Prediction of haemodynamics after interatrial shunt for heart failure using the generalized circulatory equilibrium.

AIMS: Interatrial shunting (IAS) reduces left atrial pressure in patients with heart failure. Several clinical trials reported that IAS improved the New York Heart Association score and exercise capacity. However, its effects on haemodynamics vary depending on shunt size, cardiovascular properties, and stressed blood volume. To maximize the benefit of IAS, quantitative prediction of haemodynamics under IAS in individual patients is essential. The generalized circulatory equilibrium framework determines circulatory equilibrium as the intersection of the cardiac output curve and the venous return surface. By incorporating IAS into the framework, we predict the impact of IAS on haemodynamics. METHODS AND
RESULTS: In seven mongrel dogs, we ligated the left anterior descending artery and created impaired cardiac function with elevated left atrial pressure (baseline: 7.8 ± 1.0 vs. impaired: 11.9 ± 3.2 mmHg). We established extracorporeal left-to-right atrial shunting with a centrifugal pump. After recording pre-IAS haemodynamics, we changed IAS flow stepwise to various levels and measured haemodynamics under IAS. To predict the impact of IAS on haemodynamics, we modelled the fluid mechanics of IAS by Newton's second law and incorporated IAS into the generalized circulatory equilibrium framework. Using pre-IAS haemodynamic data obtained from the dogs, we predicted the impact of IAS flow on haemodynamics under IAS condition using a set of equations. We compared the predicted haemodynamic data with those measured. The predicted pulmonary flow [r2 = 0.88, root mean squared error (RMSE) 11.4 mL/min/kg, P < 0.001), systemic flow (r2 = 0.92, RMSE 11.2 mL/min/kg, P < 0.001), right atrial pressure (r2 = 0.92, RMSE 0.71 mmHg, P < 0.001), and left atrial pressure (r2 = 0.83, RMSE 0.95 mmHg, P < 0.001) matched well with those measured under normal and impaired cardiac function. Using this framework, we further performed a simulation study to examine the haemodynamic benefit of IAS in heart failure with preserved ejection fraction. We simulated the IAS haemodynamics under volume loading and exercise conditions. Volume loading and exercise markedly increased left atrial pressure. IAS size-dependently attenuated the increase in left atrial pressure in both volume loading and exercise. These results indicate that IAS improves volume and exercise intolerance.
CONCLUSIONS: The framework developed in this study quantitatively predicts the haemodynamic impact of IAS. Simulation study elucidates how IAS improve haemodynamics under volume loading and exercise conditions. Quantitative prediction of IAS haemodynamics would contribute to maximizing the benefit of IAS in patients with heart failure.

Introduction

The number of patients with heart failure (HF) is increasing with aging of the population. Regardless of the underlying aetiology of HF, 70–90% of patients with acute decompensated HF present with pulmonary congestion resulting from elevated left atrial pressure (PLA). , Frequent occurrence of acute decompensated HF leads to progressive deterioration of cardiac function and quality of life, resulting in poor survival outcome. Therefore, we need new strategies to prevent the acute elevation of PLA in patients with HF.

Interatrial shunting (IAS) by transvenous catheter technique has been developed recently. , , , IAS translocates blood volume from the pulmonary circulation to the systemic circulation and prevents the acute increase in PLA. The degree of volume translocation depends on the pressure gradient between PLA and right atrial pressure (PRA). The interatrial shunt device system (IASD®), which was developed by Corvia Medical, Inc., is composed of left and right atrial discs (19 mm outer diameter) with an 8 mm communication. In a Phase 2 trial (REDUCE LAP‐HF I), Feldman et al. reported that IASD® improved the NYHA score, increased the distance of 6 min walk, and attenuated the increase in pulmonary capillary wedge pressure (PCWP) during exercise. In contrast, IAS had little effect on PCWP or systemic flow (QS) at rest in patients with HF and preserved ejection fraction (HFpEF). The V‐Wave® device (V‐Wave Ltd.) with a 5.1 mm inner diameter is designed to prevent right‐to‐left atrial flow. In a Phase 1 clinical trial, Del Trigo et al. reported that the V‐Wave® system improved the NYHA score and the distance of 6 min walk in patients with HF and reduced ejection fraction (HFrEF). Because various conditions other than the IAS size, such as right and left cardiac function, vascular properties, and stressed blood volume, may also affect the haemodynamic impact of IAS, the benefit of IAS varies among patients with HF. Wessler et al. reported that IASD® suppressed PCWP during exercise to a greater extent in patients with high PCWP at rest than in those with low PCWP. However, we do not have an established method or a single marker that detects responder or non‐responder to IAS or indicate the appropriate device size for individual patients with HF. Quantitative prediction of the impact of IAS on haemodynamics is crucial and may allow appropriate selection of patient and device.

Guyton proposed that the intersection of the cardiac output (CO) curve, and the venous return curve represents the circulatory equilibrium. Sunagawa et al. extended this framework to include the pulmonary circulation by introducing PLA and representing the CO curves and venous return as a function of PRA and PLA. They derived the analytical representation of the CO curve using the framework of ventricular arterial coupling and the venous return surface using the resistance‐compliance distributed circuit (generalized circulatory equilibrium). The generalized circulatory equilibrium enabled us to predict haemodynamics under extracorporeal membrane oxygenation and left ventricular assist device. , , ,

Using the concept of generalized circulatory equilibrium, we developed a simple framework to predict the impact of IAS on haemodynamics aiming to optimize IAS therapy in individual patients with HF. We validated the framework using a dog model of IAS with graded changes of the left to the right atrial shunt flow.

Methods

Theoretical considerations

Because IAS does not directly change the cardiac function or vascular properties, we consider that IAS haemodynamics can be modelled by simply applying the equation: QIAS = QP − QS in generalized circulatory equilibrium, where QIAS is the shunt flow, QP is pulmonary flow, and QS is systemic flow.

We derived the integrated CO curves from the left and right CO curves. In the left heart, the CO curve is a simple logarithmic function of PLA as follows: where SL, FL, and HL are empirical parameters of the left heart. The values of FL and HL used in this study are 2.03 and 0.8, respectively, based on a previous report. In the right heart, the downstream pressure of the pulmonary artery, that is, PLA, is not negligibly small relative to the mean pulmonary arterial pressure. We previously reported that the downstream pressure could be incorporated into the CO curves by the following equation , : where SR, FR, and HR are empirical parameters of the right heart, RVEFe is effective RV ejection fraction, and RP is pulmonary vascular resistance. In this study, we set FR = 2.13, HR = 1.9, and RVEFe = 0.6 for normal RV function, and RP = 0.1 mmHg/mL/min/kg for normal pulmonary circulation as reported previously. , ,

We previously reported that in a distributed resistance‐compliance vascular model, the following equations represent the stressed blood volume of the systemic circulation and pulmonary circulation : where VS, VP, and VT are stressed blood volume of systemic circulation, pulmonary circulation, and the sum of the two, respectively. WS, WP, CS, and CP are vascular parameters, respectively. We set WS = 0.106 min, WP = 0.024 min, CS = 2.53 mL/mmHg/kg, and CP = 0.45 mL/mmHg/kg from previous reports. , , ,

We used Newton's second law to model the IAS fluid dynamics as follows : where QIAS, Cd, SIAS, and ρ are IAS flow, discharge coefficient, cross‐sectional area of IAS, and density of blood, respectively. We set Cd = 0.74 (unitless) and ρ = 1.05 g/cm3 as reported previously. , Once we have determined SL, SR, and VT, we can predict IAS haemodynamics by simultaneously solving these seven equations. Details of the calculation are given in the Supporting Information.

Animal preparation

We used seven adult mongrel dogs weighing 14.3–17.9 kg. The investigation conforms to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 85‐23, revised 1985). The Committee on Ethics of Animal Experiments at Kyushu University Graduate School of Medical Sciences approved the experiments.

We induced anaesthesia with intravenous pentobarbital sodium (25 mg/kg) and pancuronium bromide (0.08 mg/kg), performed endotracheal intubation, and maintained an appropriate anaesthesia level during the experiment by continuous infusion of isoflurane (1–2%). We kept body temperature between 37°C and 38°C. We bilaterally denervated the carotid sinuses and vagotomised to abolish the neural reflexes including baroreflex. We inserted a 5Fr sheath into the right femoral artery to measure arterial pressure (AP). We inserted a high‐fidelity micromanometer (Millar Instruments, Houston, TX) into LV through the free wall. We inserted a pair of draining cannula and fluid‐filled catheters each into the left (LA) and right atria (RA). We connected the fluid‐filled catheters to pressure transducers (model DX‐360; Nihonkohden, Tokyo, Japan) to measure PLA and PRA. We connected the two cannulas via a centrifugal pump (CBBPX‐80; Medtronic, Minneapolis, MN) to mimic IAS and mounted an in‐line ultrasonic flowmeter (model XL; Transonics, Ithaca, NY) in the circuit to measure QIAS continuously. We also placed an ultrasonic flowmeter (model PSB; Transonic, Ithaca, NY) around the ascending aorta to measure QS (Supporting Information, ). We estimated QP as the sum of QS and QIAS (QP = QIAS + QS).

Experimental protocols

Under normal conditions, we first clamped the shunt circuit (QIAS = 0) and recorded baseline QS, QP, PLA, and PRA (Figure ). Using the baseline haemodynamic data, we estimated SL, SR, and VT from equations 1–5. We changed QIAS stepwise to vary the ratio of the pressure gradient between PLA and PRA, to QIAS at 90, 60, 30, and 10 × 10−3 mmHg/mL/min/kg. In each step, after waiting for 1 min, we recorded QS, QIAS, PLA, and PRA for 10 s. Because we created an artificial shunt, we estimated effective SIAS from QIAS and the pressure gradient between PLA and PRA using equation 7. We predicted QS, QP, PLA, and PRA from SL, SR, VT, and SIAS and compared the predicted values with those measured.

FIGURE 1

Experimental design to verify the accuracy of haemodynamic prediction. We determined SL, SR, and total stressed blood volume (VT) under baseline conditions. Then, we changed QIAS and determined SIAS from the left and right atrial pressure gradient and shunt flow (QIAS). We predicted pulmonary flow (QP), systemic flow (QS), right atrial pressure (PRA), and left atrial pressure (PLA) using the framework and compared the predicted values with measured. SL and SR are slopes of cardiac output (CO) curves; FL, HL, FR, and HR are empirical parameters of the left and right heart; WS, WP, CS, and CP are vascular parameters. Cd, discharge coefficient; RP, pulmonary vascular resistance; RVEFe, effective right ventricular ejection fraction; SIAS, functional cross‐sectional area of interatrial shunt (IAS); VP, pulmonary stressed blood volume; VS, systemic stressed blood volume; VT, total stressed blood volume; ρ, the density of blood.

After the experiment in the normal heart condition, we ligated the left anterior descending artery to create impaired cardiac function. One hour after the left anterior descending artery ligation, we repeated the same protocol as described above.

Computational simulation

Flash pulmonary oedema is a cardinal feature of HFpEF and is caused by an acute increase of PLA after volume loading or exercise. , HFpEF may be a good indication for IAS intervention because IAS prevents the acute increase in PLA. To elucidate the haemodynamic benefits of IAS in HFpEF patients, we performed a computational simulation study of haemodynamics with IAS under volume loading and exercise conditions in HFpEF patients using the proposed framework.

We determined the haemodynamic parameters of HFpEF patients based on previous reports as follows. Maeder et al. and Kaye et al. simulated exercise haemodynamics with IAS using a multi‐factor haemodynamic model. To determine the CO curve, we used the following equation that we reported previously. , where Ees, HR, R, Pa, are end‐systolic elastance of ventricles, heart rate, resistance, and atrial pressure of systemic or pulmonary circulation, respectively; k is the stiffness component of the ventricle. F and H are constants of the CO curve. We used equations 3–5 to determine the venous return surface. First, we determined Ees, R, and HR based on the simulation report of Kaye et al. We set F to 0 to simplify the equation. The remaining parameters, that is, k, H, W, and C, were determined to reproduce the haemodynamics according to previous reports. ,

To simulate the exercise condition based on the report of Kaye et al., we increased Ees, heart rate and stressed volume; decreased resistance; and assumed the exercise intensity to be 0.63 W/kg, which was the limiting exercise intensity. We changed these parameters (Ees, heart rate, stressed volume, and resistance) linearly from 0 to 1 W/kg work rate. Details of the simulation parameters are given in the Supporting Information.

Protocol for the simulation study

In the volume loading simulation, we set baseline QS at 5.3 L/min by changing stressed blood volume for various shunt sizes ranging from 0 to 20 mm in diameter. We then loaded blood volume until 1000 mL. In the exercise simulation, we set the same baseline as the volume loading simulation and changed exercise‐related parameters according to the work rate from 0 to 1 W/kg.

Data analysis

We digitized all data at 200 Hz using a 16‐bit analogue to digital converter (Power Lab 16/35; ADInstruments, NSW, Australia) and stored in a dedicated laboratory computer system. We averaged digitized data over 10 s when time‐series data reached a steady state.

Statistical analysis

We expressed data as mean ± SD and used paired t‐test to compare haemodynamics before and after the left anterior descending artery ligation. Repeated measures ANOVA was used for comparison of haemodynamic data under various IAS conditions. Differences were considered significant at P < 0.05. We performed the statistical analysis using R version 3.4.3 (R Foundation for Statistical Computing, Vienna, Austria).

Results

Creation of impaired cardiac function in dogs

Table shows haemodynamics before (Normal) and after induced myocardial infarction (Impaired). We determined SL, SR, and VT using haemodynamic data under Normal and Impaired conditions. Myocardial infarction significantly increased PLA and PRA and decreased SL. In contrast, myocardial infarction did not change SR significantly. VT remained unchanged irrespective of the induction of myocardial infarction.

TABLE 1

Haemodynamics under normal and impaired left ventricular function

	Normal	Impaired
AP (mmHg)	119.3 ± 25.8	126.2 ± 21.0
HR (b.p.m.)	147.9 ± 23.7	141.6 ± 18.5
PLA (mmHg)	7.8 ± 1.0	11.9 ± 3.2 *
PRA (mmHg)	5.5 ± 1.0	6.4 ± 1.2 *
CO (mL/min/kg)	100.6 ± 30.0	89.3 ± 35.9
Predicted SL (mL/min/kg)	50.0 ± 17.7	37.0 ± 16.6 *
Predicted SR (mL/min/kg)	80.0 ± 26.2	77.9 ± 32.1
Predicted VT (mL/kg)	30.5 ± 2.5	33.0 ± 2.6

Data are expressed as mean ± SD. SL and SR are parameters of the logarithmic function for left and right hearts, respectively. AP, arterial pressure; CO, cardiac output; HR, heart rate; PLA, left atrial pressure; PRA, right atrial pressure; VT, total stressed blood volume.

P < 0.05.

Prediction of IAS haemodynamics

Figure shows the representative time series of IAS haemodynamics. Increases in QIAS decreased AP, PLA, and QS, but increased PRA. At maximum QIAS [(PLA − PRA)/QIAS = 10 × 10−3 mmHg/mL/min/kg], the pressure difference between PLA and PRA was <1 mmHg. Haemodynamic data during IAS are summarized in Supporting Information, . As described in the Methods section, we determined SL, SR, and VT and predicted haemodynamics at various levels of IAS flow. Figure demonstrates the relationship between predicted and measured QP, QS, PRA, and PLA. The narrow error distributions and 95% confidence intervals show reasonable accuracy of the proposed framework.

FIGURE 2

Representative time series data of interatrial shunt (IAS) haemodynamics. We increased IAS flow (QIAS) stepwise by changing the speed of the centrifugal pump. The increase in IAS flow decreases arterial pressure (AP), left atrial pressure (PLA), and systemic flow (QS), but increases right atrial pressure (PRA).

FIGURE 3

Accuracy of prediction. Top panels show the relation between predicted and measured values for pulmonary flow (QP), systemic flow (QS), left atrial pressure (PLA), and right atrial pressure (PRA). Twenty‐eight data sets obtained from six dogs were plotted. Bland–Altman plots (bottom) show acceptable agreement. Open circles and filled circles represent haemodynamics under normal and impaired cardiac function, respectively. Solid lines and dashed lines represent the regression lines and 95% confidence intervals, respectively. r 2, coefficient of determination; RMSE, root mean squared error; LOA, limit of agreement (mean ± 1.96 SD).

Computational simulation study

Illustrated in Figure is the simulated IAS haemodynamics during acute volume loading in HFpEF. Volume loading markedly increased venous pressures (PRA and PLA) (Figure and D) but marginally increased CO (QP and QS) (Figure and B), illustrating volume intolerance in HFpEF patients. IAS size‐dependently attenuated the increase in PLA (Figure ), implying that IAS improves volume tolerance at the expense of increased PRA (Figure ) and QP (Figure ). The PLA‐suppressing effect diminished when the IAS size was 8 mm or larger (Figure ).

FIGURE 4

Volume loading simulation. Baseline stressed volume is set at systemic flow (QS) = 5.3 L/min for several interatrial shunt (IAS) sizes. The x‐axis shows the loading volume. The y‐axis shows IAS size. Volume loading increases pulmonary flow (QP) (A), QS (B), right atrial pressure (PRA) (C), and left atrial pressure (PLA) (D). The relationship between PLA and IAS size under volume load of 0, 500, and 1000 mL (E). Dotted lines, broken lines, and solid lines represent 0, 500, and 1000 mL of loading volume, respectively. IAS significantly antagonizes the increase in PLA in a size‐dependent manner.

Figure illustrates the simulated IAS haemodynamics during exercise in HFpEF. As in the case of volume loading, IAS attenuated the increase in PLA (Figure and E). Exercise‐induced increases in Ees and heart rate and decrease in resistance could lower PLA. However, exercise‐induced increase in stressed volume counteracts these PLA‐lowering effects and increases PLA. These results imply that volume intolerance of HFpEF leads to an increase in PLA during exercise.

FIGURE 5

Exercise simulation studies. We adjusted baseline stressed volume so that systemic flow (QS) was 5.3 L/min regardless of interatrial shunt (IAS) size. The x‐axis shows exercise intensity. The y‐axis shows the intra‐atrial shunt (IAS) size. Exercise increases pulmonary flow (QP), QS, right atrial pressure (PRA), and left atrial pressure (PLA). The relationship between PLA and IAS size under the exercise load of 0, 0.5, and 1 W/kg (E). The dotted line, broken line, and solid line represent 0, 0.5, and 1 W/kg of exercise intensity, respectively. IAS significantly attenuates the increase in PLA in a size‐dependent manner.

Discussions

In this study, we proposed a framework to predict the haemodynamic impact of IAS. In a dog model of IAS, the framework predicted haemodynamics under various IAS flow rates reasonably well in both normal and impaired cardiac function. Computational simulation study indicated that IAS below 20 mm in diameter size‐dependently attenuated the increase in PLA in both volume loading and exercise loading under the HFpEF conditions.

Prediction of interatrial shunting haemodynamics by generalized circulatory equilibrium

In theory, IAS does not alter SR, SL, pumping ability of the heart, VT, or total stressed blood volume. However, IAS translocates the stressed blood volume from the pulmonary to the systemic circulation, depending on the pressure gradient between the right and left atria as well as IAS size. Thus, we modelled IAS haemodynamics by the shunt flow from the systemic circulation to the pulmonary circulation (QIAS = QP − QS) in generalized circulatory equilibrium. As shown in Figure , the proposed framework can predict IAS haemodynamics under various shunt flow rates irrespective of cardiac function. It is well known that the generalized circulatory equilibrium accurately describes the overall integrated haemodynamics, which is defined by the pressure and flow of the right and left heart. Once we established the model using haemodynamic parameters in a given condition, we could predict haemodynamics under various conditions such as myocardial infarction, blood volume gain and/or loss, extra‐corporeal membrane oxygenation, and left ventricular assist device. , , The results of this study also support the robustness of generalized circulatory equilibrium.

Except for severe HF, QS hardly decreases because the oxygen demand of the whole body determines QS. Therefore, the presence of IAS may not reduce QS or PLA at rest. In contrast, IAS attenuates the PLA elevation against the increase of venous return to the left atrium. Because the slope of the CO curve is much steeper in the right ventricle than the left ventricle, the increase in PRA by IAS may be small compared with the decrease in PLA.

Real‐world validation

In order to validate the clinical feasibility of our proposed framework, we applied the data from the REDUCE LAP‐HF I trial , to our framework and compared the predicted values with those measured. To apply the clinical data to the simulation, we had to incorporate some assumptions into the framework. PRA and PLA were substituted by central venous pressure (CVP) and PCWP, respectively. Cd for clinical IAS was calculated from post‐IAS pressure gradient (PCWP‐CVP), QIAS, and equation 7 in the theoretical considerations section. We also assumed patients' height to be 170 cm and adjusted the body weight to match the mean BMI in the original data.

We predicted post‐IAS haemodynamics using baseline haemodynamics [CO, PCWP, CVP, systemic vascular resistance (RS), and RP]. As shown in Table (constant VT), we succeeded to predict the trend of haemodynamic changes after IAS. The predicted arterial pressure (AP), QS, and PLA are lower than those measured at 6 months after IAS. Because our proposed framework predicts acute haemodynamic change after IAS, altered VT in the chronic phase may contribute greatly to those differences. Considering this possibility, we adjusted post‐IAS VT so that mean post‐IAS AP equalled that at baseline (adjusted V) and obtained better prediction of haemodynamics.

TABLE 2

Prediction of IAS haemodynamics from real‐world data

	Baseline	Measured	Prediction from pre‐IAS
			Constant VT	Adjusted VT
QP/QS	—	1.27	1.27	1.26
QP (L/min)	4.6	6.1	5.5	5.6
QS (L/min)	4.6	4.8	4.3	4.5
AP (mmHg)	96	97	91	(96 = Baseline)
PLA (mmHg)	17.4	16.5	14.4	16.0
PRA (mmHg)	9.0	10.6	9.6	11.4

Data are expressed as mean ± SD. AP, atrial pressure; IAS, interatrial shunt; PLA, left atrial pressure; PRA, right atrial pressure; QP, pulmonary flow; QS, systemic flow; VT, total stressed blood volume.

Optimization of interatrial shunting for clinical application

We predicted post‐IAS haemodynamics using pre‐IAS CO, PLA, and PRA. Because these parameters are generally available in clinical settings, we can predict post‐IAS haemodynamics in each patient. It is well known that responders and non‐responders to IAS therapy exist because several cardiovascular properties determine the impact of IAS on haemodynamics. In addition, recent device development has allowed selection of several sizes of IAS. Because the IAS size also affects the degree of PCWP and systemic CO reduction, we need to choose the optimal device size according to cardiovascular properties, volume status, and body size in an individual patient with HF. The framework that we developed makes it possible to predict the haemodynamics after IAS and assess patient‐specific haemodynamic risks such as post‐IAS low CO, high pulmonary flow causing pulmonary hypertension, and worsening of right HF, which contributes to the selection of patient and IAS size.

Kaya et al. reported exercise haemodynamics in the presence of IAS using a multi‐element haemodynamic model. Because they adjusted model parameters from human mass haemodynamic data, they did not address haemodynamic simulation in individual patients. Our proposed framework that allows prediction of patient‐specific post‐IAS haemodynamics using pre‐IAS haemodynamic data is potentially applicable for IAS management in the clinical setting.

The results of previous clinical trials , , , indicate that HFpEF is a good indication for IAS because rapid pulmonary congestion is a cardinal manifestation of HFpEF. In our simulation of HFpEF conditions, although baseline haemodynamics is relatively normal, volume loading or exercise significantly increases PLA to above the critical level (Figures and ). IAS markedly attenuates the increase in PLA. Interestingly, IAS does not mitigate QS during volume loading or exercise much. To elucidate the relationship among the severity of diastolic dysfunction in HFpEF, IAS size, and clinical benefit of IAS, we further simulated the exercise capacity after IAS placement at various levels of diastolic function and IAS sizes.

In reference to Figure , we altered diastolic function by changing the stiffness component (k) at three levels and conducted the same simulation study, as shown in Figure . An increase in k decreased CO and increased PLA. We defined the exercise capacity by the peak exercise level when PLA reached 28 mmHg. , As shown in Figure , in mild HFpEF, PLA never reached the PLA threshold when IAS size was over 5 mm. In moderate HFpEF, IAS size‐dependently increased peak exercise. However, in severe HFpEF, the beneficial impact of IAS on exercise capacity was marginal because of high baseline PLA (24.7 mmHg). These results indicate that IAS improves exercise capacity, especially in mild to moderate HFpEF conditions. Our simulation results are consistent with previous clinical trials. , , ,

FIGURE 6

The relationship between the exercise capacity and IAS diameter under various degrees of diastolic dysfunction in heart failure with preserved ejection fraction (HFpEF) in simulation study. We assumed left atrial pressure (PLA) = 28 mmHg as the exercise capacity under IAS (A) and compared the exercise capacity among three levels of diastolic dysfunction in HFpEF condition (B). We altered diastolic function in HFpEF by changing k, which represents the ventricular stiffness and governs the curvilinearity of the cardiac output curve (mild = 1.23, moderate = 1.3, severe = 1.35). See text Methods section for detail, regarding the definition of the intensity of exercise (0 to 1 W/kg). In mild HFpEF, PLA does not exceed 28 mmHg by exercise under 1 W/kg when IAS size is over 5 mm. IAS strikingly increases exercise capacity, especially in moderate HFpEF. In severe HFpEF, IAS increases exercise capacity slightly. The solid line represents mild HFpEF, broken line represents moderate HFpEF, and dotted line represents severe HFpEF.

Regarding clinical feasibility, we need to consider IAS‐induced increment of QP at rest. Increasing shear stress due to high QP increases the expression of proliferative genes and causes endothelial dysfunction, leading to pulmonary hypertension. Therefore, shunt closure is recommended for atrial septal defect patients with QP/QS > 1.5. As our proposed prediction method only addresses the acute effect, we have to consider various factors including age, severity of pulmonary hypertension, and right heart function for long‐term risk stratification after IAS placement.

Our proposed framework could simulate the effect of IAS on haemodynamics in various cardiac conditions and perturbations (volume loading and exercise). Individualized quantitative prediction of the effect of IAS contributes to the optimization of IAS therapy.

Limitations

There are several limitations to this study. First, we conducted experiments using anaesthetised and open‐chest dogs. Anaesthesia and surgical intervention change the cardiovascular system via the autonomic nervous system, blood volume loss, and artificial ventilation. We need to examine the feasibility of the framework under conscious condition to translate this method to clinical practice. Second, we mimicked IAS by creating a shunt flow using a centrifugal pump. Although mimicked IAS was anatomically different from clinical IAS, we adjusted the shunt flow rate according to the pressure gradient between left and right atria to simulate the different sizes of IAS. Third, to evaluate the impact of interatrial shunt flow on haemodynamics, we created an external shunt flow using a centrifugal pump. The pump‐generated shunt flow in the animal model was unidirectional and constant and was different from the bidirectional and pulsatile IAS flow in patients in terms of fluid dynamics. This difference may affect the Cd (discharge coefficient) in equation 7. Because we used previously reported Cd, the accuracy of prediction of static haemodynamics by our framework should not have been affected. Nevertheless, further investigation may be needed to establish an appropriate mathematical model of IAS considering fluid dynamics to improve our IAS framework. Finally, we did not study the chronic effect of IAS, for example, ventricular remodelling. Although we speculate that the prediction in the acute phase may provide the beneficial effects in the chronic phase, further studies are needed to clarify the usability of the prediction for chronic IAS management.

Conclusions

In conclusion, we predicted the impact of IAS on haemodynamics reasonably well using the generalized circulatory equilibrium. Simulation study reveals how IAS attenuates the elevation of PLA during volume loading conditions and exercise. Computational prediction of haemodynamics before the creation of an IAS would contribute to maximizing the benefit of IAS.

Conflict of interest

Nishikawa T., Uike K., Uemura K., Tohyama T., and Yoshida K. have nothing to declare. Saku K. and Kishi T. worked in a department endowed by Omron Healthcare Co. Saku K. received honoraria from Japan ABIOMED Inc. Sunagawa K. worked in a department endowed by Omron Healthcare Co. and Actelion Pharmaceuticals Japan. Tsutsui H. received honoraria from Daiichi Sankyo, Inc., Otsuka Pharmaceutical Co., Ltd., Takeda Pharmaceutical Company Limited, Mitsubishi Tanabe Pharma Corporation, Boehringer Ingelheim Japan, Inc., Novartis Pharma K.K., Bayer Yakuhin, Ltd., Bristol‐Myers Squibb KK, and Astellas Pharma Inc., and research funding from Omron Healthcare Co, Actelion Pharmaceuticals Japan, Daiichi Sankyo, Inc., and Astellas Pharma Inc.

Funding

This work was supported by Research and Development of Supportive Device Technology for Medicine Using ICT (18he1102003h0004), AMED‐SENTAN; Development of Advanced Measurement and Analysis Systems (18hm0102041h0003), Grant‐in‐Aid for Early‐Career Scientists (18K15893, 19K20690, and 19K17529) from the Japan Society for the Promotion of Science, the research grant from Omron Healthcare Co., and the Japan Foundation for Applied Enzymology (VBIC: Vascular Biology of Innovation).

Data S1. Supporting Information

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Table S1. Haemodynamics under mimicked interatrial shunting

Table S2. Values of model parameters that vary during exercise.

Table S3. Values of model parameters that are constant during exercise.

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Figure S1 Supporting Information

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