Le Gall A, Vallée F, Pushparajah K, Hussain T, Mebazaa A, Chapelle D, Gayat É, Chabiniok R.PLoS One. 2020 May 14;15(5):e0232830. doi: 10.1371/journal.pone.0232830. eCollection 2020.PMID: 32407353 Free PMC article.

## Abstract

During general anesthesia (GA), direct analysis of arterial pressure or aortic flow waveforms may be inconclusive in complex situations. Patient-specific biomechanical models, based on data obtained during GA and capable to perform fast simulations of cardiac cycles, have the potential to augment hemodynamic monitoring. Such models allow to simulate Pressure-Volume (PV) loops and estimate functional indicators of cardiovascular (CV) system, e.g. ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility, evolving throughout GA. In this prospective observational study, we created patient-specific biomechanical models of heart and vasculature of a reduced geometric complexity for n = 45 patients undergoing GA, while using transthoracic echocardiography and aortic pressure and flow signals acquired in the beginning of GA (baseline condition). If intraoperative hypotension (IOH) appeared, diluted norepinephrine (NOR) was administered and the model readjusted according to the measured aortic pressure and flow signals. Such patients were a posteriori assigned into a so-called hypotensive group. The accuracy of simulated mean aortic pressure (MAP) and stroke volume (SV) at baseline were in accordance with the guidelines for the validation of new devices or reference measurement methods in all patients. After NOR administration in the hypotensive group, the percentage of concordance with 10% exclusion zone between measurement and simulation was >95% for both MAP and SV. The modeling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p = 0.039) and an increased CE (0.8±0.1 vs 0.73±0.11; p = 0.042) in hypotensive vs normotensive patients. Furthermore, Vva increased by 92±101%, CE decreased by 13±11% (p < 0.001 for both) and contractility increased by 14±11% (p = 0.002) in the hypotensive group post-NOR administration. In this work we demonstrated the application of fast-running patient-specific biophysical models to estimate PV loops and functional indicators of CV system using clinical data available during GA. The work paves the way for model-augmented hemodynamic monitoring at operating theatres or intensive care units to enhance the information on patient-specific physiology.

**Fig 1. Example of PV loop and its interpretation.** Cardiac bioenergetics (left): internal work (I_{w}) associated with the potential energy or the energetic expenditure necessary to reach optimal conditions for ejection; external work (E_{w}) associated with the energetic expenditure of the ejection; cardiac efficiency (CE) defined as the ratio CE=EwEw+Iw. Ventricular-arterial coupling (right): ventricular elastance *E*_{es} (slope of the end-systolic pressure-volume relationship, ESPVR, at end-systolic pressure-volume point); arterial elastance Ea=ESPSV with ESP being end-systolic pressure and SV = EDV − ESV the stroke volume (subtraction of end-diastolic and end-systolic volumes).

**Fig 2. Example of model calibration.** Solid lines represent the result of the patient-specific simulation. Dashed lines represent measured data. Blue: Hypotensive. Orange: Maximum effect of norepinephrine.

**Fig 3. Example of output of a patient-specific simulation for a hypotensive patient and at the maximum effect of norepinephrine.** Solid lines represent the dynamic pressure-volume relationship during a cardiac cycle—namely the Pressure-Volume (PV) loop. Dashed lines represent the static pressure-volume relationships—namely the End-Diastolic Pressure-Volume Relationship (EDPVR) and the End-Systolic Pressure-Volume Relationship (ESPVR). The EDPVR characterizes the ventricular volume for a given pressure at end-diastole. The ESPVR represents the ventricular pressure and volume at end-systole, prior to isovolumic relaxation. Note that the dynamic PV loop does not necessarily reach the theoretical static ESPVR curve, typically when cardiac cycle is too short.

**Fig 4. Results of calibration.** Left: Bland-Altman plots for repeated measurements representing dispersion of the difference between measurement and simulation at baseline (n = 45 patients). Blue points and bars represent the mean and standard deviation for 10 heart beats in individual patients. Dashed horizontal lines represent the limit of agreement (±1.96 times standard deviation) and the horizontal gray line represents the bias or the mean difference between measurements and simulation. Right: 4-quadrant plots representing the variation of mean pressure and stroke volume from hypotension to maximum effect of norepinephrine in patients from hypotensive group (n = 16), orange points represent mean of ten beats for each patient. LLA, lower limit of agreement; ULA, upper limit of agreement.

**Fig 5. Confidence intervals for the differences between measurements and simulations.** Dark gray boxes represent the equivalence area for the mean difference estimation (in percentage of the measured indicator), light gray boxes represent the equivalence area for confidence intervals. Limits of equivalence were defined as ±8mm Hg for pressure and ±30% for stroke volume, as recommended by international guidelines. Blue lines represent the mean and the confidence interval for the difference between measurement and simulation.

**Fig 6. Correlations between simulated and measured indicators.** A: Correlation plot representing simulated capacitance (*C*_{d}) against measured total arterial compliance (C_{tot} = SV/PP) for all 45 patients at baseline. B: 4-quadrant plot of Δ*C*_{d} against ΔC_{tot} representing difference from hypotension to maximum effect of norepinephrine for 16 hypotensive patients. C: Correlation plot representing simulated resistance (*R*_{d}) and systemic vascular resistance (SVR=MAPCO) for all 45 patients at baseline. D: 4-quadrant plot of Δ*R*_{d} against ΔSVR representing difference from hypotension to maximum effect of norepinephrine for 16 hypotensive patients. SV, stroke volume; PP, pulse pressure; MAP, mean aortic pressure.

**Fig 7. Boxplots of model parameters and the results of the simulation.** Normotensive patients are in green; hypotensive patients before and after administering norepinephrine are in blue and red color, respectively. * *p* < 0.05; ** *p* < 0.01; *** *p* < 0.001.

**Fig 8. Validation subjects.** Comparison of the simulated PV loops and of the measurements in selected validation subjects once descending aortic flow was used (as in our clinical study) or when directly measured ascending aortic flow was used.

source:https://pubmed.ncbi.nlm.nih.gov/32407353/