An in silico pipeline for subject-specific hemodynamics analysis in liver surgery planning

Examining temporal changes in model-optimized parameters using longitudinal hemodynamic measurements

BACKGROUND

We previously applied hemodynamic data to personalize a mathematical model of the circulation expressed as physically interpretable parameters. The aim of this study was to identify patterns in the data that could potentially explain the estimated parameter changes. This included investigating whether the parameters could be used to track the effect of physical activity on high blood pressure. Clinical trials have repeatedly detected beneficial changes in blood pressure after physical activity and uncovered changes in lower level phenotypes (such as stiffened or high-resistance blood vessels). These phenotypes can be characterized by parameters describing the mechanical properties of the circulatory system. These parameters can be incorporated in and contextualized by physics-based cardiovascular models of the circulation, which in combination can become tools for monitoring cardiovascular disease progression and management in the future.

METHODS

Closed-loop and open-loop models of the left ventricle and systemic circulation were previously optimized to data from a pilot study with a 12-week exercise intervention period. Basal characteristics and hemodynamic data such as blood pressure in the carotid, brachial and finger arteries, as well as left-ventricular outflow tract flow traces were collected in the trial. Model parameters estimated for measurements made on separate days during the trial were used to compute parameter changes for total peripheral resistance, systemic arterial compliance, and maximal left-ventricular elastance. We compared the changes in these cardiovascular model-based estimates to changes from more conventional estimates made without the use of physics-based models by correlation analysis. Additionally, ordinary linear regression and linear mixed-effects models were applied to determine the most informative measurements for the selected parameters. We applied maximal aerobic capacity (measured as VO2max ) data to examine if exercise had any impact on parameters through regression analysis and case studies.

RESULTS AND CONCLUSIONS

Parameter changes in arterial parameters estimated using the cardiovascular models correlated moderately well with conventional estimates. Estimates based on carotid pressure waveforms gave higher correlations (0.59 and above when p < 0.05 ) than those for finger arterial pressure. Parameter changes over the 12-week study duration were of similar magnitude when compared to short-term changes after a bout of intensive exercise in the same parameters. The short-term changes were computed from measurements made immediately before and 24 h after a cardiopulmonary exercise test used to measure VO2max . Regression analysis indicated that changes in VO2max did not account for any substantial amount of variability in total peripheral resistance, systemic arterial compliance, or maximal left-ventricular elastance. On the contrary, changes in stroke volume contributed to far more explained variability. The results suggest that more research is required to be able to accurately track exercise-induced changes in the vasculature for people with pre-hypertension and hypertension using lumped-parameter models.

Parameter estimation for closed-loop lumped parameter models of the systemic circulation using synthetic data

Physics-based models can be applied to describe mechanisms in both health and disease, which has the potential to accelerate the development of personalized medicine. The aim of this study was to investigate the feasibility of personalizing a model of systemic hemodynamics by estimating model parameters. We investigated the feasibility of estimating model parameters for a closed-loop lumped parameter model of the left heart and systemic circulation using the step-wise subset reduction method. This proceeded by first investigating the structural identifiability of the model parameters. Secondly we performed sensitivity analysis to determine which parameters were most influential on the most relevant model outputs. Finally, we constructed a sequence of progressively smaller subsets including parameters based on their ranking by model output influence. The model was then optimized to data for each set of parameters to evaluate how well the parameters could be estimated for each subset. The subsequent results allowed assessment of how different data sets, and noise affected the parameter estimates. In the noiseless case, all parameters could be calibrated to less than 10^-3% error using time series data, while errors using clinical index data could reach over 100%. With 5% normally distributed noise the accuracy was limited to be within 10% error for the five most sensitive parameters, while the four least sensitive parameters were unreliably estimated for waveform data. The three least sensitive parameters were particularly challenging to estimate so these should be prioritised for measurement. Cost functions based on time series such as pressure waveforms, were found to give better parameter estimates than cost functions based on standard indices used in clinical assessment of the cardiovascular system, for example stroke volume (SV) and pulse pressure (PP). Averaged parameter estimate errors were reduced by several orders of magnitude by choosing waveforms for noiseless synthetic data. Also when measurement data were noisy, the parameter estimation procedure based on continuous waveforms was more accurate than that based on clinical indices. By application of the step-wise subset reduction method we demonstrated that by the addition of venous pressure to the cost function, or conversely fixing the systemic venous compliance parameter at an accurate value improved all parameter estimates, especially the diastolic filling parameters which have least influence on the aortic pressure.

Predicting the risk of post-hepatectomy portal hypertension using a digital twin: A clinical proof of concept

BACKGROUND & AIMS

Despite improvements in medical and surgical techniques, post-hepatectomy liver failure (PHLF) remains the leading cause of postoperative death. High postoperative portal vein pressure (P_PV) and portocaval gradient (PCG), which cannot be predicted by current tools, are the most important determinants of PHLF. Therefore, we aimed to evaluate a digital twin to predict the risk of postoperative portal hypertension (PHT).

METHODS

We prospectively included 47 patients undergoing major hepatectomy. A mathematical (0D) model of the entire blood circulation was assessed and automatically calibrated from patient characteristics. Hepatic flows were obtained from preoperative flow MRI (n = 9), intraoperative flowmetry (n = 16), or estimated from cardiac output (n = 47). Resection was then simulated in these 3 groups and the computed P_PV and PCG were compared to intraoperative data.

RESULTS

Simulated post-hepatectomy pressures did not differ between the 3 groups, comparing well with collected data (no significant differences). In the entire cohort, the correlation between measured and simulated P_PV values was good (r = 0.66, no adjustment to intraoperative events) or excellent (r = 0.75) after adjustment, as well as for PCG (respectively r = 0.59 and r = 0.80). The difference between simulated and measured post-hepatectomy PCG was ≤3 mmHg in 96% of cases. Four patients suffered from lethal PHLF for whom the model satisfactorily predicted their postoperative pressures.

CONCLUSIONS

We demonstrated that a 0D model could correctly anticipate postoperative PHT, even using estimated hepatic flow rates as input data. If this major conceptual step is confirmed, this algorithm could change our practice toward more tailor-made procedures, while ensuring satisfactory outcomes.

LAY SUMMARY

Post-hepatectomy portal hypertension is a major cause of liver failure and death, but no tool is available to accurately anticipate this potentially lethal complication for a given patient. Herein, we propose using a mathematical model to predict the portocaval gradient at the end of liver resection. We tested this model on a cohort of 47 patients undergoing major hepatectomy and demonstrated that it could modify current surgical decision-making algorithms.