## 2 Methods  
### Model Components  
The composite model consists of a whole body human circulation model where baroreflex control is present, which is coupled to a representation of a dialysis machine. A whole body human circulation model [15,16] with known baroreflex control mechanisms [27, 28, 29] was coupled to a virtual dialysis unit [26,30] (see Figure 2 and Figures S1-S3). Model parameters were inherited from the respective calibrated parent sub-models [15,26,27]. The composite circulation model was extended to include detailed kidneys. The two detailed kidneys, left and right, were placed in parallel and both received inlet flow from the descending aorta. Further, renal microvasculature was represented within each kidney using six resistance-capacitance-resistance Windkessel representations in parallel (Supplementary Figure S1). The three element Windkessel model consists of a proximal resistance element which represents the impedance of the artery, a capacitor which represents the compliance of the elastic artery, and a distal resistor to represent the resistance of the downstream microvasculature. Each renal microvascular bed was assigned resistance and capacitance values derived from the parent model [15].  
Figure 1: Block diagram summary of the presented work with sign posting to relevant sections.  
A virtual hemodialysis system [26; 30] was incorporated to model the impact of dialysis as a clearance of solutes (toxins and water). The implementation of hemodialysis consists of three fluid compartments and two solute compartments, as well as the dialyzer unit. The fluid compartments represent intracellular, extracellular and plasma fluid volume, while the solute compartments represent the amount of intracellular and extracellular (including plasma) solutes. Flux between the compartments is governed by osmosis (fluids) and diffusion (solutes) through membranes. Similarly, solute clearance is governed by diffusive transport between ultrafiltrate (Q\({}_{\text{F}}\)) and blood flowing through the dialyzer (Q\({}_{\text{B}}\)), as described by [PERSON] et al. [26]. The ultrafiltration rate, UF, was assumed to be 0.5 L/h as in previous studies. Notably, the main influence of the dialyzer on the system is a removal of toxins and water. The presented model assumes a controllable ultra-filtration rate as an experimental parameter. As such, the model assumes high levels of toxins and water in the blood as compared to the dialysate, and initial conditions can be found in [PERSON] et al. [30]. Whereas the dialyzer alters blood composition, the cardiovascular system was assumed not to influence the dialyzer.  
A baroreflex mechanism was implemented to model sympathetic and parasympathetic control of cardiac function in response to mean arterial pressure [28; 31]. The baroreflex  
Figure 2: Schematic of presented model. (**A**) Electrical circuit analogue of the reduced order whole body human circulation model. Arrows represent direction of blood flow in arteries (red) and veins (blue). The hemodynamic symbols and their electrical analogues are shown at the bottom of the figure in panel (**B**). Symbols used in panel (**A**). _Acronyms_: Q\({}_{\text{d}}\): ultrafiltration rate. Q\({}_{\text{n}\text{f}}\): injecting flow rate of the dialyzer fluid.  
implementation is a system of first order filters that takes mean arterial pressure as an input, and outputs adjustment coefficients to the baseline values for cardiac elastances as well as a \"\(\Delta\)\" HR term which is added to the intrinsic heart rate to obtain the baroreflex controlled heart rate.