A simplified strong ion model for acid-base equilibria: application to horse plasma

Constable, Peter D. A simplified strong ion model foracid-base equilibria: application to horse plasma. J. Appl. Physiol. 83(1): 297-311, 1997.TheHenderson-Hasselbalch equation and Stewart's strong ion model arecurrently used to describe mammalian acid-base equilibria. Anomaliesexist when the Henderson-Hasselbalch equation is applied to plasma,whereas the strong ion model does not provide a practical method fordetermining the total plasma concentration of nonvolatile weak acids([A_tot]) and theeffective dissociation constant for plasma weak acids(K_a). Asimplified strong ion model, which was developed from the assumptionthat plasma ions act as strong ions, volatile buffer ions(HCO₃), or nonvolatile buffer ions,indicates that plasma pH is determined by five independent variables:PCO₂, strong ion difference, concentration of individual nonvolatile plasma buffers (albumin, globulin, and phosphate), ionic strength, and temperature. The simplified strong ion model conveys on a fundamental level the mechanism for change in acid-base status, explains many of the anomalies when the Henderson-Hasselbalch equation is applied to plasma,is conceptually and algebraically simpler than Stewart's strong ionmodel, and provides a practical in vitro method for determining[A_tot] andK_a of plasma.Application of the simplified strong ion model toCO₂-tonometered horse plasmaproduced values for[A_tot] (15.0 ± 3.1 meq/l) and K_a(2.22 ± 0.32 × 10⁷ eq/l) that weresignificantly different from the values commonly assumed for humanplasma ([A_tot] = 20.0 meq/l, K_a = 3.0 × 10⁷ eq/l).Moreover, application of the experimentally determined values for[A_tot] andK_a to publisheddata for the horse (known PCO₂,strong ion difference, and plasma protein concentration) predictedplasma pH more accurately than the values for[A_tot] andK_a commonlyassumed for human plasma. Species-specific values for[A_tot] andK_a should beexperimentally determined when the simplified strong ion model (orstrong ion model) is used to describe acid-base equilibria.

     

Compensation for changes in the acid-base balance in intact newborn calves and in experimental metabolic acidosis and alkalosis

The quantitative parameters of the new-born calves acid-alkali balance in the early period of their life has been defined to be essentially changed. Considering the latter their organism acid-base balance natural stabilization is characterized by the certain dynamics which is being disturbed displays a quick development of adaptive reactions. The new-born ones' organism capability to support the acid-base homeostasis has been identified as considerably determined by their tissues alkaline reserve level.     

Modern and traditional approaches combined into an effective gray-box mathematical model of full-blood acid-base

Background

The acidity of human body fluids, expressed by the pH, is physiologically regulated in a narrow range, which is required for the proper function of cellular metabolism. Acid-base disorders are common especially in intensive care, and the acid-base status is one of the vital clinical signs for the patient management. Because acid-base balance is connected to many bodily processes and regulations, complex mathematical models are needed to get insight into the mixed disorders and to act accordingly. The goal of this study is to develop a full-blood acid-base model, designed to be further integrated into more complex human physiology models.

Results

We have developed computationally simple and robust full-blood model, yet thorough enough to cover most of the common pathologies. Thanks to its simplicity and usage of Modelica language, it is suitable to be embedded within more elaborate systems. We achieved the simplification by a combination of behavioral Siggaard-Andersen’s traditional approach for erythrocyte modeling and the mechanistic Stewart’s physicochemical approach for plasma modeling. The resulting model is capable of providing variations in arterial pCO2, base excess, strong ion difference, hematocrit, plasma protein, phosphates and hemodilution/hemoconcentration, but insensitive to DPG and CO concentrations.

Conclusions

This study presents a straightforward unification of Siggaard-Andersen’s and Stewart’s acid-base models. The resulting full-blood acid-base model is designed to be a core part of a complex dynamic whole-body acid-base and gas transfer model.

     

Calcium and myotonia: A mathematical model

A mathematical model was developed in order to investigate the possible role of the modified Ca permeability through the muscle membrane in the genesis of myotonic state. It was demonstrated that the existence of such possibilities and their corresponding characteristics in terms of various membrane parameters have been defined.     

Muscle metabolic status and acid-base balance during 10-s work:5-s recovery intermittent and continuous exercise

Gastrocnemius muscle phosphocreatine ([PCr]) and hydrogen ion ([H(+)]) were measured using (31)P-magnetic resonance spectroscopy during repeated bouts of 10-s heavy-intensity (HI) exercise and 5-s rest compared with continuous (CONT) HI exercise. Recreationally active male subjects (n = 7; 28 yr ± 9 yr) performed on separate occasions 12 min of isotonic plantar flexion (0.75 Hz) CONT and intermittent (INT; 10-s exercise, 5-s rest) exercise. The HI power output in both CONT and INT was set at 50% of the difference between the power output associated with the onset of intracellular acidosis and peak exercise determined from a prior incremental plantar flexion protocol. Intracellular concentrations of [PCr] and [H(+)] were calculated at 4 s and 9 s of the work period and at 4 s of the rest period in INT and during CONT exercise. [PCr] and [H(+)] (mean ± SE) were greater at 4 s of the rest periods vs. 9 s of exercise over the course of the INT exercise bout: [PCr] (20.7 mM ± 0.6 vs. 18.7 mM ± 0.5; P < 0.01); [H(+)] (370 nM ± 13.50 vs. 284 nM ± 13.6; P < 0.05). Average [H(+)] was similar for CONT vs. INT. We therefore suggest that there is a glycolytic contribution to ATP recovery during the very short rest period (<5 s) of INT and that the greater average power output of CONT did not manifest in greater [H(+)] and greater glycolytic contribution compared with INT exercise.     

Adrenergic involvement in blood oxygen transport and acid-base balance during hypercapnic acidosis in the Rainbow Trout,Salmo gairdneri

Summary Rainbow trout (Salmo gairdneri) were subjected to 12 h of external hypercapnia (1% CO₂ in air) during - and/or -adrenoceptor blockade in order to assess the importance of adrenergic responses in modulating blood oxygen transport and acid-base balance during an acute acidotic stress. External hypercapnia caused an elevation of blood carbon dioxide tension and a reciprocal decrease in whole blood pH. A gradual elevation of blood bicarbonate levels caused whole blood pH to increase toward pre-hypercapnic values throughout the hypercapnic period. Pre-treatment of fish with propranolol (a -adrenoceptor antagonist) or phentolamine (an -adrenoceptor antagonist) did not affect their ability to regulate extracellular acid-base status during hypercapnia. On the other hand, adrenergic responses were essential in the maintenance of arterial blood oxygen content during hypercapnia despite the severe extracellular acidosis and a marked Root effect in trout blood, in vitro. Important adrenergic responses included pronounced increases in haematocrit (an -adrenergic effect) and arterial oxygen tension (- and -adrenergic effects) as well as partial regulation of red blood cell pH (a -adrenergic effect). Although pre-treatment of fish with either propranolol or phentolamine caused a reduction in blood oxygen content during hypercapnia, fish died only during complete adrenoceptor blockade, presumably due to severe hypoxemia.Symbols and abbreviations total concentration of oxygen or carbon dioxide, respectively - hct haemotocrit - rbc red blood cell     

Effects of acetazolamide on cerebral acid-base balance

Acetazolamide (AZ) inhibition of brain and blood carbonic anhydrase increases cerebral blood flow by acidifying cerebral extracellular fluid (ECF). This ECF acidosis was studied to determine whether it results from high PCO2, carbonic acidosis (accumulation of H2CO3), or lactic acidosis. Twenty rabbits were anesthetized with pentobarbital sodium, paralyzed, and mechanically ventilated with 100% O2. The cerebral cortex was exposed and fitted with thermostatted flat-surfaced pH and PCO2 electrodes. Control values (n = 14) for cortex ECF were pH 7.10 +/- 0.11 (SD), PCO2 42.2 +/- 4.1 Torr, PO2 107 +/- 17 Torr, HCO3- 13.8 +/- 3.0 mM. Control values (n = 14) for arterial blood were arterial pH (pHa) 7.46 +/- 0.03 (SD), arterial PCO2 (PaCO2) 32.0 +/- 4.1 Torr, arterial PO2 (PaO2) 425 +/- 6 Torr, HCO3- 21.0 +/- 2.0 mM. After intravenous infusion of AZ (25 mg/kg), end-tidal PCO2 and brain ECF pH immediately fell and cortex PCO2 rose. Ventilation was increased in nine rabbits to bring ECF PCO2 back to control. The changes in ECF PCO2 then were as follows: pHa + 0.04 +/- 0.09, PaCO2 -8.0 +/- 5.9 Torr, HCO3(-)-2.7 +/- 2.3 mM, PaO2 +49 +/- 62 Torr, and changes in cortex ECF were as follows: pH -0.08 +/- 0.04, PCO2 -0.2 +/- 1.6 Torr, HCO3(-)-1.7 +/- 1.3 mM, PO2 +9 +/- 4 Torr. Thus excess acidity remained in ECF after ECF PCO2 was returned to control values. The response of intracellular pH, high-energy phosphate compounds, and lactic acid to AZ administration was followed in vivo in five other rabbits with 31P and 1H nuclear magnetic resonance spectroscopy.(ABSTRACT TRUNCATED AT 250 WORDS)     

On indicator dilution and perfusion heterogeneity: A stochastic model

Unidirectional extraction of a substrate S in the capillaries following the arterial injection of a bolus containing S and a reference tracer R is assumed to follow first-order kinetics. If C_R and C_S denote normalized venous effluent concentrations of R and S, respectively, let L(t)=ln[C_R(t)⧸C_S(t)]. We derive a formula which expresses the experimental L(t) data in terms of the mean μ(t) and variance of the transit times of those capillaries which are contributing indicators at each sample time t. We examine the information thus contained in the L data about capillary and noncapillary transit times under several kinematic assumptions. We show that if the capillary and noncapillary transit times are stochastically independent with frequency functions h_c(t) and h_av(t), respectively, then the shapes of the graphs of L(t) and μ(t) depend on the variances and skewnesses of h_c(t) and h_av(t). Specifically, let r₂ be the ratio of the variance of h_c(t) to the variance of h_av(t), and let r₃ be the ratio of skewnesses in the same order. Then the graph of μ(t) is concave downward if r₂⧸r₃ > 1, concave upward if r₂⧸r₃< 1, and linear if r₂⧸r₃ = 1. If the fraction of S extracted is not too large, L(t) has nearly the same shape as μ(t), and therefore, L(t) contains information about h_c(t) and h_av(t).     

A mathematical model of periodic processes in membranes (with application to cell cycle regulation)

A mathematical model of the regulation of the cell cycle by the plasma membrane is suggested. The model is based on the hypothesis that structural transitions of the cell membrane play an important role in the regulation of cell division. Conditions of transition from the proliferating state to the resting state and back are investigated. Possible qualitative differences between models of the cell cycle of a normal and a tumour cell are pointed out.     

A mathematical model of cleavage

In the present paper, we propose a mathematical model of cleavage. Cleavage is a process during the early stages of development in which the fertile egg undergoes repeated division keeping the cluster size almost constant. During the cleavage process individual cells repeat cell division in an orderly manner to form a blastula, however, the mechanism which achieves such a coordination is still not very clear. In the present research, we took sea urchin as an example and focused on the diffusion of chemical substances from the animal and vegetal pole. By considering chemotactic motion of the centrosomes, we constructed a mathematical model that describes the processes in the early stages of cleavage.     

Ventilation and acid-base balance in awake dogs exposed to heat and CO2

Some awake quiet dogs pant at cool ambient temperature (Ta) and some do not pant even when acutely exposed to heat. The purpose of the study was to determine whether this puzzling variability in respiratory behavior diminished during prolonged heat. The contributions of thermal and CO2 drives to respiratory adaptations were also examined. Five awake dogs acclimated to 20 degrees C were studied before and 2 and 48 h following exposure to 30-31 degrees C. Rectal temperature did not change; the important thermal stimulus, even at 48 h, appeared to be the increase in peripheral temperature. Variability between nonpanting and panting persisted over 48 h. On the average, ventilation (VE) doubled during heat, largely due to increased dead space ventilation. Nonpanting dogs at cool Ta decreased the threshold of the ventilatory response to CO2. A panting dog at cool Ta changed its slope of the ventilatory response from negative to positive. During hypercapnia in acute heat, ventilatory pattern changed so that frequency increased and tidal volume decreased for a given VE. By 48 h of heat, the ventilatory response to CO2 returned to control in only two dogs, but the ventilatory pattern during hypercapnia returned to control in four dogs. Since thermal stimuli remained unchanged at 48 h, adaptations of respiratory control may have been related to progressive adjustments of strong ions and acid-base balance.     

A mathematical model of phytoremediation for petroleum-contaminated soil: model development

We present a simple model for root length density that combines the generally accepted spatial (exponential decrease with depth) and temporal (sinusoidal) variability of root length. Parameters in this model for root length density can be determined from assumed or measured information regarding the annual biomass turnover, maximum standing biomass, and maximum depth of root penetration. The root length density model, coupled with information regarding the average root lifespan, gives specific root growth and senescence functions that are the forcing functions for the phytoremediation model. We present a screening level mathematical model for phytoremediation that accounts for the growth and senescence of roots in the system. This is an important factor for recalcitrant, immobile compounds found in weathered crude oil contaminated soils. The phytoremediation model is based on variable volume compartments that have individual first-order degradation rate constants; as the roots move through the soil, the soil cycles through the rhizosphere zone, decaying root zone and bulk soil zone. Thus, although the oil is immobile, as the roots penetrate through the soil the oil is brought into contact with the rhizosphere.