A diagnostic, monitoring, and predictive tool for patients with complex valvular, vascular and ventricular diseases

Hemodynamics quantification is critically useful for accurate and early diagnosis, but we still lack proper diagnostic methods for many cardiovascular diseases. Furthermore, as most interventions intend to recover the healthy condition, the ability to monitor and predict hemodynamics following interventions can have significant impacts on saving lives. Predictive methods are rare, enabling prediction of effects of interventions, allowing timely and personalized interventions and helping critical clinical decision making about life-threatening risks based on quantitative data. In this study, an innovative non-invasive imaged-based patient-specific diagnostic, monitoring and predictive tool (called C3VI-CMF) was developed, enabling quantifying (1) details of physiological flow and pressures through the heart and circulatory system; (2) heart function metrics. C3VI-CMF also predicts the breakdown of the effects of each disease constituents on the heart function. Presently, neither of these can be obtained noninvasively in patients and when invasive procedures are undertaken, the collected metrics cannot be by any means as complete as the ones C3VI-CMF provides. C3VI-CMF purposefully uses a limited number of noninvasive input parameters all of which can be measured using Doppler echocardiography and sphygmomanometer. Validation of C3VI-CMF, against cardiac catheterization in forty-nine patients with complex cardiovascular diseases, showed very good agreement with the measurements.

Cardiovascular disease is the leading cause of death globally, taking more lives than all forms of cancer combined and is the leading cause of burden on healthcare around the world as well. It is expected to remain the first cause of death by 2030 in the world 1 [2][3][4][5][6] . Examples of components of C3VI include: valvular disease (e.g., aortic valve stenosis, mitral valve stenosis, aortic valve regurgitation and mitral valve insufficiency), ventricular disease (e.g., left ventricle dysfunction and heart failure), vascular disease (e.g., hypertension), paravalvular leaks, and LV outflow tract obstruction in patients with implanted cardiovascular devices such as transcatheter valve replacement (TVR), changes due to surgical procedures for C3VI (e.g., valve replacement and left ventricular reconstructive surgery) and etc 2,[4][5][6][7] .

. Complex valvular-vascular-ventricular interactions (C3VI) is the most general and fundamentally challenging condition in which multiple valvular, vascular and ventricular pathologies have mechanical interactions with one another wherein physical phenomena associated with each pathology amplify effects of others on the cardiovascular system
"Cardiology is flow" 8 . The main functions of the cardiovascular system are to transport, control and maintain blood flow in the entire body. Abnormal hemodynamics greatly alters this tranquil picture, leading to initiation and progression of disease 9 . These abnormalities are often manifested by disturbed fluid dynamics 10 (local hemodynamics), and in many cases by an increase in the heart workload (global hemodynamics). Hemodynamicsquantification can be greatly useful for accurate and early diagnosis butwe still lack proper diagnostic methods for many cardiovascular diseases [11][12][13] because the hemodynamics analysis methods that can be used as engines of new diagnostic tools are not well developed yet. Furthermore, as most interventions intend to recover the healthy condition, the ability to monitor and predict hemodynamics following particular interventions can have significant impacts on saving lives. Despite remarkable advances in medical imaging, imaging on its own is not predictive 11,14 . Predictive methods are rare. They are extensions of diagnostic methods, enabling

Lumped parameter model
The developed algorithm (C3VI-CMF) consists of a parameter estimation algorithm (see below) and a lumped-parameter model that includes several sub-models allowing analysis of any combination of complex valvular, vascular and ventricular diseases in both pre and post intervention conditions: (1) left atrium, (2) left ventricle, (3) aortic valve, (4) mitral valve, (5) systemic circulation, and 6) pulmonary circulation ( Fig. 1; Table 1). This paper reports an innovative method to integrate the parameter-estimation algorithm, the lumped-parameter model and non-invasive clinical Doppler echocardiography and sphygmomanometer measurements to make a patient-specific in silico model of the cardiovascular system. The algorithm uses the following input parameters that all can be reliably measured using Doppler echocardiography: forward left ventricular outflow tract stroke volume, heart rate, ejection time, ascending aorta area, left ventricular outflow tract area, aortic valve effective orifice area, mitral valve effective orifice area, and grading of aortic and mitral valves regurgitation severity. These parameters are measured in the parasternal long axis, parasternal short axis, apical two-chamber, apical four-chamber, and apical five-chamber views of the heart (Fig. 2). Other input parameters of the model are systolic and diastolic blood pressures measured using sphygmomanometers. Note that the proposed method does not need any catheter data as input parameters of the model. This innovative lumped-parameter model calculations were validated against cardiac catheterization data (the instantaneous pressures in the aorta and LV) in forty-nine patients with C3VI (see Results section for validation, Table 1 for patient-specific input parameters and Table 2 for patient's characteristics). Two sub-models (aortic stenosis and aortic regurgitation) have already been used 7,20,21 and validated against in vivo cardiac catheterization (N = 34) 15 and in vivo MRI data (N = 57) 22 . Heart-arterial model. Left ventricle. Coupling between LV pressure and volume was performed through a time varying elastance E(t), a measure of cardiac muscle stiffness.
( ) and V 0 are left ventricle time-varying pressure, time-varying volume and unloaded volume, respectively 15 . The amplitude of E(t) can be normalized with respect to maximal elastance E max , i.e., the slope of the end-systolic pressure-volume relation, giving E N (t N )=E(t)/E max . Time then can be normalized with respect to the time to reach peak elastance, T Emax (t N = t/T Emax ).
www.nature.com/scientificreports www.nature.com/scientificreports/ To model the normalized elastance function of the LV, we tried three functions: (1) a summation of Gaussian functions 23,24 , (2) a Boltzmann Distribution 25 , and (3) a double Hill function 26,27 . We simulated the  Table 1. Input parameters were measured using Doppler echocardiography and sphygmomanometer. Data Acquisition: A computational mechanics framework based on non-invasive clinically measured hemodynamic metrics (brachial blood pressure and Doppler echocardiography measurements) was developed to estimate local and global hemodynamics.  www.nature.com/scientificreports www.nature.com/scientificreports/ lumped-parameter model using these elastance functions for several different patient input parameters and found that the double Hill function model gave the most accurate (physiologically realistic) results for the pressure, flow, and volume waveforms. The use of the double Hill function was motivated by myocyte recruitment during preload, which is fundamentally a cooperative process 28 and consequently, is modeled by a sigmoidal Hill function 29 . Both the Gaussian function and Boltzmann distribution not only gave sub-par results compared to the Hill model, but also did not model the myocyte recruitment mechanism: The Gaussian function is symmetric about a mean 23 , which is not correct for our model because contraction and relaxation are not symmetric processes [30][31][32][33][34][35][36][37][38][39] . The Boltzmann distribution is a probability distribution of physical states 25 , and hence does not capture the dynamic cooperativity of myocytes recruitment. Consequently, to model the LV normalized time-varying elastance curves (E N ), we used a double Hill function as the following 26,27 : where N , τ 1 , τ 2 , m 1 , m 2 , and E min are elastane normalization, ascending time translation, descending time translation, ascending gradient, descending gradient, and minimum elastance, respectively (see Table 1). A double Hill function was deemed necessary to model the contraction and relaxation in the heart chambers: in Eq. 3, the first term in brackets corresponds to the contraction of the chamber and the second term in brackets corresponds to the relaxation of the chamber. τ 1 , τ 2 , m 1 , m 2 govern the time translation and gradient of the elastance function, respectively. Parameter values used for the elastance function were adapted from [30][31][32][33][34][35][36][37][38][39] to obtain physiologically realistic waveforms for pressure, volume, and flow (See Table 1).
Left atrium. Coupling between LA pressure and volume was performed through a time varying elastance E(t), a measure of cardiac muscle stiffness, using the same procedure as outlined above for the LV. The elastance function used for the LA is as defined in Eqs. 2 and 3 26,27 ; parameter values used can be found in Table 1. Additionally, to take into account the relative onset of contraction for the LA and LV, a phase lag was used in the LA elastance function 26 . Specifically, LV contraction was initiated at T = 0, and LA contraction was initiated at 0.85 T 26 , resulting in a time delay of 0.15 T.
Modeling heart valves. Modeling aortic valve. Aortic valve. Aortic valve was modeled using the net pressure gradient formulation PG ( ) net across the aortic valve during LV ejection. This formulation expresses the instantaneous net pressure gradient across the aortic valve (after pressure recovery) as a function of the instantaneous flow rate and the energy loss coefficient and links the LV pressure to the ascending aorta pressure: where E Co L AV , EOA AV , A AO , ρ and Q are the valvular energy loss coefficient, the effective orifice area, ascending aorta cross sectional area, fluid density and transvalvular flow rate, respectively. E Co L AV , representing the 'recovered EOA' , denotes valve effective orifice area adjusted for the area of the aorta at the level of sinotubular junction. Aortic regurgitation. Aortic regurgitation (AR) was modeled using the same analytical formulation as aortic stenosis as the following. AR pressure gradient is the difference between aortic pressure and LV pressure during diastole. www.nature.com/scientificreports www.nature.com/scientificreports/ where E Co L AR , EOA AR and A LVOT are regurgitation energy loss coefficient, regurgitant effective orifice area and LVOT area, respectively. www.nature.com/scientificreports www.nature.com/scientificreports/ Modeling mitral valve. Mitral valve. Mitral valve (MV) was modeled using the analytical formulation for the net pressure gradient (PG net MV ) across the MV during LA ejection. This formulation expresses the instantaneous net pressure gradient across the LA and vena contracta as an unsteady incompressible inviscid flow, where viscous effect is ignored, with a constant blood density. PG net MV expresses as a function of ρ, Q MV , EOA MV and M MV where these quantities represent the density of fluid, transvalvular flow rate, effective orifice area and inertance, respectively. In this formulation, the pressure recovery phenomenon was ignored because the effect is negligible due to the large volume of the LV 40 .
Mitral regurgitation Mitral regurgitation (MR) was modeled using Eq. 8. MR pressure gradient is the difference between mitral pressure and LA pressure during systole.
where EOA MR is MR effective orifice area.
Pulmonary flow. The pulmonary valve flow waveform was simulated by a rectified sine curve with duration t ee and amplitude Q MPV as the following.  www.nature.com/scientificreports www.nature.com/scientificreports/ considered the aortic resistance, R ao , and systemic vein resistance, R SV , as constants and adjusted the systemic artery resistance,R SA , according to the obtained total systemic resistance. Systemic artery resistance was evaluated using an optimization scheme outlined in the patient-specific parameter estimation section.
Physiologically, arterial hypertension is determined by two factors: the degree of reduction in the caliber of small arteries or arterioles with an ensuing increase in systemic vascular resistance and mean blood pressure, and the extent of reduction in the arterial compliance with a resulting increase in pulse pressure (systolic minus diastolic blood pressure). For each degree of hypertension, we fit the predicted pulse pressure to the actual pulse pressure (known by arm cuff sphygmomanometer) obtained from clinical study by adjusting compliances (aorta (C ao ) and systemic (C SAC )). Therefore, for each degree of arterial hypertension, the compliance was evaluated using an optimization scheme outlined in the patient-specific parameter estimation section. patient-specific parameter estimation. The lumped-parameter model took the following patient-specific parameters as its inputs: forward left ventricular outflow tract stroke volume (Forward LVOT-SV), cardiac cycle time (T), ejection time (T EJ ), EOA AV , EOA MV , A AO , A LVOT , EOA AR , EOA MR and brachial systolic and diastolic pressures measured by a sphygmomanometer. The following procedure was used to set up the patient-specific lumped-parameter model in the following sequence:

1) Flow inputs:
The lumped-parameter model used only one reliably measured flow parameter as an input: forward left-ventricular outflow tract stroke volume (Forward LVOT-SV) (Eq. 10). Forward LVOT-SV is defined as the volume of blood that passes through the LVOT cross sectional area every time the heart beats.

2) Time inputs:
Cardiac cycle time (T) and ejection time (T EJ ) were measured using Doppler echocardiography.

3) Aortic valve inputs:
A AO and EOA AV were calculated using Eqs. 11 and 12, respectively.

AV AO
where D AO and VTI AO are the diameter of the ascending aorta and velocity time integral in the ascending aorta, respectively (Fig. 3). VTI AO is the amount of the blood flow going through the aorta which was obtained by tracing the aorta pulse wave flow Doppler envelope (Fig. 3). To model the blood flow in the forward direction, A AO and EOA AV were then substituted into Eq. (4) and the constant inductance ( πρ ) and variable resistance ) parameters were calculated.

4) Aortic regurgitation inputs:
To model blood flow in the reverse direction (aortic valve insufficiency), EOA AR and A LVOT were substituted into Equation (6)  ) parameters. For patients with no insufficiency, the reverse branch is not included.
A LVOT was quantified using Doppler echocardiography measurements (Fig. 3). The EOA AR can be calculated by dividing the regurgitant volume by the time-velocity integral of regurgitant flow using continuous wave Doppler. However, such a calculation does not always yield a correct EOA AR and therefore is not deemed to be reliable. Therefore, to quantify Doppler aortic regurgitant effective orifice area (EOA AR ), aortic valve regurgitation was investigated using color Doppler images in both the long axis and short axis views by experienced cardiologists and graded qualitatively as either mild regurgitation (equivalent to EOA AR < 0.1 mm 2 ), mild to moderate regurgitation (equivalent to 0.1 mm 2 < EOA AR < 0.2 mm 2 ), moderate to severe regurgitation (equivalent to 0.2 www.nature.com/scientificreports www.nature.com/scientificreports/ mm 2 < EOA AR < 0.3 mm 2 ), or severe regurgitation (equivalent to EOA AR > 0.3 mm 2 ) (see Fig. 4 for an example of moderate to severe aortic valve regurgitation in a patient with AS who received TAVR) 41,42 . Mitral valve is approximately an ellipse and its area was quantified using A MV = π ⁎ ⁎ d d 4 1 2 where d 1 and d 2 are mitral-valve diameters measured in the apical two-chamber and apical four-chamber views, respectively (Fig. 5).

6) Mitral regurgitation inputs:
To model blood flow in the reverse direction (mitral-valve insufficiency), EOA MR is substituted into Eq. (9) to calculate the variable resistance ( ) parameters. For patients with no insufficiency, the reverse branch was not included. As described for the aortic-valve regurgitation, calculation of the regurgitant effective orifice area by dividing the regurgitant volume by the time-velocity integral of regurgitant flow using continuous wave Doppler is not reliable. Therefore, to quantify mitral regurgitant effective orifice area (EOA MR ), mitral valve regurgitation was investigated using color Doppler images in the apical four-chamber, parasternal long axis, and apical two-chamber views by experienced cardiologists and graded qualitatively as either mild regurgitation (equivalent to EOA MR < 0.1 mm 2 ), mild to moderate regurgitation (equivalent to 0.1 mm 2 < EOA MR < 0.2 mm 2 ), moderate to severe regurgitation (equivalent to 0.2 mm 2 < EOA MR < 0.3 mm 2 ), or severe regurgitation (equivalent to EOA MR > 0.3 mm 2 ) (see Fig. 6 for an example of severe mitral-valve regurgitation in a patient who received TAVR).

7) End systolic volume and end diastolic volume:
End systolic volume (ESV) or end diastolic volume (EDV) measured using Doppler echocardiography was fed to the lumped-parameter model to adjust starting and ending volumes in the P-V loop diagram. For this purpose, the Biplane Ellipsoid model was used to calculate the instantaneous LV volume at the end of diastole and the end of systole using the following Equation.
where A 1 , A 2 , L 1 , L 2 and AVG (L 1 &L 2 ) are LV area measured in the apical four-chamber view, LV area measured in the apical two-chamber view, LV length measured in the apical four-chamber view, LV length measured in the apical two-chamber view, and average of these two LV lengths, respectively (Refer to Fig. 7 for an example). Ejection Fraction was then calculated as follow:

8) Left-ventricle inputs:
The cardiac cycle time (T) was substituted into τ 1 , τ 2 , m 1 and m 2 in Table 1 and then those values were substituted into Equation 3 to determine the elastance function.

9) Left-atrium inputs:
The cardiac cycle time (T) was substituted into τ 1 , τ 2 , m 1 and m 2 in Table 1 and then those values were substituted into Equation 3 to determine the elastance function.

10) Parameter estimation for systemic circulation:
Parameters R SA , C SVC , and C ao were optimized so that the aorta pressure calculated using the model matched the patient's systolic and diastolic brachial pressures measured using a sphygmomanometer (see computational algorithm section for details). The initial values of these parameters are given in Table 1.

11) Simulation execution:
Please see the computational algorithm section. www.nature.com/scientificreports www.nature.com/scientificreports/ computational algorithm. The lumped-parameter model was analyzed numerically by creating and solving a system of ordinary differential equations in Matlab Simscape (MathWorks, Inc.), enhanced by adding additional functions written in Matlab and Simscape. Matlab's ode23t trapezoidal rule variable-step solver was used to solve the system of differential equations with an initial time step of 0.1 milliseconds. The convergence residual criterion was set to 10 −6 and initial voltages and currents of capacitors and inductors were set to zero. The model was run for several cycles to reach steady state before starting the response optimization process, described below.
A double Hill function representation of a normalized elastance curve for human adults 26,27 was used to generate a signal to model LV elastance. It was shown that this elastance formulation can correctly represent the LV function independent from its healthy and/or pathological conditions. Simulations started at the onset of isovolumic contraction. The instantaneous LV volume, V(t), was calculated using the LV pressure, P LV , and the time varying elastance (Eq. 1). The LV flow rate was subsequently calculated as the time derivative of the instantaneous LV volume. The same approach was used to obtain the left-atrium volume, pressure and flow rate. P LV was first calculated using the initial values of the model input parameters from Table 1. The Forward LVOT-SV calculated using the lumped-parameter model was then fitted to the one measured (Equation10) by optimizing Q MPV (as detailed below). Finally, for each patient, R SA , C SVC , and C ao were optimized to fit the aorta pressure from the model to the patient systolic and diastolic pressures measured using a sphygmomanometer.
Patient-specific response optimization. In order to correctly simulate the conditions of the body of each patient, some of the parameters of the model were optimized so that the lumped-parameter model reproduced the physiological measurements performed in the patient. We conducted an extensive parameter sensitivity analysis that revealed negligible effects of changes in the pulmonary parameters (e.g., C PVC ) on the model output variables. We, therefore, did not include these pulmonary parameters in the parameter-identification process and used the values given in Table 1.
Simulink Design Optimization toolbox was used to optimize the response of the lumped-parameter model using the trust region reflective algorithm implemented in Matlab fmincon function. The response optimization was performed in two sequential steps with tolerances of 10 −6 (Fig. 8, flow chart). In the first step, Q MPV , the mean www.nature.com/scientificreports www.nature.com/scientificreports/ flow rate of the pulmonary valve, was optimized to minimize the error between the Forward LVOT-SV calculated by the lumped-parameter model and the one measured in each patient. In the second step, R SA , C SVC , and C ao were optimized so that maximum and minimum of the aorta pressure were respectively equal to the systolic and diastolic pressures measured using a sphygmomanometer in each patient.

Study population.
Forty-nine patients with C3VI who underwent TAVR or mitral valvuloplasty (see Table 2 for  www.nature.com/scientificreports www.nature.com/scientificreports/ Statistical analysis. All results were expressed as mean ± standard deviations (SD). Statistical analyses were performed using SigmaStat software (Version 3.1, Systat Software, SanJose, CA, USA). Normal distribution was assessed with the Shapiro-Wilk test.

Results
Validation: C3VI-CMF results vs. in vivo measurements. Our novel non-invasive image-based computational mechanics tool (C3VI-CMF), described above, was validated against cardiac catheterization in 49 human subjects as follows: Pressure waveforms. The beat-to-beat pressure calculations of C3VI-CMF were compared with cardiac catheter pressure measurements in all 49 subjects. Figure 9 shows examples of comparisons of C3VI-CMF calculations with catheter data in 3 patients (Patients #1, #2 and #3). Results of C3VI-CMF show good qualitative agreements with catheter measurements in terms of both shape of the waveform, and specific wave features such as the amplitude and the timing of the systolic peak in the left ventricle and aorta. In all subjects (n = 49), the calculations done by C3VI-CMF had an average RMS error of 11.8 mmHg in the LV pressure, and an average RMS error of 9.9 mmHg in the aorta pressure.
Peak pressure. The Peak pressures calculated by C3VI-CMF (LV: 164.5 ± 30.7 mmHg, aorta: 133.88 ± 14.25 mmHg) were in close agreement with the catheter measurements (LV: 165.9 ± 30.9 mmHg, aorta: 133.75 ± 14.67 mmHg) in all subjects (n = 49). Peak pressures resulted from C3VI-CMF correlated well with the catheter measurements as indicated by high coefficients of determination in Fig. 10 (LV: R 2 = 0.982; aorta: R 2 = 0.933). Maximum relative errors of 4.49% and 4.33% were respectively observed in the aorta and LV pressure in all C3VI subjects, consistent with high correlations.

C3VI-CMF quantifies hemodynamics metrics of circulatory and cardiac function.
Metrics of circulatory function. The sophisticated vascular network connected to the heart, impose boundary conditions on it. As the local flow dynamics are influenced by downstream and upstream conditions, replicating correct flow and pressure conditions is critical in developing a patient-specific cardiovascular simulator. This not only gives patient-specific flow and pressure conditions to the local flow but also enables investigation of the effects of www.nature.com/scientificreports www.nature.com/scientificreports/ local hemodynamics on the global circulatory physiology. Investigating the details of flow and pressures in the presence of C3VI is very challenging because of the interactions between disease constituents and amplifying adverse effects of one another. Although cardiac catheterization is the gold standard for evaluating pressure and flow through the heart and circulatory system in clinics, it is invasive, expensive, and high risk and therefore not practical for diagnosis in routine daily clinical practice or serial follow-up examinations. Most importantly, cardiac catheterization only provides access to the blood pressure in very limited regions rather than details of the physiological pulsatile flow and pressures throughout the heart and the circulatory system.
In contrast, C3VI-CMF can non-invasively quantify details of the physiological pulsatile flow and pressures throughout the heart and the circulatory system in patients with C3VI. It provides instantaneous quantities such as left-ventricle pressure, aorta pressure, mitral and left-ventricle flow, left ventricle and left atrium volumes, etc. Figures 11 to 13 show samples of C3VI-CMF calculations for the same C3VI patients (Patients #1, #2 and #3) whose catheter and C3VI-CMF data for validation were shown (Fig. 9) and discussed above. Patient #1 (Fig. 11) underwent TAVR (Edwards biological prosthesis) andhad the following conditions: Pre-TAVR: severe calcific aortic stenosis, mild aortic regurgitation (AR), moderate to severe mitral regurgitation (MR) and moderate to severe concentric hypertrophy; Post-TAVR: mild to moderate paravalvular leakage, moderate to severe MR with moderate concentric hypertrophy and hypertension. Patient #2 (Fig. 12) underwent TAVR (Edwards biological prosthesis) and had the following conditions: Pre-TAVR: severe aortic stenosis, mild AR, mild MR and severe www.nature.com/scientificreports www.nature.com/scientificreports/ concentric hypertrophy; Post-TAVR: trace MR, moderate concentric hypertrophy and hypertension. Patient #3 (Fig. 13) underwent mitral dilatation (valvuloplasty) and had the following conditions: Pre-valvuloplasty: mitral valve stenosis, moderate AS and mild AR. Post-valvuloplasty: mitral valve stenosis, mild to moderate MR, moderate AS and mild AR. Figures 11 to 13 demonstrate that in all three patients with various C3VI disease combinations, C3VI-CMF was able to quantify details of the physiological pulsatile flow and pressures through the heart and circulatory system (local hemodynamics).

Metrics of cardiac function.
In the presence of C3VI, the heart is overloaded since the healthy instantaneous LV pressure and/or flow are altered. There are no methods that can invasively or non-invasively quantify the heart workload (global function) and provide contribution breakdown of each component of the cardiovascular system. The heart workload is the integral of LV pressure and its volume change and was estimated as the area covered by the LV pressure-volume loop. This is especially crucial in C3VI because quantifications of the LV workload and its breakdown are vital to guide prioritizing interventions. Figures 11 and 12 show the pre and post intervention LV workload in C3VI Patients #1& #2 who received TAVR. Pre intervention, untreated aortic stenosis increased the burden on the LV due to the augmented flow resistance which causes a LV pressure overload in the pre-intervention status. Post intervention, TAVR was accompanied by reduction in LV workload in both patients reducing the LV workload (by 27% and 33.7% in Patient #1 and #2, respectively). Figure 13 shows LV workload in Patient #3 in pre and post valvuloplasty status. Instead of improving the heart condition by reducing the LV workload, valvuloplasty caused an increase in the LV workload due to worsening the mitral regurgitation. Figures 11 to 13 demonstrate that in all three patients with various C3VI disease combinations, C3VI-CMF was able to quantify the heart workload (global hemodynamics). Figure 14 summarizes an example of calculations for analyzing the breakdown of the contributions of the disease constituents on the LV workload in Patient #1. In the pre-intervention state, this patient had severe calcific www.nature.com/scientificreports www.nature.com/scientificreports/ aortic stenosis, mild aortic regurgitation, moderate to severe mitral regurgitation and concentric hypertrophy. In order to plan valve interventions, each of the valvular disease constituents were replaced by the normal condition one-at-a-time and the LV workload was calculated and shown in the left panel of Fig. 14. As the right panel of Fig. 14 shows, both mitral valve regurgitation (49.5% increase) and aortic valve stenosis (24% increase) had  www.nature.com/scientificreports www.nature.com/scientificreports/ substantial contributions to increasing the workload. However, because mitral valve regurgitation had the greatest contribution, correcting it should have had the highest priority in the sequence of interventions. Considering the conditions of this patient, the decision of whether to also perform mitral intervention at the time of aortic valve intervention might have been carefully evaluated and considered. However, in reality, this patient only underwent transcatheter aortic valve replacement, TAVR (Fig. 11). The presented simulation results (Fig. 14) predict that fixing aortic valve stenosis alone can reduce the workloadby 24% which agrees with the actual measurement data post-intervention (Fig. 11) in this patient (workload was reduced by18% after TAVR).

Discussions
Due to the wide inter-subject variability in cardiovascular anatomy and pathophysiology, it is ideally necessary to design individualized treatment plans based on the diagnosis data and the predictions made about individuals' risk of the intervention. The C3VI-CMF framework developed here is an innovative patient-specific non-invasive diagnostic, monitoring, and predictive tool that can investigate and quantify effects of C3VI constituents on the heart function, and the circulatory system. The basis of C3VI-CMF is calculations of the local hemodynamics (detailed information of the fluid dynamics of the circulatory system, e.g., flow and pressure in different regions) and global hemodynamics (the heart workload). This tool can provide the breakdown of the effects of disease constituents on the global function of the heart as well so it can help predicting the effects of interventions and planning for the sequence of interventions. C3VI-CMF is capable of tracking cardiac and vascular state based on accurate time-varying models that reproduce physiological responses. While such information is vitally needed for effectively using advanced therapies to improve clinical outcomes and guiding interventions in C3VI patients, they are not currently accessible in clinic.
We evaluated our method under pathophysiologic conditions and assessed its performance in forty-nine C3VI patients with a substantial inter-and intra-patient variability with a wide range of disease. The presented results demonstrate not only repeatability but also validity even in vastly different physiologic conditions (Figs. 9 and 10; Table 2). This demonstrates the ability of C3VI-CMF to track changes in both cardiac, and vascular states. C3VI-CMF purposefully uses reliable non-invasive input parameters to continuously calculate patient-specific hemodynamics quantities to be used for diagnosis, monitoring, and prediction of cardiac function and circulatory state with direct clinical relevance.
C3VI-CMF can be potentially used as: (1) a personal wearable device or as a mobile application for patient monitoring; (2) a module incorporated in the software of Doppler echocardiography machines for diagnosis and prediction; and (3) a monitoring and diagnostic device for ambulatory care and intensive and critical care unit.

Limitations
This study was performed on 49 patients with C3VI. Future studies must consider further validation of C3VI-CMF in a larger population of C3VI patients. www.nature.com/scientificreports www.nature.com/scientificreports/

Data availability
The development and validation of the proposed method require the retrospective clinical data routinely measured in clinics (Doppler ultrasound and catheter data). These data were transferred as the de-identified & anonymized data from St. Joseph's Healthcare and Hamilton Health Sciences (Hamilton, ON, Canada) and Hospital Universitario Marques de Valdecilla (IDIVAL, Santander, Spain) 6 . The code and the optimization algorithm used for C3VI-CMF are available from the author upon request. www.nature.com/scientificreports www.nature.com/scientificreports/