Validation of an integrative mathematical model of dehydration and rehydration in virtual humans.

Water homeostasis is one of the body's most critical tasks. Physical challenges to the body, including exercise and surgery, almost always coordinate with some change in water handling reflecting the changing needs of the body. Vasopressin is the most important hormone that contributes to short-term water homeostasis. By manipulating vascular tone and regulating water reabsorption in the collecting duct of the kidneys, vasopressin can mediate the retention or loss of fluids quickly. In this study, we validated HumMod, an integrative mathematical model of human physiology, against six different challenges to water homeostasis with special attention to the secretion of vasopressin and maintenance of electrolyte balance. The studies chosen were performed in normal men and women, and represent a broad spectrum of perturbations. HumMod successfully replicated the experimental results, remaining within 1 standard deviation of the experimental means in 138 of 161 measurements. Only three measurements lay outside of the second standard deviation. Observations were made on serum osmolarity, serum vasopressin concentration, serum sodium concentration, urine osmolarity, serum protein concentration, hematocrit, and cumulative water intake following dehydration. This validation suggests that HumMod can be used to understand water homeostasis under a variety of conditions.

Introduction

Water homeostasis is an important physiological task to study: hospital readmissions due to dehydration are critical sources of cost following bariatric surgery, ileostomy, and pancreaticoduodenectomy (Whipple), as well as in end‐of‐life care. For example, a readmission increases the 180 day cost of bariatric surgery by $180,000 (Encinosa et al. 2006). Dehydration was reported at 2% of readmissions from roux‐en‐Y gastric bypass and 11% of adjustable gastric banding surgeries (Dorman et al. 2012). For ileostomy, 43% of the 16% readmission rate is attributable to dehydration (Messaris et al. 2012). For pancreaticoduodenectomy, the readmission rate is 28%, with 16% due to dehydration (Hari and Rosenzweig 2012). Additionally, patient quality of life is implicitly reduced by readmission, so ethical considerations lend additional import to better understanding dehydration and rehydration.

Water homeostasis in humans, even in the acute setting, is managed by multiple control systems that interact with one another, but these efforts are led by AVP (vasopressin or antidiuretic hormone, ADH). Additional controlling factors include the baroreflexes (carotid and cardiac, which also induce AVP secretion), the autonomic nervous system, capillary filtration and lymph flow, AVP, and atrial natriuretic peptide (ANP), as well as the roles played by individual subcompartments of the circulatory system such as the splanchnic circulation and the large veins. It is challenging to understand all these interactions in both acute and chronic settings. One way to understand and analyze complicated physiological systems is through mathematical modeling.

Most mathematical models of physiology are intended to address a single aspect of a theory. This serves a dual purpose: it simplifies model construction, and it expedites model analysis. However, simple models do not suffice for complex physiological systems. As previously described, water homeostasis involves multiple systems at different times. Each of these systems may be modeled in a simple way, and integrating these simple models together generates a powerful tool for understanding water homeostasis in healthy and disease states.

The first integrative physiological model involving water homeostasis was that of Guyton, Coleman, and Granger (Guyton et al. 1972) which was designed to test the role of fluid volumes and the kidney in chronic blood pressure control. That model has been expanded to include 14 organ systems, modulated by an autonomic nervous system and an endocrine system, with the capacity for postural changes, exercise, multiple pharmaceutical interventions, hemorrhage, and dozens of other normo‐ and pathophysiologic conditions (Abram et al. 2007; Hester et al. 2011). A robust validation of these efforts has not been published. In this paper, we summarize the systems controlling short‐term water homeostasis in the model and attempt to validate it in the setting of dehydration and the transient response to rehydration. Here we demonstrate the capacity of our model to simulate dehydration/rehydration experiments previously published in human populations and to validate the model for further investigations into water homeostasis in man. The goal is not an exhaustive description of the model, but rather a multifaceted demonstration of the model's ability to reproduce different aspects of the human response to these types of challenges. To our knowledge, no integrative model of serum osmolarity and AVP exists.

Methods

Model

We utilize the integrative mathematical simulator HumMod, a well‐established interactive physiological model comprising some 8000 variables which has been developed over the past 40 years (Hester et al. 2011). HumMod's focus is on integrating all facets of cardiovascular control (neural, hormonal, and fluid‐dynamic) to produce a robust model of circulatory physiology, with auxiliary endocrine, metabolic, and respiratory models providing more details. Precursors of this model have been used in numerous studies whose intent was to provide a more detailed understanding of the physiologic mechanisms at play in common clinical conditions (Summers et al. 1997, 2007, 2009, 2011; Summers and Coleman 2002; Abram et al. 2007). The model is composed of mathematical expressions of the relationships between physiological variables based upon well‐understood cell/tissue/organ physiology. The details of model structure are beyond the scope of this article, and have been described previously (Hester et al. 2011). We will, however, summarize the elements of water homeostasis in the model. These fall into three categories: (1) water compartments and the ability of water to transfer from one compartment to another; (2) the kidney; and (3) the endocrine modulators of pressure and renal function. In these sections, a description and diagram of the model contents are given.

In HumMod, the body is divided into three general water spaces: intracellular, intravascular, and interstitial. The ratio of intracellular to extracellular volumes is mediated by the osmolarity of each space. Water flows between the interstitial and intravascular compartment via lymph flow and capillary filtration/reabsorption. Lymph flow is assumed to depend only on increases in interstitial pressure as valves prevent backflow (Swartz 2001), whereas capillary filtration/reabsorption is determined by Starling forces, the interactions between fluid and oncotic pressures. These transitions are calculated at three different levels to account for the differential effect of gravity in orthostatic challenges.

The kidney is modeled as a single nephron, whose action is multiplied by the number of available filtering nephrons. Flow through the afferent arteriole/glomerulus/efferent arteriole complex is calculated as an ohmic (resistance) system with no compliance. The afferent arteriole is the target of tubuloglomerular feedback originating from the macula densa (MD) as a function of sodium concentration leaving the loop of Henle (LH). The efferent arteriolar resistance is modulated by angiotensin II. Together, these act to buffer pressure changes to maintain adequate filtration at the glomerulus. The nephron itself is divided into proximal tubule (PT), LH, MD, distal tubule (DT), and collecting duct (CD). The reabsorption and secretion actions of these segments exceed the level of detail of this manuscript, but are included for completeness in the Appendix.

The endocrine modulators of water homeostasis are AVP, ANP, and renin/angiotensin II/aldosterone. AVP is released from the posterior pituitary gland in response to increased serum osmolarity or increased activity of the cardiac baroreceptors due to hypervolemia. The hormone is created in the hypothalamus and transported to the neurohypophysis for secretion. It acts in the CD to increase water reabsorption through regulation of the aquaporin‐2 channels. It also acts in the vasculature to increase resistance, which acutely increases systemic pressure and drives greater renal filtration and increased urine osmolarity. Its half‐life in circulation is 10–35 min (Mitra et al. 2011). Because we focus on AVP and serum osmolarity, a brief description of the renal model, the body water homeostasis model, AVP synthesis and secretion, and AVP dynamics and kinetics is given in the Appendix.

HumMod is available for academic download www.hummod.org/projects/.

Protocols

In all cases, we selected studies from the literature with protocols that used hypo‐, iso‐, and hypertonic infusions or oral loads to perturb the water/salt balance in normal humans. Although exercise protocols have been used to study dehydration, we chose to focus on simpler protocols to reduce confounding effects from metabolism and mechanical reflexes, especially the exercise pressor effect, temperature elevations, and acute electrolyte disturbances more associated with exercise activity than hydration status. The protocols used are summarized in Table 1.

Table 1

Summary of experimental and simulation protocols

Protocol	Summary	Reference
A	Water load from basal state	Goldsmith et al. (1986)
B	36 h water deprivation followed by 15 mL/kg oral water	Williams et al. (1989)
C	24 h water deprivation with 80 mmol NaCl, followed by 10 mL/kg oral water	Seckl et al. (1986)
D	24 h water deprivation with 80 mmol NaCl, followed by 10 mL/kg oral 1.2% saline	Seckl et al. (1986)
E	5% saline infusion for 2 h at 0.7 mL/kg, followed by ad libidum oral water	Thompson et al. (1987)
F	5% saline infusion for 2 h at 0.7 mL/kg followed by no water	Thompson et al. (1987)

The first study we simulated (Protocol A) investigated the suppression of AVP following an oral water load (Goldsmith et al. 1986). Following determination of baseline serum osmolarity and AVP, an oral water load of 20 mL/kg over 20 min was given and the same measurements were repeated an hour later.

The second study (Protocol B) tested the effects of drinking volume on AVP and ANP in humans (Williams et al. 1989). Normal volunteers were assessed at baseline, after 36 h of water deprivation, and at 5, 10, 15, 30, and 60 min after different interventions. The interventions included oral intake of water, either drinking 15 mL/kg in 3.5 min (protocol DH 36H + oral H2O 15), or 1 mL/kg in 3 min (protocol DH 36H + oral H2O 1). Water deprivation was accomplished by stopping all water intake for 36 h. This protocol was replicated in HumMod based on an initial virtual body weight of 74 kg before the experiment began; this value was used to generate the total amounts of water ingested. The intake was specified as a constant rate.

The third (C) and fourth (D) protocols we simulated were designed to test the differential effects of either water or hypertonic saline on suppressing AVP secretion (Seckl et al. 1986). Six healthy volunteers were subjected to a 24 h dehydration (with an 80 mmol NaCl pill delivered during the twelfth hour). Following dehydration, subjects ingested 10 mL/kg of tap water (Protocol C) or 10 mL/kg oral saline (180 mmol/L, Protocol D) over the course of 2 min. Blood samples were drawn at 5, 10, 15, 30, and 60 min following administration of fluids. The protocol was replicated in HumMod, with the “pill” being an oral load consisting of 1 mL water and 80 mmol NaCl. Again, the measured weight of the HumMod individual was 74 kg, and intake during the drinking period was specified as constant rate.

The fifth (E) and sixth (F) protocols we simulated AVP responses in hypernatremic individuals (Thompson et al. 1987). Seven healthy volunteers were subjected to an overnight fast with ad libitum water. After a blood draw, subjects received a 2 h infusion of 5% NaCl solution at 0.06 mL/kg/min. After the infusion, a 15 min equilibration period was followed by 30 min of ad libitum tap water (Protocol E) or nothing (Protocol F). Measurements were taken every 30 min following the initiation of saline infusion. The protocol was replicated in HumMod, with “overnight fast” being defined as 10 h with no food intake, and ad lib. water defined by the model's thirst functions.

Analysis

The results between studies are compared, with Z‐scores, the magnitude of the difference between experimental mean and HumMod results divided by the experimental standard deviation. Additionally, root mean square error is computed for each variable observed in each protocol.

Results

We used four different primary sources for data, each using different but related protocols. This was done to demonstrate the ability of the simulation, but it requires confirmation that the studies are consistent between one another. We compared each endpoint shared between at least three protocols: osmolarity (mOsm/kg) (4 studies), AVP (pg/mL) (5 studies), hematocrit (%) (3 studies), and plasma sodium concentration (mmol/L) (4 studies). These are shown in Figure 1, with the baseline HumMod value shown as a dotted line in each figure. All comparisons are made at baseline, before any insult or intervention. HumMod was within a single standard deviation of serum osmolarity and hematocrit in all cases. AVP differed significantly between the studies, although not within studies with multiple arms. HumMod was within one standard deviation of Seckl's results (Protocols C and D) (Seckl et al. 1986), which fell between Goldsmith's (Protocol A) (Goldsmith et al. 1986) relatively higher and Thompson's (Protocol E and F) relatively lower results (Thompson et al. 1987). Serum sodium was similar in HumMod to both arms of Seckl's study (C and D) and one of Thompson's “drinking” protocol (E). HumMod differed from Thompson's nondrinking protocol by less than two standard deviations (F). The nondrinking arm was significantly different than the drinking arm as well (E and F).

Figure 1

We compare the baseline variable values shared between at least three different protocols. In each case, the dashed line indicates the value of the HumMod simulation at baseline for comparison. Error bars denote standard deviation. Panel A shows baseline serum osmolarity, Panel B shows serum AVP levels, Panel C shows hematocrit, and Panel D shows plasma sodium concentration.

All protocols were divided into four different types of challenges to physiological homeostasis. The first protocol was the response to water loading from the basal state. Second was the response to dehydration over a period of 24–36 h. Third, we considered the response of the dehydrated individual to fluids following fluid restriction. Fourth was the reaction to hypertonic infusion and recovery from the same with water. These divisions will guide the remainder of the results. In all cases, the original human data are redrawn against HumMod's results for easy comparison. Additionally, HumMod's responses are shown as dashed lines, and the experimental results are shown as solid lines.

Goldsmith tested the response of serum osmolarity, AVP, and urine osmolarity to a water load (A). HumMod successfully replicated the osmolarity and AVP responses, staying within a single standard deviation at the pre and postexperimental data points (Fig. 2). HumMod's urine osmolarity did not fall as far as did the patients' in the study. HumMod predicted U osm = 324 mOsm/kg, whereas the experiment showed U osm = 133 ± 86 mOsm/kg. Sodium excretion concentration only fell by 25% (data not shown), whereas water excretion rose 20‐fold (from 0.58 to 11.89 mL/min).

Figure 2

We show the HumMod simulation of Goldsmith's protocol (Protocol A), along with Goldsmith's data. Dashed lines represent simulations, whereas solid lines represent experimental data.

The studies of Williams (B), Seckl (C and D), and Thompson (E and F) were dehydration studies. Williams and Seckl used water restriction and Thompson used hypertonic saline infusion to achieve this end. They shared two measurements in common: AVP and serum osmolarity. These are shown in Figure 3 for Protocols B, C, and E, as D and F were statistically equivalent to C and E during the dehydration period. Both quantities changed significantly in the dehydration period, and HumMod showed similar changes, within one standard deviation of the experimental changes in both quantities in both Seckl's and Thompson's studies. HumMod's basal AVP was less than two standard deviations from Thompson, as was noted in Figure 1; HumMod additionally had a more significant increase in serum osmolarity than Thompson reported (<2 standard deviations). The only other observed variable that changed robustly during dehydration was serum sodium, as observed in Seckl's study. We observed a similar change, again with both endpoints being within one standard deviation of the experimental results (included in supplement).

Figure 3

Protocols B–F began with a dehydration period. The effects of dehydration on serum AVP and osmolarity were reported at the beginning and end of dehydration, and are here compared to the simulated results from HumMod. Protocols C and D were statistically equivalent during dehydration, as were Protocols E and F, so we show only Protocols B,C, and F for clarity. Dashed lines represent simulations, whereas solid lines represent experimental data.

In both Williams' study (Protocol B) and the water arm of Seckl's study (Protocol C and D), hypotonic fluids were used to recover from water restriction. These observations yielded the acute human response to moving from a hypertonic to hypotonic state through oral intake (Fig. 4). In HumMod, serum osmolarity remained within one standard deviation of all experiments at each time point except the first in the 36 h dehydration study. The experimental serum sodium response to water loading after 24 h dehydration was similar for each measurement, as was the total serum protein response to saline loading. Williams' study (Protocol B) reported no significant changes in heart rate, and HumMod's responses were similar (remaining within a standard deviation of experimental results, data not shown). In HumMod, total serum protein dipped during recovery from water restriction (Fig. 4A), while no change was seen experimentally. Williams recorded hematocrit throughout the experiment, which we used as a proxy for the proportion of infused water that remains within the vasculature. Model hematocrit and protein changed together on a percentage basis (data not shown), indicating that increased volume caused the excessive dip. This may have been due to overly aggressive water reabsorption in the GI lumen following dehydration.

Figure 4

The water restriction protocols (Protocols B, C, and D) are shown along with their responses to rehydration. Serum osmolarity, AVP, and protein were measured in all three protocols and are shown for comparative purposes. Dashed lines represent simulations, whereas solid lines represent experimental data.

For further confirmation of the validity of model response, the Δ[AVP] and Δ[Osm] curves for 24 and 36 h dehydration (Protocols B and C) with oral water recovery are shown in Figure 5. For clarity, error bars are dropped, and change from baseline is shown rather than absolute values. The curves are qualitatively similar, and the simulation curves lie within the first standard deviation of the experimental curves.

Figure 5

The relationship of AVP and serum osmolarity is shown in the experimental and simulation protocols B (top) and C (bottom). Dashed lines represent simulations, whereas solid lines represent experimental data.

Thompson investigated the effects of ad libidum water versus no water in the response to hypervolemic hypernatremia following saline infusion (Protocols E and F). These protocols involve the patient choosing their own drinking rate and total water intake. This presents a different set of challenges to the model. Figure 6 illustrates the primary elements of the validation study. In HumMod, the change in AVP throughout the dehydration similarly reflected that seen in the actual experiments, although the absolute magnitudes were somewhat different. Recall from Figure 1 that Thompson's AVP measurements were significantly lower at baseline than that seen in the other experiments. In Protocol F, HumMod replicated the rise in serum osmolarity near perfectly; in Protocol E, the model had a persistent bias of 3 mOsm/L (data not shown). The change in serum osmolarity throughout the dehydration process did approximate the experimental record to within a standard deviation at each measurement. Serum sodium remained within 1 standard deviation at all points in Protocol F, and exceeded this bound only at the initial and final time step of the dehydration process in Protocol E. The change in hematocrit was observed as a proxy for vascular‐extravascular balance, and remained within bounds in both protocols for every measurement except the last time point of Protocol E. Again, this likely reflects water being absorbed too rapidly in the GI tract. The cumulative water intake in HumMod was similar to the experimental results (Fig. 7). At 5 and 10 min after drinking was allowed (minutes 140 and 145 of Protocol E), the model underestimated drinking rate, but the aforementioned dips in protein and hematocrit indicate that absorption was overpaced even at the reduced intake.

Figure 6

We show AVP, sodium, and hematocrit in the experimental and simulated response to hypertonic saline infusion, followed by either ad libidum water or no water (Protocols E and F). Dashed lines represent simulations, whereas solid lines represent experimental data. The gray bar in Panel A shows the water intake period.

Figure 7

Comparison between the cumulative water intake during the ad libidum water period in Protocol E. Dashed lines represent simulations, whereas solid lines represent experimental data.

The overall validity of the model was determined by Z‐score analysis. Each measured experimental endpoint was simulated, and the simulated value was given a z‐score based on the experimental distribution. The outcome of this study is shown in Figure 8. The model predictions lay more than two standard deviations from the experimental results 5 of 161 times, and between one and two standard deviations from the experimental mean 19 of 161 times. Additionally, root mean square errors are shown for each protocol and variable as a measure of the deviation of the error of the simulation as compared to the particular observation and protocol.

Figure 8

This heat map shows the Z‐scores of HumMod compared to every measurement discussed in this manuscript. White indicates Z < 1, black indicates Z > 2, and the grayscale varies with Z between 1 and 2.

Discussion

Water homeostasis is one of the body's most critical tasks. Physical challenges to the body, including exercise and surgery, almost always coordinate with some change in water handling reflecting the changing needs of the body. Maintenance of water homeostasis in a healthy individual is a matter of multiple control systems that interact directly and indirectly. The partition of extracellular water into interstitial and vascular compartments, the actions of the kidneys to rid the body of excess fluids and salt, and the renal hormones, both vasoactive and inactive, combine to form a complex network of forces competing to accomplish similar and parallel goals: the preservation or diminution of the body's sodium and water loads.

In this work, we tested the validity of HumMod, an integrative physiological mathematical model, in a variety of challenges to water homeostasis, emphasizing its performance in simulating changes in serum osmolarity, serum sodium concentration, and serum AVP. This effort is not intended to describe the method of parameterization of the model, which was done by on a relationship‐by‐relationship basis to best fit experimental data, mostly from animals. We present the model's responses to under‐ and over‐hydration, and recovery from these states via a variety of strategies. The protocols we used replicate human experiments, and we transcribed data from a small collection of papers to demonstrate HumMod's validity. We only concentrated on dehydration through water restriction and through hypertonic infusion and not an exercise protocol in order to minimize the confounding effects of metabolic and sympathetic disturbances. The original results for the experimental studies were reported as mean and standard error; we converted these to standard deviations to allow an intuitive z‐score analysis. As well, we present the root mean square error of each variable observed in the protocols to numerically quantify model error. Although the model could more closely replicate these protocols, changing model parameters would result in a rejection of the relation‐level calibration, and would nullify any claims made as to the validity of the model.

Most mathematical models simulate a single process or small network of processes, trading breadth for accuracy with respect to a small number of studies. HumMod is designed to be a different type of model, encompassing multiple control systems, each built originally as a small model but sewn together to create a multisystem model. The purpose of HumMod is to simulate as many physiological actions as possible in a computationally efficient framework. We sacrifice many complexities of physiology for this purpose: pulse waves, local tissue effects at the microscopic level, and action potentials are all ignored in our model. Instead, we reduce the human body to organ or tissue level (e.g., α, β, γ, and δ cells in the pancreas) to allow system‐level interactions to develop, similar to the approach of Guyton and Coleman (Guyton et al. 1972). This allows more complex validation to take place. Rather than considering the model response to a single type of challenge, or to a single system, the model can be tested simultaneously in multiple ways, adding confidence that the simulation outputs reflect reality. In our case, the three types of prefix protocols: restriction hypernatremia, salt loading hypernatremia, and normal state, are combined with four types of suffix protocols: water restriction, ad libidum water, water loading, and saline loading. These protocols offer challenges to salt retention, water partition, and water retention. In the studies we used to validate our model, plasma renin activity was observed but did not significantly change. HumMod behaved similarly, so those results were not included. Significant changes in AVP, serum osmolarity, and serum sodium were observed in multiple studies, so we focused our exposition on these factors.

In all cases, HumMod was able to match the overall changes in serum osmolarity, AVP, urine osmolarity, hematocrit, serum protein concentration, ANP, and serum sodium concentration, only falling outside the first standard deviation 23 times, and outside of the second standard deviation 4 times, over 161 total observations. Moreover, the AVP‐osmolarity serum curves were very similar to those extracted from two different published experimental protocols. Recalling that the secretion mechanism for AVP is also influenced by nervous reflexes associated with pressure, we believe that this demonstrates a successful integration of multiple systems.

The most integrated response we observed, however, is cumulative water intake (CWI) following induced hypernatremia with normovolemia (Protocol E). This response integrates serum sodium and osmolarity with AVP, the thirst mechanisms, and the gastrointestinal tract's absorption of water. Taken together, the closely fitted responses of CWI, AVP, sodium concentration, and serum osmolarity indicate that our model captures all of the important apparent features of the human response to acute hypernatremia, which has not been successfully replicated before.

The most challenging aspect of AVP secretion to quantify experimentally is the interaction of neural stimulus and osmolarity. Only two of the protocols we considered, Thompson's hypervolemic hypernatremia (E and F) measured pressure, and no significant differences were observed throughout the protocol in either the human experiments or the model. The model did not predict significant changes to mean arterial pressure in the other protocols either, so it is possible we were able to restrict our attention to only the osmolarity stimulus, the thirst mechanism, the partition of body water, and the actions of the kidney toward fluid maintenance.

One limitation of the model was in predicting urine osmolarity after an acute water load in Protocol A. Goldsmith did not report data other than urine osmolarity, which makes comparison difficult. The significant increase in water excretion matches the rates of 20 L of water intake observed at balance in human patients with diabetes insipidus (DI), which suggests that salt retention, or lack thereof, may be the source of the discrepancy. While the model demonstrated a 33% increase in ANP after acute water load, one source noted no significant change in ANP in a similar study (Burrell et al. 1991).

In conclusion, HumMod provides a realistic simulation of the selected protocols challenging interstitial fluid balance, intracellular/extracellular fluid balance, AVP secretion and action, and thirst. We believe that HumMod demonstrates sufficient similarity to reported responses to salt/water homeostasis to serve as a basis for future investigations.

Conflict of Interest

None declared.

Table A1

Volume and water transport regulation. Total body water is calculated by the sum of three regions (torso compartments), each of which is divided into intracellular and interstitial spaces. Important calculation, variables, parameters are listed. Also included is a diagram of the water flux between the total intracellular, interstitial, and plasma fluid spaces with approximate volumes

Table A2

ADH synthesis and secretion. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect. Calculations are provided for some variables

Table A3

Control of renal vascular resistance and GFR. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect

Table A4

Control of sodium reabsorption in the nephron. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect

Table A5

Control of water reabsorption in the nephron. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect. Calculations are provided for some variables

Table A6

Rcts that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect. Calculations are provided for some variables

Table A7

Regulation of tubuloglomerular feedback (TGF) and renal hormones. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect. Calculations are provided for some variables where indicated

Table A8

Regulation of relevant nonrenal hormones. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect. Calculations are provided for some variables where indicated

Table A9

Control of organ vascular conductance. The dependent variables are displayed in the left column, whereas factors and effects that impact the dependent variables are listed in the middle column, along with their effect range and input variable that determines the effect. Conductance is calculated from the product of the effects and the baseline conductance. “Local” tissues are the GI tract, Bone, Adipose tissue, and nonspecific other tissue. Skin flow, with its dependence on temperature, is not shown here