Implementation of a model of bodily fluids regulation

Abstract

The classic model of blood pressure regulation by Guyton et al. (Annu Rev Physiol 34:13-46, 1972a; Ann Biomed Eng 1:254-281, 1972b) set a new standard for quantitative exploration of physiological function and led to important new insights, some of which still remain the focus of debate, such as whether the kidney plays the primary role in the genesis of hypertension (Montani et al. in Exp Physiol 24:41-54, 2009a; Exp Physiol 94:382-388, 2009b; Osborn et al. in Exp Physiol 94:389-396, 2009a; Exp Physiol 94:388-389, 2009b). Key to the success of this model was the fact that the authors made the computer code (in FORTRAN) freely available and eventually provided a convivial user interface for exploration of model behavior on early microcomputers (Montani et al. in Int J Bio-med Comput 24:41-54, 1989). Ikeda et al. (Ann Biomed Eng 7:135-166, 1979) developed an offshoot of the Guyton model targeting especially the regulation of body fluids and acid-base balance; their model provides extended renal and respiratory functions and would be a good basis for further extensions. In the interest of providing a simple, useable version of Ikeda et al.'s model and to facilitate further such extensions, we present a practical implementation of the model of Ikeda et al. (Ann Biomed Eng 7:135-166, 1979), using the ODE solver Berkeley Madonna.

Fig. 1

a Simulation of oral water intake (solid lines) and intravenous infusion of physiological saline (dashed lines), both at a rate of 1000 ml per 5 min (see Fig. 10 in Ikeda et al. (1979)). b The same simulations were carried out in Berkeley-Madonna. We simulate, during 3 h, the responses of body fluid and kidney parameters to acute water loading (solid lines) at a rate of 200 ml/min during 5 min (rate of drinking, QIN=0.2 l/min from t = 5 to 10 min) and to intravenous normal saline infusion (dashed lines), solution of 0.9 % w/v of NaCl, containing 154 mEq/l of ${\text{Na}}^{+}$ and ${\text{Cl}}^{-}$, at the same rate during 5 min (from t = 5 to 10 min, the rate of intravenous water input was QVIN = 0.2 l/min , and intake rate of sodium and chloride was YNIN = YCLI = 30.8 mEq/min). For the simulation of oral water intake (Online Resource 02), the user must replace the following line of BM code: QIN = 0.001 with: QIN = IF (TIME $\ge$ 5 AND TIME $\le$ 10) THEN 0.2 ELSE 0.001. For the simulation of intravenous infusion of physiological saline (Online Resource 03), the user must replace the following lines of BM code: QVIN = 0, YCLI = 0.1328 and YNIN = 0.12 with: QVIN = IF (TIME $\ge$ 5 AND TIME $\le$ 10) THEN 0.2 ELSE 0, YCLI = IF (TIME $\ge$ 5 AND TIME $\le$ 10) THEN 154*0.2 ELSE 0.1328, YNIN = IF (TIME $\ge$ 5 AND TIME $\le$ 10) THEN 154*0.2 ELSE 0.12. We observe the rate of urinary output (QWU), the plasma volume (VP), the volume of extracellular fluid (VEC), the intracellular fluid volume (VIC), the plasma osmolality (OSMP), the interstitial fluid volume (VIF), the systemic arterial pressure (PAS), the standard bicarbonate at pH = 7.4 (STBC), the effect of antidiuretic hormone (ADH), and the effect of aldosterone (ALD)

Fig. 2

a Simulation of the transient response of the respiratory system to 5 % ${\text{CO}}_2$ inhalation (see Fig. 11 in Ikeda et al. Ikeda et al. (1979)). b The same simulation was carried out in Berkeley-Madonna (Online Resource 04). We simulate, during 1 h, the transient response of the respiratory parameters to the inhalation of 5 % ${\text{CO}}_2$ in air over 30 min (volume fraction of ${\text{CO}}_2$ in dry inspired gas FCOI = 0.05 from t = 5 to 35 min). The user must replace the following line of BM code: FCOI = 0 with: FCOI = IF (TIME $\ge$ 5 AND TIME $\le$ 35) THEN 0.05 ELSE 0. We observe the alveolar ventilation (VI), the pressure of ${\text{CO}}_2$ and ${\text{O}}_2$ in the alveoli (PCOA and PO2A), and the concentration of bicarbonate of the extracellular fluid (XCO3)

Fig. 3

a Simulation (Fig. 12 in Ikeda et al. Ikeda et al. (1979)) of the glucose tolerance curve with the extracellular fluid potassium concentration. b The same simulation was carried out in Berkeley-Madonna (Online Resource 05). We simulate, during 3 h, a test of glucose metabolism, corresponding to the infusion of glucose at a rate of 1 g/min during 50 min (intake rate of glucose YGLI = 1000 from t = 5 to t = 55 min). The user must replace the following line of the BM code: YGLI = 0 with: YGLI = IF (TIME $\ge$ 5 AND TIME $\le$ 55) THEN 1000 ELSE 0. We observe the ECF glucose concentration (XGLE), the ECF potassium concentration (XKE), the plasma osmolality (OSMP), the rate of urinary output (QWU), the renal excretion of glucose (YGLU), and the rate of renal loss of potassium (YKU)

Fig. 4

a Simulation (Fig. 13 in Ikeda et al. Ikeda et al. (1979)) of respiratory acidosis and alkalosis with renal compensation. Point O shows the normal value of the model of the pH-[${\text{HCO}}_3$] plane. Triangle indicates the plotting of simulated response to 10 % ${\text{CO}}_2$ inhalation for 48 h, and Filled circle indicates that of hyperventilation, in which VI was fixed at 15 1/min. Equi-pressure lines of ${\text{PCO}}_2$ are shown with dotted lines for the ${\text{PCO}}_2$ values of 13.3, 40.0, and 73.0  mmHg. b The same simulations were carried out in Berkeley-Madonna. We first simulate (Online Resource 06), during 48  h, the response to 10 % ${\text{CO}}_2$ inhalation (volume fraction of ${\text{CO}}_2$ in dry inspired gas FCOI at the value of 0.1, rather than 0, during the whole simulation and equation (1) unmodified). The bicarbonate concentration of the extracellular fluid (XCO3) and the pH of arterial blood (PHA) are measured at various times from 12 min to 48 h and plotted with Triangle line. We then simulate (Online Resource 07) during 48 h the response to hyperventilation, in which VI was raised to three times normal (alveolar ventilation VI is kept constant to 15  l/min, VI=15, replacing equation (1) of the BM code during the whole simulation). The volume fraction of ${\text{CO}}_2$ in dry inspired gas FCOI is set at its normal value 0. XCO3 and PHA are measured at various times from 12 min to 48 h and plotted with Filled circle line