Understanding and recognition of the right ventricular function and dysfunction via a numerical study

The role played by the right ventricular (RV) dysfunction has long been underestimated in clinical practice. Recent findings are progressively confirming that when the RV efficiency deteriorates both the right and the left circulation is (significantly) affected, but studies dedicated to a detailed description of RV hemodynamic role still lack. In response to such a gap in knowledge, this work proposes a numerical model that for the first time evaluates the effect of isolated RV dysfunction on the whole circulation. Lumped parameter modelling was applied to represent the physio-pathological hemodynamics. Different grades of impairment were simulated for three dysfunctions i.e., systolic, diastolic, and combined systolic and diastolic. Hemodynamic alterations (i.e., of blood pressure, flow, global hemodynamic parameters), arising from the dysfunctions, are calculated and analysed. Results well accord with clinical observations, showing that RV dysfunction significantly affects both the pulmonary and systemic hemodynamics. Successful verification against in vivo data proved the clinical potentiality of the model i.e., the capability of identifying the degree of RV impairment for given hemodynamic conditions. This study aims at contributing to the improvement of RV dysfunction recognition and treatment, and to the development of tools for the clinical management of pathologies involving the right heart.


Hemodynamic model
To simulate the blood circulation, we used the lumped parameters methodology. It allows to represent the vascular compartments of the body, i.e., any vascular segment that it is necessary to describe, by pressure and flow rate, and the heart. This methodology is widely used to simulate the whole In this work, the great vessels were reproduced considering the compliance and resistance effects, and the vascular bed was represented by the resistance effect (supplementary Fig. S2). This holds for both the systemic and pulmonary circulations. This choice allows to reproduce the elastic properties and small dissipative effects of the arteries and veins, and the dissipation effects that characterize the small vessels of the vascular bed. Notice that preliminary tests showed that the adoption of a Windkessel model with more elements than those here included does not significantly refine the results of right ventricular dysfunction simulations. Finally, the heart valves were represented as an ideal diode associated to a 38 resistance. They open and close instantaneously and they allow the blood to flow through only when there is a positive pressure gradient across them, forcing a unidirectional flow. The equation is with and the pressure upstream and downstream, respectively, R the valve resistance and Q the flow rate.
Note that, the present model does not account for chamber interaction via septa 61-63 .

Time-varying elastance
To simulate the right ventricular dysfunction, the right time-varying elastances were modified.
Supplementary Fig. S3 shows the right time-varying elastance for the systolic, diastolic, and combined dysfunctions, resulted from the change of the parameters of Eq. (1), as described in Section Dysfunctional case. In the systolic dysfunction ( Fig. S3a), , the maximum contraction force, decreases linearly with p increasing, from 0.45 mmHg/mL in the healthy condition to the minimum value of for the complete impairment ( = 0.035 mmHg/mL). At the same time, the ejection time increases as well as the acceleration time, resulting in a delayed of the peak as the pathology worsens. On the contrary, in the diastolic dysfunction ( Fig. S3b), is rather constant and the systolic phase slightly varies with p, ranging between the 37% and the 40% of the heartbeat. However, an increase of ventricular stiffness and the decrease of the deceleration times are due to larger value of and , respectively.
Finally, in the combined dysfunction (Fig. S3c) the combination of the previous effects is visible. lines; the corresponded degree of RV impairment, p, from 10% to 100%.

Sensitivity analysis
A sensitivity analysis as in Mynard 19 was conducted to evaluate the sensitivity of the model. Input parameters were increased by 25%, one at a time, assessing the changes in the outputs. The sensitivity was computed considering the mean value of the outputs over one heartbeat as where and are the input at baseline and 25% increased value, respectively, and and are the outputs with baseline and 25% increased inputs, respectively. Note that a positive value of indicates that an increase in determines an increase in , whereas, a negative value of S shows that an increase in causes a decrease in 19 . Particularly, we evaluated 16 inputs and 20 outputs of the model. Table   S3 reports Tables   Table S1. Input parameters required to run the simulation: heart parameters, resistances and compliances of the circulation, and the initial values of the variables.