluation phases of a PCLC medical device to support the engineering design and improve safety aspects. Uncertainties about the fidelity of these models and ambiguities about the choice of measures for modeling performance need to be addressed before a reliable PCLC evaluation can be achieved. This research develops tools for evaluating the accuracy of physiological models and establishes fundamental measures for predictive capability assessment across different physiological models. As a case study, we built a refined physiological model of blood volume (BV) response by expanding an original model we developed in our prior work. Using experimental data collected from 16 sheep undergoing hemorrhage and fluid resuscitation, first, we compared the calibration performance of the two candidate physiological models, i.e., original and refined, using root-mean-squared error (RMSE), Akiake information criterion (AIC), and a new multi-dimensional approach utilizing normalized features extracted from the fitting error. Compared to the original model, the refined model demonstrated a significant improvement in calibration performance in terms of RMSE (9%, P = 0.03) and multi-dimensional measure (48%, P = 0.02), while a comparable AIC between the two models verified that the enhanced calibration performance in the refined model is not due to data over-fitting. Second, we compared the physiological predictive capability of the two models under three different scenarios: prediction of subject-specific steady-state BV response, subject-specific transient BV response to hemorrhage perturbation, and leave-one-out inter-subject BV response. Results indicated enhanced accuracy and predictive capability for the refined physiological model with significantly larger proportion of measurements that were within the prediction envelope in the transient and leave-one-out prediction scenarios (P < 0.02). All together, this study helps to identify and merge new methods for credibility assessment and physiological model selection, leading to a more efficient process for PCLC medical device evaluation.

Mathematical model of volume kinetics and renal function after burn injury and resuscitation

This paper presents a mathematical model of blood volume kinetics and renal function in response to burn injury and resuscitation, which is applicable to the development and non-clinical testing of burn resuscitation protocols and algorithms. Prior mathematical models of burn injury and resuscitation are not ideally suited to such applications due to their limited credibility in predicting blood volume and urinary output observed in wide-ranging burn patients as well as in incorporating contemporary knowledge of burn pathophysiology. Our mathematical model consists of an established multi-compartmental model of blood volume kinetics, a hybrid mechanistic-phenomenological model of renal function, and novel lumped-parameter models of burn-induced perturbations in volume kinetics and renal function equipped with contemporary knowledge on burn-related physiology and pathophysiology. Using the dataset collected from 16 sheep, we showed that our mathematical model can be characterized with physiologically plausible parameter values to accurately predict blood volume kinetic and renal function responses to burn injury and resuscitation on an individual basis against a wide range of pathophysiological variability. Pending validation in humans, our mathematical model may serve as an effective basis for in-depth understanding of complex burn-induced volume kinetic and renal function responses as well as development and non-clinical testing of burn resuscitation protocols and algorithms.

Closed-Loop Control for Fluid Resuscitation: Recent Advances and Future Challenges

Fluid therapy is extensively used to treat traumatized patients as well as patients during surgery. The fluid therapy process is complex due to interpatient variability in response to therapy as well as other complicating factors such as comorbidities and general anesthesia. These complexities can result in under- or over-resuscitation. Given the complexity of the fluid management process as well as the increased capabilities in hemodynamic monitoring, closed-loop fluid management can reduce the workload of the overworked clinician while ensuring specific constraints on hemodynamic endpoints are met with higher accuracy. The goal of this paper is to provide an overview of closed-loop control systems for fluid management and highlight several key steps in transitioning such a technology from bench to the bedside.

Practical Use of Regularization in Individualizing a Mathematical Model of Cardiovascular Hemodynamics Using Scarce Data

Individualizing physiological models to a patient can enable patient-specific monitoring and treatment in critical care environments. However, this task often presents a unique "practical identifiability" challenge due to the conflict between model complexity and data scarcity. Regularization provides an established framework to cope with this conflict by compensating for data scarcity with prior knowledge. However, regularization has not been widely pursued in individualizing physiological models to facilitate patient-specific critical care. Thus, the goal of this work is to garner potentially generalizable insight into the practical use of regularization in individualizing a complex physiological model using scarce data by investigating its effect in a clinically significant critical care case study of blood volume kinetics and cardiovascular hemodynamics in hemorrhage and circulatory resuscitation. We construct a population-average model as prior knowledge and individualize the physiological model via regularization to illustrate that regularization can be effective in individualizing a physiological model to learn salient individual-specific characteristics (resulting in the goodness of fit to individual-specific data) while restricting unnecessary deviations from the population-average model (achieving practical identifiability). We also illustrate that regularization yields parsimonious individualization of only sensitive parameters as well as adequate physiological plausibility and relevance in predicting internal physiological states.

Development and In Silico Evaluation of a Model-Based Closed-Loop Fluid Resuscitation Control Algorithm

OBJECTIVE

To develop and evaluate in silico a model-based closed-loop fluid resuscitation control algorithm via blood volume feedback.

METHODS

Model-based adaptive control algorithm for fluid resuscitation was developed by leveraging a low-order lumped-parameter blood volume dynamics model, and then in silico evaluated based on a detailed mechanistic model of circulatory physiology. The algorithm operates in two steps: (1) the blood volume dynamics model is individualized based on the patient's fractional blood volume response to an initial fluid bolus via system identification; and (2) an adaptive control law built on the individualized blood volume dynamics model regulates the blood volume of the patient.

RESULTS

The algorithm was able to track the blood volume set point as well as accurately estimate and monitor the patient's absolute blood volume level. The algorithm significantly outperformed a population-based proportional-integral-derivative control.

CONCLUSION

Model-based development of closed-loop fluid resuscitation control algorithm may enable regulation of blood volume and monitoring of absolute blood volume level.

SIGNIFICANCE

Model-based closed-loop fluid resuscitation algorithm may offer opportunities for standardized and patient-tailored therapy and reduction of clinician workload.

Control-oriented physiological modeling of hemodynamic responses to blood volume perturbation

This paper presents a physiological model to reproduce hemodynamic responses to blood volume perturbation. The model consists of three sub-models: a control-theoretic model relating blood volume response to blood volume perturbation; a simple physics-based model relating blood volume to stroke volume and cardiac output; and a phenomenological model relating cardiac output to blood pressure. A unique characteristic of this model is its balance for simplicity and physiological transparency. Initial validity of the model was examined using experimental data collected from 11 animals. The model may serve as a viable basis for the design and evaluation of closed-loop fluid resuscitation controllers.

In-human subject-specific evaluation of a control-theoretic plasma volume regulation model

The goal of this study was to conduct a subject-specific evaluation of a control-theoretic plasma volume regulation model in humans. We employed a set of clinical data collected from nine human subjects receiving fluid bolus with and without co-administration of an inotrope agent, including fluid infusion rate, plasma volume, and urine output. Once fitted to the data associated with each subject, the model accurately reproduced the fractional plasma volume change responses in all subjects: the error between actual versus model-reproduced fractional plasma volume change responses was only 1.4 ± 1.6% and 1.2 ± 0.3% of the average fractional plasma volume change responses in the absence and presence of inotrope co-administration. In addition, the model parameters determined by the subject-specific fitting assumed physiologically plausible values: (i) initial plasma volume was estimated to be 36 ± 11 mL/kg and 37 ± 10 mL/kg in the absence and presence of inotrope infusion, respectively, which was comparable to its actual counterpart of 37 ± 4 mL/kg and 43 ± 6 mL/kg; (ii) volume distribution ratio, specifying the ratio with which the inputted fluid is distributed in the intra- and extra-vascular spaces, was estimated to be 3.5 ± 2.4 and 1.9 ± 0.5 in the absence and presence of inotrope infusion, respectively, which accorded with the experimental observation that inotrope could enhance plasma volume expansion in response to fluid infusion. We concluded that the model was equipped with the ability to reproduce plasma volume response to fluid infusion in humans with physiologically plausible model parameters, and its validity may persist even under co-administration of inotropic agents.