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.
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1 Introduction
Computational modelling in physiology has contributed to many significant breakthroughs, but the models themselves have usually not become working tools for experimentalists nor even for other modellers outside the developer’s own group. We provide here a practical implementation of one of the classic and most complete models of body fluid and acid–base regulation, and we give several examples of the use of the model. We give the complete model description in the language of Berkeley Madonna, which is very easy to read and can readily be converted for other numerical solvers. Physiologists and clinicians will find this model easy to use, and this complete example will facilitate extensions in order to simulate related clinical situations or new experimental findings.
Inspired by the classic model of blood pressure regulation by Guyton et al. (1972a), Ikeda et al. (1979) adopted the same symbolic representation to illustrate model structure, but since their focus was on body fluids and acid–base balance, which have a slower time course than, say, autonomic regulation of cardiovascular variables, they simplified the representation of the cardiovascular system but greatly extended the renal and respiratory systems. Their model consists of a set of nonlinear differential and algebraic equations with more than 200 variables and has subsystems for circulation, respiration, renal function, and intra- and extra-cellular fluid spaces.
2 Materials and Methods
2.1 Model Description
The original article of Ikeda et al. (1979) describes the details of the model, so we will not give a complete description here (the program code, Online Resource 01, given in the Electronic Supplementary Material and described in the Appendix, has all the explicit equations); our implementation closely follows the description in their article, especially in their diagrams of the seven blocks that constitute the model, namely, the circulation and body fluids (blocks 1, 3, and 4), respiration (block 2), and renal function (blocks 5, 6, and 7). Initial values and many other details are given not only in the text but also on the diagrams and in the tables of the original article. Here, we give just a brief explanation of the basic content of the model and Ikeda et al.’s general strategy.
As in Ikeda et al. (1979), the model assumes a healthy male of approximately 55 kg body weight, and parameter values used here are those given in the original article. Calibration of the model for other body weights or for females would be a valuable extension of the model but is beyond the goals of the present work. Such extension would involve re-calibration not only of extracellular and intracellular fluid volumes (and thus with impact on solute contents of those compartments), but also of less straightforward parameters such as metabolic rate, respiratory volume, cardiac output, and the like.
The cardiovascular/circulatory (CV) system, quite complex in Guyton’s model, was considerably simplified by Ikeda et al. (1979) to a simple steady state that represents the system’s state after settling from transient local autoregulation or stress relaxation.
By contrast with the simplified CV system, and in keeping with their focus on acid–base and fluid physiology, Ikeda et al. (1979) included much more elaborate representations of the respiratory system, intracellular and extracellular electrolytes and solutes, and of course the kidney. For example:
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Alveolar ventilation (VI) is calculated as a function of blood pH, \(\hbox {P}_{\hbox{CO}_{2}}\), and \(\hbox {P}_{\hbox{O}_{2}}\);
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The blood buffer system is treated using the Henderson–Hasselbalch equation, an equation for the oxygen saturation curve, and an equation for the in vivo \(\hbox{CO}_{2}\) dissociation curve, thus the model takes account of the haemoglobin buffer system, the Bohr effect, and the Haldane effect;
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The model treats intra- and extra-cellular electrolytes and acid–base balance and also glucose metabolism and insulin secretion—disorders of glucose metabolism can be modelled by varying the parameters CGL1, CGL2 and CGL3;
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Plasma osmolality in the model depends on the concentrations not only of sodium, potassium, glucose, and urea, but also of mannitol, included in the model because of its frequent therapeutic use;
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The renal blocks treat reabsorption and excretion not only of water, sodium, and potassium, but also of bicarbonate, calcium, magnesium, phosphate, and organic acids; proximal tubule reabsorption depends on volume expansion or pressure diuresis (THDF); aldosterone is assumed to act on the distal tubule to increase sodium reabsorption, decrease potassium secretion, and increase excretion of titratable acid; urine pH and excretion of ammonia, titratable acid, phosphate, and organic acids are included in the model; glomerular filtration rate (GFR), represented as a sigmoid function of arterial pressure, is controlled by extracellular volume (VEC) and depends on antidiuretic hormone (ADH) and aldosterone (ALD) and on THDF;
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The renin–angiotensin–aldosterone system (RAAS) is represented here simply as a transfer function by which ALD secretion depends on extracellular fluid (ECF) potassium concentration, tubular sodium concentration, arterial pressure, and volume receptor signals.
In addition to this incomplete list, the model contains many other interesting features that the reader should glean from the original Ikeda et al. (1979) article.
2.1.1 Berkeley Madonna Description
Berkeley Madonna is a fast, robust, multi-platform solver of systems of ordinary differential-algebraic equations. Compared with other such solvers, it is extremely easy to program (a simple list of the equations in any order), has a very effective user interface for plotting or tabulating the results and varying the parameters (simple “sliders” can be easily defined to vary individual model variables or parameters, with instant re-run of the model), and it has proven to be very fast compared to other solvers we have used.
3 Results
To demonstrate several interesting features of the model and also to show that the Berkeley Madonna implementation presented here is an accurate representation of the Ikeda et al. model, we show that it faithfully reproduces the results of four simulations whose results are shown in the figures of their article. The BM codes used to generate the results of the following simulations are all provided as Electronic Supplementary Material (see Appendix).
Figure 1 shows the results of a simulation of oral water intake (1 l over 5 min) and intravenous infusion of physiological saline; the left panel shows Fig. 10 from the Ikeda article, and the right panel shows results from our BM model, which are clearly a good match to those in their article.
Figure 2 shows the transient response of respiratory parameters to inhalation of 5 % \(\hbox {CO}_2\) over 30 minutes; the left panel shows Fig. 11 from the Ikeda article, and the right panel shows results from our BM model.
Figure 3 shows results from a simulation of glucose tolerance test (infusion of 50 g of glucose over 1 h), including insulin secretion due to a concomitant decrease of extracellular fluid potassium concentration; as above, the left panel shows Fig. 12 from the Ikeda article, and the right panel shows the corresponding results from our BM model.
Figure 4 shows, in acid–base disturbances, the central role of the kidney in the compensatory reactions of the body when the normal response of respiration does not occur. The long-term time course of the model behavior in respiratory acidosis or alkalosis is depicted on the pH-[\(\hbox {HCO}_{3}\)] diagram. The response to 10 % \(\hbox {CO}_2\) inhalation and the response to hyperventilation are observed. The right panel shows the results from our BM model, which are in good agreement with the results of Ikeda article, shown on the left panel. The sequence of steps necessary to reproduce this figure with BM implementation is detailed in the specific BM code listing (Online Resources 06 & 07).
4 Discussion
Efforts towards reusability and interoperability have made progress in recent years, not only in the modeling of kidney physiology (Thomas 2009) but also in the wider context of physiology and systems biology (Hunter et al. 2013). For instance, SBML (the Systems Biology Markup language)Footnote 1 (Hucka et al. 2003) is widely used for metabolic networks and models of cell signal transduction, the CellML repositoryFootnote 2 contains several hundred marked-up legacy models (mostly at the level of membrane transport or signal transduction), the JSim Consolidated Model DatabaseFootnote 3 indexes 73390 models across five archives, and annotation tools such as the RICORDOFootnote 4 resource (de Bono et al. 2011) and the ApiNATOMYFootnote 5 (de Bono et al. 2012) project now facilitate the sharing (and even the merging) of physiology and systems biology models.
The present work complements previous re-implementations of the Ikeda model; e.g., a Pascal version was used in teaching at the University of Limburg, Maastricht (Min (1982); Pascal source code in Min (1993)), and extensions of parts of the Ikeda model were used in the Golem simulator (Kofranek et al. 2001). The present Berkeley Madonna version also complements our re-implementations of the early Guyton models (Hernandez et al. 2011; Moss et al. 2012; Thomas et al. 2008) and recent models focused on the kidney itself (Karaaslan et al. 2005, 2014; Moss et al. 2009; Moss and Thomas 2014) or on the role of the kidney in blood pressure regulation (Averina et al. 2012; Beard and Mescam 2012). We provide here a convenient implementation of the Ikeda et al. (1979) model in order to facilitate not only its use in its original form but also to enable its extension. One such improvement would be the incorporation of a more complete model of the RAAS system, which is now much better understood and for which a detailed model has recently been published (Guillaud and Hannaert 2010).
References
Averina VA, Othmer HG, Fink GD, Osborn JW (2012) A new conceptual paradigm for the haemodynamics of salt-sensitive hypertension: a mathematical modelling approach. J Physiol 590:5975–5992. doi:10.1113/jphysiol.2012.228619
Beard DA, Mescam M (2012) Mechanisms of pressure-diuresis and pressure-natriuresis in Dahl salt-resistant and Dahl salt-sensitive rats. BMC Physiol 12:6. doi:10.1186/1472-6793-12-6
de Bono B, Grenon P, Sammut SJ (2012) ApiNATOMY: a novel toolkit for visualizing multiscale anatomy schematics with phenotype-related information. Hum Mutat 33(5):837–848
de Bono B, Hoehndorf R, Wimalaratne S, Gkoutos G, Grenon P (2011) The RICORDO approach to semantic interoperability for biomedical data and models: strategy, standards and solutions. BMC Res Notes 4:313
Guillaud F, Hannaert P (2010) A computational model of the circulating renin-angiotensin system and blood pressure regulation. Acta Biotheor 58:143–170. doi:10.1007/s10441-010-9098-5
Guyton AC, Coleman TG, Granger HJ (1972a) Circulation: overall regulation. Annu Rev Physiol 34:13–46
Guyton AC, Coleman TG, Cowley AW Jr, Liard JF, Norman RA Jr, Manning RD Jr (1972b) Systems analysis of arterial pressure regulation and hypertension. Ann Biomed Eng 1:254–281
Hernandez AI, Le Rolle V, Ojeda D, Baconnier P, Fontecave-Jallon J, Guillaud F, Grosse T, Moss RG, Hannaert P, Thomas SR (2011) Integration of detailed modules in a core model of body fluid homeostasis and blood pressure regulation. Progr Biophys Mol Biol 107:169–182. doi:10.1016/j.pbiomolbio.2011.06.008
Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H, Arkin AP, Bornstein BJ, Bray D, Cornish-Bowden A, Cuellar AA, Dronov S, Gilles ED, Ginkel M, Gor V, Goryanin II, Hedley WJ, Hodgman TC, Hofmeyr JH, Hunter PJ, Juty NS, Kasberger JL, Kremling A, Kummer U, Le Novere N, Loew LM, Lucio D, Mendes P, Minch E, Mjolsness ED, Nakayama Y, Nelson MR, Nielsen PF, Sakurada T, Schaff JC, Shapiro BE, Shimizu TS, Spence HD, Stelling J, Takahashi K, Tomita M, Wagner J, Wang J (2003) The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4):524–531
Hunter P, Chapman T, Coveney PV, de Bono B, Diaz V, Fenner J, Frangi AF, Harris P, Hose R, Kohl P, Lawford P, McCormack K, Mendes M, Omholt S, Quarteroni A, Shublaq N, Skr J, Stroetmann K, Tegner J, Thomas SR, Tollis I, Tsamardinos I, van Beek JHGM, Viceconti M (2013) A vision and strategy for the virtual physiological human: 2012 update Interface Focus 3 doi:10.1098/rsfs.2013.0004
Ikeda N, Marumo F, Shirataka M, Sato T (1979) A model of overall regulation of body fluids. Ann Biomed Eng 7:135–166
Karaaslan F, Denizhan Y, Kayserilioglu A, Gulcur HO (2005) Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion. Ann Biomed Eng 33:1607–1630
Karaaslan F, Denizhan Y, Hester R (2014) A mathematical model of long-term renal sympathetic nerve activity inhibition during an increase in sodium intake. Am J Physiol Regul Integr Comp Physiol 306:R234–R247. doi:10.1152/ajpregu.00302.2012
Kofranek J, Lu Danh Vu, Snaselova H, Kerekes R, Velan T (2001) GOLEM—multimedia simulator for medical education. Proceedings of MEDINFO 2001. Stud Health Technol Inform 84:1042–1046
Min FB (1982) Computersimulatie en wiskundige modellen in het medisch onderwijs: Het RLCS System. PhD Thesis (in Dutch) University of Limbug, Maastricht
Min FB (1993) Fluid volumes: the program “FLUIDS”. In: van Wijk van Brievingh RP, Möller DPF (eds) Biomedical modeling and simulation on a PC—A workbench for physiology and biomedical engineering. Springer, New York
Montani JP, Adair TH, Summers RL, Coleman TG, Guyton AC (1989) A simulation support system for solving large physiological models on microcomputers. Int J Bio-medical Comput 24:41–54
Montani JP, Van Vliet BN (2009a) Commentary on ‘Current computational models do not reveal the importance of the nervous system in long-term control of arterial pressure’. Exp Physiol 94:396–397
Montani JP, Van Vliet BN (2009b) Understanding the contribution of Guyton’s large circulatory model to long-term control of arterial pressure. Exp Physiol 94:382–388
Moss R, Grosse T, Marchant I, Lassau N, Gueyffier F, Thomas SR (2012) Virtual patients and sensitivity analysis of the Guyton model of blood pressure regulation: towards individualized models of whole-body physiology. PLoS Comput Biol 8:e1002571. doi:10.1371/journal.pcbi.1002571
Moss R, Kazmierczak E, Kirley M, Harris P (2009) A computational model for emergent dynamics in the kidney. Philos Trans A Math Phys Eng Sci 367:2125–2140. doi:10.1098/rsta.2008.0313
Moss R, Thomas SR (2014) Hormonal regulation of salt and water excretion: a mathematical model of whole-kidney function and pressure-natriuresis. Am J Physiol Renal Physiol. doi:10.1152/ajprenal.00089.2013
Osborn JW, Averina VA, Fink GD (2009a) Current computational models do not reveal the importance of the nervous system in long-term control of arterial pressure. Exp Physiol 94:389–396. doi:10.1113/expphysiol.2008.043281
Osborn JW, Averina VA, Fink GD (2009b) Commentary on ‘Understanding the contribution of Guyton’s large circulatory model to long-term control of arterial pressure’. Exp Physiol 94:388–389. doi:10.1113/expphysiol.2008.046516
Thomas SR, Baconnier P, Fontecave J, Francoise JP, Guillaud F, Hannaert P, Hernandez A, Le Rolle V, Maziere P, Tahi F, White RJ (2008) SAPHIR: a physiome core model of body fluid homeostasis and blood pressure regulation. Philos Trans A Math Phys Eng Sci 366(1878):3175–3197
Thomas SR (2009) Kidney modeling and systems physiology Wiley interdisciplinary reviews: systems. Biol Med 1:172–190
Acknowledgments
This work was funded by the following Grants: VPH NoE (EU FP7, Grant 23920) (http://cordis.europa.eu/fp7/ict/); SAPHIR project, Grant ANR-06-BYOS-0007-01, Agence Nationale de la Recherche (http://www.agence-nationale-recherche.fr/en/); and BIMBO project, Grant ANR-09-SYSCOMM-002, Agence Nationale de la Recherche (http://www.agence-nationale-recherche.fr/en/).
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Appendix
Appendix
1.1 Program Code
The source code for our implementation of the model of Ikeda et al. (1979), using the ODE solver Berkeley Madonna, is available as Supplementary Material on the website of Acta Biotheoretica. In addition to the basic version that corresponds strictly to the description in the original article, we also provide variants used to produce the figures of the present article.
We release the model codes under the CeCill free software license agreement (a copy of the CeCill free software license agreement is included as Online Resource 00, file: ESM_00).
We provide the following Berkeley Madonna source code files:
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1.
Online Resource 01 (file: “ESM_01”): Basic code for simulation of the model in steady-state (file: “ESM_01”)
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2.
Oral water intake and intravenous infusion of physiological saline (Fig. 10 of Ikeda et al. (1979))
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Online Resource 02, file: “ESM_02”—Simulation of water intake at a rate of 1000 ml per 5 min.
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Online Resource 03, file: “ESM_03”—Simulation of intravenous infusion of physiological saline at a rate of 1000 ml per 5 min.
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3.
Transient response of the respiratory system to 5 % \(\hbox {CO}_2\) inhalation (Fig. 11 of Ikeda et al. (1979))
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Online Resource 04, file: “ESM_04”—Simulation of the inhalation of 5 % \(\hbox {CO}_2\) in air over 30 min.
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4.
Glucose tolerance curve with the extracellular potassium concentration (Fig. 12 of Ikeda et al. (1979))
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Online Resource 05, file: “ESM_05”—Simulation during 3 h of a test of glucose metabolism, corresponding to the infusion of glucose at a rate of 1 g/min during 50 min.
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5.
Respiratory acidosis and alkalosis with renal compensation (Fig. 13 of Ikeda et al. (1979)).
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Online Resource 06, file: “ESM_06”—Simulation of 10 % \(\hbox {CO}_2\) inhalation during 48 h.
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Online Resource 07, file: “ESM_07”—Simulation of ventilation at 15 l/min during 48 h.
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1.2 List of Variables
Here we give the table of variables, with units and normal or initial values.
STPD refers to “standard temperature and pressure, dry”, denoting a volume of dry gas at 0 \(^{\circ }\)C and a pressure of 760 mmHg.
Symbol | Definition | Normal value |
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ADH | Effect of antidiuretic hormone (ratio to normal) | 1 |
ALD | Effect of aldosterone (ratio to normal) | 1 |
CFC | Capillary filtration coefficient | 0.007 l/min/mmHg |
CGL1 | Parameter of glucose metabolism | 1 |
CGL2 | Parameter of glucose metabolism | 1 |
CGL3 | Parameter of glucose metabolism | 0.03 |
CHEI | Transfer coefficient of hydrogen ion into ICF | 5 |
CKAL | Weight of effect of XKE on aldosterone secretion | 0.5 |
CNAL | Weight of effect on YNH on aldosterone secretion | 0.1 |
CPAL | Weight of effect of PAS on aldosterone secretion | 0.01 |
CPVL | Weight of effect of PVP on aldosterone secretion | 0.1 |
COAD | Weight of effect of OSMP on ADH secretion | 0.5 |
CPAD | Weight of effect of PVP on ADH secretion | 1.0 |
CKEI | Potassium transfer coefficient from ECF to ICF | 0.001 |
CPRX | Excretion ratio of filtered load after proximal tubule | 0.2 |
CRAV | Arterial resistance/venous resistance | 5.93 |
CSM | Transfer coefficient of water from ECF to ICF | 0.0003 \(\hbox {l}^2/\hbox {mEq}/\hbox {min}\) |
DCLA | Chloride shift | 0 mEq/l |
DEN | Proportional constant between QCO and VB | 1 |
FCOA | Volume fraction of \(\hbox {CO}_2\) in dry alveolar gas | 0.0561 |
FCOI | Volume fraction of \(\hbox {CO}_2\) in dry inspired gas | 0 |
FO2A | Volume fraction of \(\hbox {O}_2\) in dry alveolar gas | 0.1473 |
FO2I | Volume fraction of \(\hbox {O}_2\) in dry inspired gas | 0.21 |
GFR | Glomerular filtration rate | 0.1 l/min |
GFR0 | Normal value of GFR | 0.1 l/min |
HF0-HF4 | Parameters related to the abnormal state of the heart | 0 |
HT | Hematocrit | 45 % |
KL | Parameter of left heart performance | 0.2 |
KR | Parameter of right heart performance | 0.3 |
MRCO | Metabolic production rate of \(\hbox {CO}_2\) | 0.2318 l(STPD)/min |
MRO2 | Metabolic production rate of \(\hbox {O}_2\) | 0.2591 l(STPD)/min |
OSMP | Plasma osmolality | 287 mOsm/l |
OSMU | Urine osmolality | 461 mOsm/l |
PAP | Pulmonary arterial pressure | 20 mmHg |
PAS | Systemic arterial pressure | 100 mmHg |
PBA | Barometric pressure | 760 mmHg |
PBL | PBA-Vapor pressure | 713 mmHg |
PC | Capillary pressure | 17 mmHg |
PCOA | \(\hbox {CO}_2\) tension in alveoli | 40 mmHg |
PF | Filtration pressure | 0.3 mmHg |
PHA | pH of arterial blood | 7.4 |
PHI | pH of intracellular fluid | 7.0 |
PHU | pH of urine | 6.0 |
PICO | Interstitial colloid osmotic pressure | 5.0 mmHg |
PIF | Interstitial fluid pressure | \(-\)6.3 mmHg |
PO2A | \(\hbox {O}_2\) tension in alveoli | 105 mmHg |
PPCO | Plasma colloid osmotic pressure | 28 mmHg |
PVP | Pulmonary venous pressure | 4 mmHg |
PVP0 | Parameter of left heart performance | 0 mmHg |
PVS | Systemic venous pressure | 3 mmHg |
PVSO | Parameter of right heart performance | 0 mmHg |
QCFR | Capillary filtration rate | 0.002 l/min |
QCO | Cardiac output | 5 l/min |
QIC | Rate of water flow into intracellular space | 0 l/min |
QIN | Drinking rate | 0.001 l/min |
QIWL | Rate of insensible water loss | 0.0005 l/min |
QLF | Rate of lymph flow | 0.02 l/min |
QMWP | Rate of metabolic water production | 0.0005 l/min |
QPLC | rate of protein through capillary | 0.000799 l/min |
QVIN | Rate of intravenous water input | 0 l/min |
QWD | Rate of urinary excretion in distal tubule | 0.01 l/min |
QWU | Urine output | 0.001 l/min |
RTOP | Total resistance in pulmonary circulation | 3 mmHg.min/l |
RTOT | Total resistance in systemic circulation | 20 mmHg.min/l |
STBC | Standard bicarbonate at pH = 7.4 | 24 mEq/l |
TADH | Time constant of ADH secretion | 30 min |
TALD | Time constant of aldosterone secretion | 30 min |
THDF | Effect of third factor (ratio to normal) | l |
UCOA | Content of \(\hbox {CO}_2\) in arterial blood | 0.5612 l(STPD)/l.blood |
UCOV | Content of \(\hbox {CO}_2\) in venous blood | 0.6075 l(STPD)/l.blood |
UHB | Blood \(\hbox {O}_2\) combining power | 0.2 l.02 (STPD)/l.blood |
UHBO | Blood oxyhemoglobin | 0.2 l.02 (STPD)/l.blood |
UO2A | Content of \(\hbox {O}_2\) in arterial blood | 0.2033 l(STPD)/l.blood |
UO2V | Content of \(\hbox {O}_2\) in venous blood | 0.1515 l(STPD)/l.blood |
VAL | Total alveolar volume | 3 l |
VB | Blood volume | 4 l |
VEC | Extracellular fluid volume | 11 l |
VI | Ventilation | 5 l/min |
VI0 | Normal value of ventilation | 5 l/min |
VIC | Intracellular fluid volume | 20 l |
VIF | Interstitial fluid volume | 8.8 l |
VP | Plasma volume | 2.2 l |
VRBC | Volume of red blood cells | 1.8 l/min |
VTW | Total body fluid volume | 31 l |
XCAE | ECF calcium concentration | 5 mEq/l |
XCLA | Arterial chloride concentration | 104 mEq/l |
XCLE | ECF chloride concentration | 104 mEq/l |
XCO3 | ECF bicarbonate concentration | 24 mEq/l |
XGL0 | Reference value of ECF glucose concentration | 108 mg/dl |
XGLE | ECF glucose concentration | 6 mg/l |
XHB | Blood hemoglobin concentration | 15 g/dl |
XKE | ECF potassium concentration | 4.5 mEq/l |
XKI | ICF potassium concentration | 140 mEq/l |
XMGE | ECF magnesium concentration | 3 mEq/l |
XMNE | ECF mannitol concentration | 0 mEq/l |
XNE | ECF sodium concentration | 140 mEq/l |
XOGE | ECF organic acid concentration | 6 mM/l |
XPIF | Interstitial protein concentration | 20 g/l |
XPO4 | ECF phosphate concentration | 1.1 mM/l |
XPP | Plasma protein concentration | 70 g/l |
XSO4 | ECF sulphate concentration | 1 mEq/l |
XURE | ECF urea concentration | 2.5 mM/l |
YCA | Renal excretion rate of calcium | 0.007 mEq/min |
YCAI | Intake rate of calcium | 0.007 mEq/min |
YCLI | Intake rate of chloride | 0.1328 mEq/min |
YCLU | Renal excretion rate of chloride | 0.1328 mEq/min |
YCO3 | Renal excretion rate of bicarbonate | 0.015 mEq/min |
YGLI | Intake rate of glucose | 0 mg/min |
YGLU | Renal excretion of glucose | 0 mg/min |
YINS | Intake rate of insulin | 0 U/min |
YKD | Rate of potassium excretion in distal tubule | 0.1205 mEq/min |
YKIN | Intake rate of potassium | 0.047 mEq/min |
YKU | Renal excretion rate of potassium | 0.047 mEq/min |
YMG | Renal excretion rate of magnesium | 0.008 mEq/min |
YMGI | Intake rate of magnesium | 0.008 mEq/min |
YMNI | Intake rate of mannitol | 0 mM/min |
YMNU | Renal excretion rate of mannitol | 0 mM/min |
YND | Rate of sodium excretion in distal tubule | 1.17 mEq/min |
YNH | Rate of sodium excretion in Henle loop | 1.4 mEq/min |
YNH0 | Normal excretion rate of ammonium | 0.024 mEq/min |
YNH4 | Renal excretion rate of ammonium | 0.024 mEq/min |
YNIN | Intake rate of sodium | 0.12 mEq/min |
YNU | Renal excretion rate of sodium | 0.12 mEq/min |
YOGI | Intake rate of organic acid | 0.01 mM/min |
YORG | Renal excretion rate of organic acid | 0.01 mM/min |
YPG | Flow of protein into interstitial gel | 0 g/min |
YPLC | Flow of protein through capillary | 0.04 g/min |
YPLF | Flow of protein in lymphatic vessel | 0.04 g/min |
YPLG | Flow of protein into pulmonary fluid | 0 g/min |
YPLV | Destruction rate of protein in liver | 0 g/min |
YPO4 | Renal excretion rate of phosphate | 0.025 mM/min |
YPOI | Intake rate of phosphate | 0.025 mM/min |
YSO4 | Renal excretion rate of sulphate | 0.02 mEq/min |
YSOI | Intake rate of sulphate | 0.02 mEq/min |
YTA | Renal excretion rate of titratable acid | 0.0168 mEq/min |
YTA0 | Normal excretion rate of titratable acid | 0.0068 mEq/min |
YURI | Intake rate of urea | 0.15 mM/min |
YURU | Renal excretion rate of urea | 0.15 mM/min |
ZCAE | ECF calcium content | 55 mEq |
ZCLE | ECF chloride content | 1144 mEq |
ZGLE | ECF glucose content | 66 mg |
ZKE | ECF potassium content | 49.5 mEq |
ZKI | ICF potassium content | 2800 mEq |
ZMGE | ECF magnesium content | 33 mEq |
ZMNE | ECF mannitol content | 0 mM |
ZNE | ECF sodium content | 1540 mEq |
ZOGE | ECF organic acid content | 66 mM |
ZPG | Protein content in interstitial gel | 20 g |
ZPIF | ISF protein content | 176 g |
ZPLG | Protein content in pulmonary fluid | 70 g |
ZPO4 | ECF phosphate content | 12.1 mM |
ZPP | Plasma protein content | 154 g |
ZSO4 | ECF sulphate content | 11 mEq |
ZURE | ECF urea content | 77.5 mM |
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Fontecave-Jallon, J., Thomas, S.R. Implementation of a Model of Bodily Fluids Regulation. Acta Biotheor 63, 269–282 (2015). https://doi.org/10.1007/s10441-015-9250-3
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DOI: https://doi.org/10.1007/s10441-015-9250-3