## 4 Limitations and Future Directions  
Whereas blood is known to be a non-Newtonian liquid [38] whose rheology depends on blood vessel size, especially at special scales, from coronary epicardial vessels to capillaries, the extant literature appears to use standard blood viscosity and density values [31, 32, 33]. Inclusion of detailed blood rheology into the model is planned but is not expected to alter presented results. Further development of the presented model will lead to its clinical applicability. The sensitivity of FFR to heart rate requires further investigation. Although the sensitivity analysis presented heart rate as a primary regulator of FFR, the results of past work indicate its significance is unsettled. [PERSON] et al. [39] found a significant correlation between FFR and heart rate in the LAD yet no correlation in the RCA in their porcine model. However, an investigation by [PERSON] et al. [40] found no statistically significant effect on mean FFR due to fluctuations in HR. Due to the increasing prominence of FFR regarding revascularization procedure design, further investigation into the measurement of heart rate as a potential FFR affecting factor is necessary. Patient specific model identification will increase the applicability of the model and reduce its prediction uncertainty. The inclusion of vessel-specific biomechanical properties and inclusion of a reactive vascular tone module [41, 42, 43] is expected to allow simulation of clinical parameters such as pulse wave velocities and residence times [44, 45, 46, 47, 48, 49]. The inclusion of autoregulatory processes will further assist making the model's FFR estimates quantitatively reliable [50]. Although lumped parameter models for clinical bedside patient-specific hemodynamic simulation have potential, a significant limitation is the identification of initial parameters to ensure accuracy. The vessel parameters and microvascular impedances in this study were summarized from the literature [27, 30]. Estimating the resistances, compliances, and inductances, for each three-element Windkessel model representing each blood vessel requires measurements of blood vessel diameters and lengths. Patient-specific model identification will increase the applicability of the model and reduce its prediction uncertainty. Time domain or frequency domain methods for parameter investigations from pressure and flow profiles have been developed [51, 52]. Recent work demonstrated the capability of the unscented Kalman filter to personalize parameters for lumped parameter models using iterative simulations between 0D and 3D [53]. However, this method extinguishes the advantage of time and resource use by resorting to multi-scale simulations. Advancements in image processing algorithms for the visualization and quantification of vessel morphometry can be used to calculate the necessary parameters [13, 54, 55]. In addition, this study demonstrates that further investigation into the influence of cardiac parameters is permitted. Whereas a detailed heart model [56] was incorporated into the lumped parameter description [27], the simulated aortic root inflow to the coronary vasculature remains generic. Upon availability, patient-specific aortic root blood flow profiles will alleviate the limitation. Furthermore, the parameters of the heart model, such as ventricular and atrial elastances, require personalization. The development of high-resolution echocardiography and magnetic resonance imaging have demonstrated potential in estimating heart chamber volume [57, 58]. Patient-specific estimation of blood rheology parameters such as blood viscosity will require clinical measurements [38]. By measurement of blood pressure and heart rate, the blood flow into the coronaries can be personalized. Using routine hematocrit blood tests, the viscosity can be personalized to a certain extent [20]. Also with potential, 4D flow MRI data can provide subject-specific temporal inlet flow information.