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

A Lumped-Parameter Model of the Cardiovascular System Response for Evaluating Automated Fluid Resuscitation Systems

Physiological closed-loop controlled (PCLC) medical devices, such as those designed for blood pressure regulation, can be tested for safety and efficacy in real-world clinical settings. However, relying solely on limited animal and clinical studies may not capture the diverse range of physiological conditions. Credible mathematical models can complement these studies by allowing the testing of the device against simulated patient scenarios. This research involves the development and validation of a low-order lumped-parameter mathematical model of the cardiovascular system's response to fluid perturbation. The model takes rates of hemorrhage and fluid infusion as inputs and provides hematocrit and blood volume, heart rate, stroke volume, cardiac output and mean arterial blood pressure as outputs. The model was calibrated using data from 27 sheep subjects, and its predictive capability was evaluated through a leave-one-out cross-validation procedure, followed by independent validation using 12 swine subjects. Our findings showed small model calibration error against the training dataset, with the normalized root-mean-square error (NRMSE) less than 10% across all variables. The mathematical model and virtual patient cohort generation tool demonstrated a high level of predictive capability and successfully generated a sufficient number of subjects that closely resembled the test dataset. The average NRMSE for the best virtual subject, across two distinct samples of virtual subjects, was below 12.7% and 11.9% for the leave-one-out cross-validation and independent validation dataset. These findings suggest that the model and virtual cohort generator are suitable for simulating patient populations under fluid perturbation, indicating their potential value in PCLC medical device evaluation.

Parametric Modeling and Deep Learning for Enhancing Pain Assessment in Postanesthesia

OBJECTIVE

The problem of reliable and widely accepted measures of pain is still open. It follows the objective of this work as pain estimation through post-surgical trauma modeling and classification, to increase the needed reliability compared to measurements only.

METHODS

This article proposes (i) a recursive identification method to obtain the frequency response and parameterization using fractional-order impedance models (FOIM), and (ii) deep learning with convolutional neural networks (CNN) classification algorithms using time-frequency data and spectrograms. The skin impedance measurements were conducted on 12 patients throughout the postanesthesia care in a proof-of-concept clinical trial. Recursive least-squares system identification was performed using a genetic algorithm for initializing the parametric model. The online parameter estimates were compared to the self-reported level by the Numeric Rating Scale (NRS) for analysis and validation of the results. Alternatively, the inputs to CNNs were the spectrograms extracted from the time-frequency dataset, being pre-labeled in four intensities classes of pain during offline and online training with the NRS.

RESULTS

The tendency of nociception could be predicted by monitoring the changes in the FOIM parameters' values or by retraining online the network. Moreover, the tissue heterogeneity, assumed during nociception, could follow the NRS trends. The online predictions of retrained CNN have more specific trends to NRS than pain predicted by the offline population-trained CNN.

CONCLUSION

We propose tailored online identification and deep learning for artefact corrupted environment. The results indicate estimations with the potential to avoid over-dosing due to the objectivity of the information.

SIGNIFICANCE

Models and artificial intelligence (AI) allow objective and personalized nociception-antinociception prediction in the patient safety era for the design and evaluation of closed-loop analgesia controllers.

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.

Development and validation of a mathematical model to simulate human cardiovascular and respiratory responses to battlefield trauma

Mathematical models of human cardiovascular and respiratory systems provide a viable alternative to generate synthetic data to train artificial intelligence (AI) clinical decision-support systems and assess closed-loop control technologies, for military medical applications. However, existing models are either complex, standalone systems that lack the interface to other applications or fail to capture the essential features of the physiological responses to the major causes of battlefield trauma (i.e., hemorrhage and airway compromise). To address these limitations, we developed the cardio-respiratory (CR) model by expanding and integrating two previously published models of the cardiovascular and respiratory systems. We compared the vital signs predicted by the CR model with those from three models, using experimental data from 27 subjects in five studies, involving hemorrhage, fluid resuscitation, and respiratory perturbations. Overall, the CR model yielded relatively small root mean square errors (RMSEs) for mean arterial pressure (MAP; 20.88 mm Hg), end-tidal CO₂ (ETCO₂ ; 3.50 mm Hg), O₂ saturation (SpO₂ ; 3.40%), and arterial O₂ pressure (PaO₂ ; 10.06 mm Hg), but a relatively large RMSE for heart rate (HR; 70.23 beats/min). In addition, the RMSEs for the CR model were 3% to 10% smaller than the three other models for HR, 11% to 15% for ETCO₂ , 0% to 33% for SpO₂ , and 10% to 64% for PaO₂ , while they were similar for MAP. In conclusion, the CR model balances simplicity and accuracy, while qualitatively and quantitatively capturing human physiological responses to battlefield trauma, supporting its use to train and assess emerging AI and control systems.

A system theory based digital model for predicting the cumulative fluid balance course in intensive care patients

Background: Surgical interventions can cause severe fluid imbalances in patients undergoing cardiac surgery, affecting length of hospital stay and survival. Therefore, appropriate management of daily fluid goals is a key element of postoperative intensive care in these patients. Because fluid balance is influenced by a complex interplay of patient-, surgery- and intensive care unit (ICU)-specific factors, fluid prediction is difficult and often inaccurate. Methods: A novel system theory based digital model for cumulative fluid balance (CFB) prediction is presented using recorded patient fluid data as the sole parameter source by applying the concept of a transfer function. Using a retrospective dataset of n = 618 cardiac intensive care patients, patient-individual models were created and evaluated. RMSE analyses and error calculations were performed for reasonable combinations of model estimation periods and clinically relevant prediction horizons for CFB. Results: Our models have shown that a clinically relevant time horizon for CFB prediction with the combination of 48 h estimation time and 8-16 h prediction time achieves high accuracy. With an 8-h prediction time, nearly 50% of CFB predictions are within ±0.5 L, and 77% are still within the clinically acceptable range of ±1.0 L. Conclusion: Our study has provided a promising proof of principle and may form the basis for further efforts in the development of computational models for fluid prediction that do not require large datasets for training and validation, as is the case with machine learning or AI-based models. The adaptive transfer function approach allows estimation of CFB course on a dynamically changing patient fluid balance system by simulating the response to the current fluid management regime, providing a useful digital tool for clinicians in daily intensive care.

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.

Low cost circulatory pressure acquisition and fluid infusion rate measurement system for clinical research

Acquiring patient physiological waveforms is useful for studying hemodynamic management and developing medical monitoring systems. A low cost, Arduino controlled data acquisition system acquires arterial pressure waveforms (Edwards Lifesciences TruWave compatible) and measures fluid infusion rate using hanging scales. This system can be used at the same time as a clinical monitor, enabling recording of patient arterial pressure and fluid delivery for clinical research. The system is powered via a USB connection, which additionally provides serial output, aiding compatibility and customisation. A simple software user interface, developed in Python, shows outputs. Each data acquisition system, including all necessary connection cables costs ~US$90 and is multiple-use.

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.

Analysis on the application value of goal-directed fluid therapy in patients undergoing laparoscopy-assisted radical gastrectomy with fast-track anesthesia

OBJECTIVE

To explore the application value of goal-directed fluid therapy (GDFT) in patients undergoing laparoscopy-assisted radical gastrectomy with fast-track anesthesia.

METHODS

From December 2016 to December 2019, 74 patients who underwent laparoscopy-assisted radical gastrectomy under the concept of enhanced recovery after surgery (ERAS) in gastrointestinal Surgery department of Tongling People's Hospital were selected as research participants. They were divided into two groups: the routine group (patients were treated with conventional fluids) (n=37) and the GDFT group (patients were treated with GDFT) (n=37). In the two groups, patients were compared in terms of intraoperative fluid inflow and outflow, hemodynamic indexes before operation for 30 min (T0), after anesthesia induction for 30 min (T1), during operation for 0.5 h (T2) and 1.5 h (T3) and after operation (T4), postoperative complications, postoperative recovery, mini-mental state examination (MMSE) scores on the first day (d0) before operation and the first day (d1), the third day (d2) and the seventh day (d3) after operation, and inflammatory factor levels.

RESULTS

The amount of crystal input, colloid, blood loss, fluid replacement and urine volume in the GDFT group were significantly less than those in the routine group (P < 0.05). From T1 to T4, the values of mean arterial pressure (MAP) and central venous pressure (CVP) in the GDFT group were higher than those in the routine group (p < 0.05). The total incidence of postoperative complications in the GDFT group was lower than that in the routine group (P < 0.05). Compared with those in the routine group, the postoperative anus exhaust time, the first time of starting to eat, the time of leaving bed, the duration of stay in the postanesthesia care unit and the hospital stay were significantly shorter in the GDFT group (P < 0.05). From D1 to D3, the MMSE score in the GDFT group was higher than that in the routine group, while the levels of C-reactive protein (CPR), interleukin 6 (IL-6) and procalcitonin (PCT) were lower than those in the routine group (P < 0.05).

CONCLUSION

GDFT has a better effect on the rapid rehabilitation of patients undergoing laparoscopy-assisted radical gastrectomy during fast-track anesthesia, and it also has a positive effect on maintaining the stability of hemodynamics, reducing systemic inflammation and decreasing postoperative complications.

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.

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.

Evaluation of Fluid Resuscitation Control Algorithms via a Hardware-in-the-Loop Test Bed

OBJECTIVE

This paper presents a hardware-in-the-loop (HIL) testing platform for evaluating the performance of fluid resuscitation control algorithms. The proposed platform is a cyber-physical system that integrates physical devices with computational models and computer-based algorithms.

METHODS

The HIL test bed is evaluated against in silico and in vivo data to ensure the hemodynamic variables are appropriately predicted in the proposed platform. The test bed is then used to investigate the performance of two fluid resuscitation control algorithms: a decision table (rule-based) and a proportional-integral-derivative (PID) controller.

RESULTS

The statistical evaluation of test bed indicates that similar results are observed in the HIL test bed, in silico implementation, and the in vivo data, verifying that the HIL test bed can adequately predict the hemodynamic responses. Comparison of the two fluid resuscitation controllers reveals that both controllers stabilized hemodynamic variables over time and had similar speed to efficiently achieve the target level of the hemodynamic endpoint. However, the accuracy of the PID controller was higher than the rule-based for the scenarios tested in the HIL platform.

CONCLUSION

The results demonstrate the potential of the HIL test bed for realistic testing of physiologic controllers by incorporating physical devices with computational models of physiology and disturbances.

SIGNIFICANCE

This type of testing enables relatively fast evaluation of physiologic closed-loop control systems to aid in iterative design processes and offers complementary means to existing techniques (e.g., in silico, in vivo, and clinical studies) for testing of such systems against a wide range of disturbances and scenarios.

Credibility Evidence for Computational Patient Models Used in the Development of Physiological Closed-Loop Controlled Devices for Critical Care Medicine

Physiological closed-loop controlled medical devices automatically adjust therapy delivered to a patient to adjust a measured physiological variable. In critical care scenarios, these types of devices could automate, for example, fluid resuscitation, drug delivery, mechanical ventilation, and/or anesthesia and sedation. Evidence from simulations using computational models of physiological systems can play a crucial role in the development of physiological closed-loop controlled devices; but the utility of this evidence will depend on the credibility of the computational model used. Computational models of physiological systems can be complex with numerous non-linearities, time-varying properties, and unknown parameters, which leads to challenges in model assessment. Given the wide range of potential uses of computational patient models in the design and evaluation of physiological closed-loop controlled systems, and the varying risks associated with the diverse uses, the specific model as well as the necessary evidence to make a model credible for a use case may vary. In this review, we examine the various uses of computational patient models in the design and evaluation of critical care physiological closed-loop controlled systems (e.g., hemodynamic stability, mechanical ventilation, anesthetic delivery) as well as the types of evidence (e.g., verification, validation, and uncertainty quantification activities) presented to support the model for that use. We then examine and discuss how a credibility assessment framework (American Society of Mechanical Engineers Verification and Validation Subcommittee, V&V 40 Verification and Validation in Computational Modeling of Medical Devices) for medical devices can be applied to computational patient models used to test physiological closed-loop controlled systems.

Advancing Regulatory Science With Computational Modeling for Medical Devices at the FDA's Office of Science and Engineering Laboratories

Protecting and promoting public health is the mission of the U.S. Food and Drug Administration (FDA). FDA's Center for Devices and Radiological Health (CDRH), which regulates medical devices marketed in the U.S., envisions itself as the world's leader in medical device innovation and regulatory science-the development of new methods, standards, and approaches to assess the safety, efficacy, quality, and performance of medical devices. Traditionally, bench testing, animal studies, and clinical trials have been the main sources of evidence for getting medical devices on the market in the U.S. In recent years, however, computational modeling has become an increasingly powerful tool for evaluating medical devices, complementing bench, animal and clinical methods. Moreover, computational modeling methods are increasingly being used within software platforms, serving as clinical decision support tools, and are being embedded in medical devices. Because of its reach and huge potential, computational modeling has been identified as a priority by CDRH, and indeed by FDA's leadership. Therefore, the Office of Science and Engineering Laboratories (OSEL)-the research arm of CDRH-has committed significant resources to transforming computational modeling from a valuable scientific tool to a valuable regulatory tool, and developing mechanisms to rely more on digital evidence in place of other evidence. This article introduces the role of computational modeling for medical devices, describes OSEL's ongoing research, and overviews how evidence from computational modeling (i.e., digital evidence) has been used in regulatory submissions by industry to CDRH in recent years. It concludes by discussing the potential future role for computational modeling and digital evidence in medical devices.