External Balance of Electrolytes and Acids and Alkali

This chapter will cover discussions on principles of external balance for electrolytes, and for acids and bases. The first section will deal with discussions on principles of electrolyte balance in general, and the second section discusses the acid–base balance.

Principles of Electrolyte Balance

Why is Balance Always Restored?

The underlying mechanism that allows eventual restoration of balance is perfect and foolproof. As an example, the kidney is a central player in the restoration and achievement of fluid and electrolyte balance in living organisms, but the smartness of the kidney is not the reason for perfect balance. The kidney merely accelerates the process by utilizing a principle ubiquitous in nature, but it does not determine its ultimate outcome. The most crucial element of the control system that restores ultimate balance is that a discrepancy between intake and output inevitably leads to a change in total content of the element in the system, and the uncorrected imbalance is cumulative. When input is greater than output the content increases, and the continued imbalance keeps increasing the content. When output is greater than input the content decreases, and the continuing imbalance keeps decreasing the content. In a system with a limited capacity, a change in content of a substance alters its concentration; this invariably affects output, and sometimes also input. The key points here are: (1) an uncorrected balance invariably leads to a change in content; (2) a change in content leads to a change in concentration; (3) an altered concentration affects output or input; and (4) these effects are cumulative.

Is the Capacity of any System Always Limited?

Is the capacity of any system always limited? The answer is yes. We often say: the sky has no limit. Yet there is a limit even to the capacity of atmospheric air volume. The apparent air volume is about 4.08×10 ²¹ liters. (The apparent air volume is calculated considering that air is denser at sea level, and density declines progressively with rising altitude until there are no more air molecules. Thus, the apparent air volume is the theoretical volume that would be required if all the gases in the air were contained at the same concentrations as those at sea level at a pressure of 760 mmHg when the 1 mole of gas is contained in 22.4 liters.)

In recent years, the rising CO ₂ concentration of the atmosphere and its impact on global warming is the source of a great deal of public concern. The rising CO ₂ concentration implies that the amount of CO ₂ added to the atmosphere is more than the amount eliminated from the atmosphere. However, the discrepancy will not and cannot remain permanent, because the CO ₂ concentration in the atmosphere has a positive influence on the rate of its removal from the atmosphere. The main source of CO ₂ addition to the air is the burning of fossil fuels (oil, gas, and coal). The total amount of CO ₂ added is about 30 billion tons per year. This amount added to the air volume of 4.08×10 ²¹ liters would increase atmospheric CO ₂ concentration by about 3.74 ppm per year. Currently, the actual rise in CO ₂ concentration is about 2 ppm per year. The difference, 1.74 ppm, is absorbed by the oceans, mostly by direct diffusion and some by diffusion into rain water entering the ocean. In the ocean, CO ₂ is in equilibrium with bicarbonate and carbonate. As the atmospheric CO ₂ concentration increases, the amount entering the ocean would increase progressively. Since the industrial revolution, the atmospheric CO ₂ level has been rising rapidly, because the rate of CO ₂ addition has been increasing rapidly with the progressively greater consumption of fossil fuel worldwide. Once the rate of fossil fuel consumption stops increasing further, the rate of CO ₂ removal will eventually equal the rate of CO ₂ addition. Of course, it is quite likely that at the time of new balance, the earth could be much warmer and the ocean much more acidic, with major ecological changes. Nevertheless, imbalance does not last forever, because imbalance always leads to a new balance.

Many substances in the human body utilize the same principles to reach a state of balance. For example, if creatinine production is doubled in the absence of any change in GFR, serum creatinine would exactly double, at which point the renal excretion of creatinine would also double. At this point a new balance is reached between production and excretion. For some substances, a new balance is accelerated by physiological control mechanisms. For example, if sodium intake is doubled, renal sodium excretion will also double, but doubling of renal sodium excretion does not require doubling of serum sodium or total body sodium content, only a slight increase in sodium content of the body, because of the excellent renal regulation of sodium balance. By the same token, a reduction in sodium intake to 1/10 of the usual amount does not require sodium content of the body to decrease to 1/10 of normal when the balance is restored.

In the human body, the capacity for most substances is quite limited, and daily variations for most electrolytes are quite large in relation to total body content. Furthermore, there is a limit to which the organism can tolerate a deviation in the content of these substances. Therefore, survival of the organism demands the existence of certain physiological mechanisms to accelerate the compensation processes, to prevent a deviation from occurring to a lethal level.

Following is the sequence of events in the control system: a certain amount of an element is contained in a compartment, if input of the element into the compartment exceeds its output, the content will increase. The higher content influences the control mechanisms to reduce input or to increase output. As long as the discrepancy remains, the content will keep increasing, because the consequence of discrepancy is cumulative; the higher the content, the greater the effect on input or output. A cumulative change stops only when input equals output. When input is less than output, the opposite sequence of events restores the balance ( Figure 10.1 ).

Restoration of salt balance will be used as an example. A person in a state of sodium balance has been ingesting 10 g of salt per day, and excreting 10 g of salt per day. Now, assume that a diuretic is given to this person. On the first day of diuretic therapy, salt output is 20 g per day, with net loss of 10 g of salt. The next day, although the diuretic dosage remains unchanged, salt excretion has to be less, for example, 15 g a day, because the reduction in effective vascular volume caused by the previous day’s salt loss has activated salt-retaining mechanisms, and has reduced salt losing hormones. Still, the overall result is an additional negative balance of 5 g of salt. Although the negative balance is less on the second day, the cumulative loss (15 g) is greater on the second day than on the first, and the effective vascular volume is even lower on the second day than the first. The lower effective volume reduces salt output further to 12 g per day on the third day, with an additional negative balance of 2 g. The overall cumulative loss is now 17 g, resulting in a further decrease in effective vascular volume. As long as the salt output remains greater than salt intake, cumulative salt loss becomes larger and larger, albeit less steeply than before. Cumulative salt loss stops only when salt output equals salt intake. Indefinite net salt loss is theoretically impossible, because continued salt loss will ultimately cause such severe volume depletion that the person will become hypotensive, and salt excretion would stop completely. Of course, long before reaching such an extreme state, renal excretion of salt would decrease to a level equaling intake.

In the example given, what causes restoration of balance is not the smartness of the kidney or the cleverness of humoral mechanisms, but the principle of balance restoration, which is ubiquitous in nature. For example, sodium balance in a person on chronic diuretic therapy would still be restored in the absence of aldosterone, in which case the person could be quite sick with dehydration when balance is attained.

The same control mechanism explains why urinary excretion of potassium does not remain greater than intake in patients with primary hyperaldosteronism. With increased aldosterone, K output will initially exceed K intake. The resulting negative K balance causes hypokalemia, which in turn reduces urine K excretion. As long as K excretion exceeds K intake, serum K will decrease progressively until K excretion equals K intake. Occasionally, a patient dies of a cardiac arrhythmia before balance is attained. In the vast majority of cases, balance is achieved before the patient dies.

Speed of Balance Restoration

In a living organism, the speed of restoration of balance is teleologically determined. If an organism can tolerate protracted imbalance of a particular element without death or severe disability, balance need not be restored promptly. If quick restoration of balance is vital for survival, a mechanism for rapid restoration of balance is necessarily acquired in the process of evolution. Thus, the acceptable duration of discrepancy or alternatively speed with which restoration of balance is achieved, depends on the importance of maintaining the content of an element within a narrow range, in order to prevent the demise or serious disability of the organism. Four main factors influence the speed of balance restoration ( Table 10.1 ).

For example, an adult of average size has about 40 liters of total body water, and daily intake and output of water is about 2 liters. Obviously, water output exceeding water intake by one liter a day would lead to fatal dehydration in 10 days to two weeks. Conversely, water intake exceeding water output by the same magnitude would lead to water intoxication and death. An opposite example is calcium balance. The total body calcium content of an average adult man is about 1,200,000 mg (60,000 mEq), and net daily external flux is about 150 mg (7.5 mEq). A daily negative balance of calcium of 100 mg for one year would reduce total body calcium by mere 36,500 mg; 3% of total body calcium content. Obviously, a negative calcium balance of such a magnitude, even for a protracted period, is not incompatible with life. Indeed, during the period of development of osteoporosis, a substantial negative balance of calcium for 10 years or longer is a common occurrence. Similarly, a positive caloric balance of 500 calories a day for a year will result in a total positive balance of 182,500 calories (500×365=182,500). This amount would result in an increase in adipose tissue weight of about 50 lbs, an undesirable situation, but with no immediate effect on survival.

A large storage capacity does not guarantee a protracted imbalance. A quantitative analysis must be applied before that conclusion is reached. Once it was widely accepted that a large store of alkali of the bone was responsible for the maintenance of stable serum bicarbonate concentrations in chronic renal failure, despite a substantial daily positive balance of acid. However, this conclusion was reached without quantitative analysis. The bone content of alkali is indeed very large, but it is not sufficiently large to provide 19 mEq of alkali per day for six years in chronic renal failure. Since the total content of acid in the bone is about 25,000 mEq, a quick calculation would indicate that at a rate of consumption at 19 mEq per day, the entire bone content of alkali would be gone in about 3.6 years. Clearly, uremic patients with metabolic acidosis are in states of good or near acid–base balance, i.e., acid production equals acid excretion.

The cumulative net loss of a substance from the body cannot exceed the total amount of that substance contained in the body ( Table 10.2 ). For example, one can conclude with certainty that a person who has total body sodium content of 3500 mEq could not have been in daily negative balance of sodium by 10 mEq per day for one year, since the total loss of 3650 mEq (10×365=3650) would exceed the total body store of sodium. Even before exceeding the total body content, one cannot exceed a physiological limit of deficit for the substance. For example, potassium loss in excess of a third of the body store (3000 mEq) is usually fatal. Hence, you would reject a claim that a patient with Conn’s tumor has been losing 20 mEq of potassium daily for three months, since loss of such an amount (20×30×3=1800 mEq) would certainly be lethal. In contrast, the body can tolerate a greater fraction of sodium loss. A person who loses half of the body’s sodium would be gravely ill, but still alive.

While the total stored amount sets the absolute upper limit on losses, the amount that can be gained depends on the additional storage capacity, which varies widely with electrolytes. In the case of sodium, the storage capacity for additional Na ⁺ in the body is enormous. In certain edema-forming states, the Na ⁺ content may increase by 300% of the basal amount. Caloric balance is another example. In a normally-built adult, the total stored in fat and protein is about 130,000 calories. At the caloric consumption rate of 1200 calories per day, about 50% of the stored calories would be consumed in 55 days. In contrast, a person can gain as much as 500 lbs of fat, which are equal to 4,500,000 calories, about 35 times the normal caloric storage.

Mechanism of Balance Restoration

All control mechanisms are activated by the introduction of a new influence into a system that causes imbalance between input and output of an element, and this leads to an alteration in a parameter of the element in the system. In biological systems, parameters that are most often disturbed are concentrations of elements in the plasma. Other disturbed parameters include pressure, volume, temperature, and body weight. Alterations in a parameter affect either input or output, which in turn affects the parameter directly or indirectly. Examples of an element that is directly responsible for a change in a parameter are balance of potassium (element) affecting plasma potassium concentration (parameter), and balance of magnesium (element) affecting the plasma magnesium concentration (parameter). Examples of an element that is indirectly responsible for a change in parameter include the balance of sodium (element) affecting the effective vascular volume (parameter), and the balance of calories (element) affecting body weight (parameter).

The effectiveness of the compensation mechanism determines the degree of deviation of a parameter from the baseline value when the balance is restored. A poor compensation mechanism restores balance with the parameter greatly deviated from the baseline value. An example of a poor compensation mechanism is a change in plasma urea concentration with a change in the rate of urea production. When urea production doubles, the renal excretion will eventually also double and equal the increased production rate. However, at equilibrium the plasma urea concentration will be twice the baseline value. An example of a good compensation mechanism is a change in a sodium content of the body in response to a change in sodium intake. When salt intake is doubled, renal excretion of salt will eventually double; at this point the total body sodium content would be very slightly greater than the baseline value.

Models of External Balance

The pattern of restoration of new balance for control of various elements in the human body is broadly classified into three models. The main source of input for most electrolytes in our body is oral intake and the main output the renal excretion, with some additional output through the GI tract.

Model A

This model is depicted in Figure 10.2 as a cylinder filled with water. Water enters from a faucet into the cylinder, and leaves through a hole at the bottom. The height of the water column depends on water input and water output, and water output in turn depends on the size of the hole at the bottom and the hydrostatic pressure. The hydrostatic pressure in turn depends on the height of water column. Under these conditions, only two factors can change the height of the water column permanently; the rate of water input and the size of the hole. If the rate of water input is doubled while the size of the outlet hole is kept constant, water output will also double when the balance is restored.

With the same size outlet hole, doubling of water output would require doubling of hydrostatic pressure, which in turn requires doubling of the water column height. Before balance is restored, the water column height rises, because water input exceeds water output. The rise in the water column height gradually increases the hydrostatic pressure, and therefore the water output. Hence the discrepancy between the water input and the water output gradually lessens. However, as long as water input remains greater than water output, the water level will keep rising, and the rise will stop only when the water output equals the water input; this occurs when the water column height is exactly doubled.

Conversely, decreasing the size of the outlet hole to double the resistance to water flow, with an unchanged rate in the water input, would initially reduce the water output to half. The ensuing imbalance between the water output and the water input would cause a rise in the water column height. A higher hydrostatic pressure resulting from the rise in the water column would allow more water to come out through a narrower hole. Thus, in this example, doubling of the water column height will restore the water output to the baseline value.

The main characteristic of this type of compensation is that the alteration in content or concentration caused by a disturbance is directly or inversely proportionate to the magnitude of the alteration in input or output function. For example, if the input of a substance is doubled, the content or concentration of the substance will be doubled when balance is restored. If input is increased three-fold, the content or concentration will be tripled. Similarly, if the output function is halved, the content or concentration will be doubled when balance is restored. If the output function is reduced to one tenth of the baseline, the content or concentration will be increased ten-fold when balance is restored.

Many substances in the body follow this pattern of compensation mechanism in order to achieve a new balance. When a substance follows this pattern of compensation, the body must have a high degree of tolerance for a large deviation in the body content or concentration for the substance. For example, if creatinine clearance diminishes to half of the baseline value with an unchanged creatinine production rate, serum creatinine concentration will double in order to achieve the same rate. Similarly, if creatinine production is reduced to half of the baseline value with the same renal creatinine clearance, serum creatinine concentration will be half of the original value. Likewise, if urea production is doubled, with unchanged kidney function, serum urea concentration is doubled when balance is restored.

Model B

In this model, the cylinder has a wedge-shaped slit on its side instead of a hole at the bottom ( Figure 10.3 ). Water enters the cylinder from a faucet, and leaves through the slit. As in model A, water output depends on the height of the water column. But, because of the wedge shaped slit, the effect of a rise in water level on water output is exponential. Therefore, when water intake doubles, doubling of water output does not require doubling of the water column height. Depending on the shape of the slit, the water level may rise only slightly before a new balance is restored. In other words, an increase in water output in response to a change in the height of water column is magnified in this system. Furthermore, unlike model A, when the water level drops below the lowest part of the slit, water output stops altogether.

The regulation of the body content or plasma concentration of most electrolytes and other essential body elements utilizes this type of compensation. For example, when potassium intake is increased five-fold, plasma potassium concentration does not increase five-fold when balance is restored. In the presence of normal renal function and normal aldosterone response, plasma potassium concentration will increase only slightly. Likewise, a five-fold increase in sodium intake causes only a slight increase in body sodium content or plasma sodium concentration; when sodium intake is greatly reduced, the body sodium content decreases only slightly before renal sodium excretion ceases.

Model C

The pattern of water excretion in model C ( Figure 10.4 ) is similar to model A, but in this model two cylinders, one big (A) and the other small (B), are connected at the bottom. Water enters only into cylinder A, but once it enters, it equilibrates with cylinder B. Ordinarily, because cylinder A has a bigger hole than cylinder B, the water output is determined primarily by the size of hole A. However, as the size of hole A decreases, the role of hole B increases. When water input is doubled, the height of the water column will have to be doubled in order to permit establishment of a new steady-state. On the other hand, when the resistance to flow through hole A is doubled, the height of the water column will be less than doubled when balance is restored, provided that the size of hole B is unchanged.

When the excretion rate through hole A decreases, the excretion through hole B becomes more important. The regulation of plasma concentration of uric acid follows the pattern in model C. Uric acid is cleared by the kidney, and is also cleared metabolically by colonic bacteria. The renal clearance of uric acid is normally about 8 liters per day, and the colonic clearance is about 4 liters per day. Thus, 2/3 of the uric acid produced is cleared by the kidney and 1/3 by the colon. If the plasma concentration of uric acid is 5 mg/dl (50 mg/L), renal excretion of uric acid would be 400 mg per day (uric acid clearance of 8 liters per day), and the amount cleared by the colonic bacteria would be 200 mg, with a total uric acid removal rate of 600 mg per day. If chronic renal disease reduces the renal clearance of uric acid to 4 L a day (half of normal), total uric acid clearance would now be 8 liters per day, if the colonic clearance remained unchanged at 4 liters per day. If the rate of production remained the same (600 mg/day), plasma uric acid concentration would not double to 10 mg/dl, but would increase to 7.5 mg/dl, because total body uric acid clearance would be 8 liters per day (4+4=8 liters); at this concentration, the total amount of uric acid cleared would be 600 mg/day (75 mg/L×8 L/day=600 mg/day).

The regulation of plasma creatinine concentration follows the same type of compensation as shown in model C. Normally, creatinine is cleared mainly by the kidney, with a daily clearance of about 180 liters, but the colonic bacteria also remove a small amount of creatinine, providing about 3 liters of creatinine clearance per day. Thus, normally the colonic clearance, which constitutes less than 2% of the total creatinine clearance, has little impact on the plasma concentration of creatinine. However, in the presence of advanced renal failure, which does not diminish the colonic clearance of creatinine, it could have a substantial impact on plasma concentration of creatinine. For example, in a person who has 5 ml/min of renal creatinine clearance (7.2 liters per day), 3 liters of colonic clearance would now represent about 30% of the total creatinine clearance. For these reasons, the rate of rise in serum creatinine in advanced renal failure is not exactly inversely proportionate to the reduction in renal clearance of creatinine.

Infinite Gain Control Mechanism

The ultimate aim of all compensation mechanisms is restoration of balance between input and output, after balance is disturbed by introduction of an abnormality. In most instances restoration of balance is possible only when the abnormality persists. For example, increased renal excretion of potassium by primary hyperaldosteronism will result in imbalance between input and output, with output exceeding input. Development of hypokalemia is needed for output to decrease to match input, and hypokalemia is the price that must paid in order to restore balance. Similarly, an increase salt intake would result in chronic volume expansion, in order for salt excretion to increase to equal the increased intake. The infinite gain control mechanism, to be discussed below, is unique in that the abnormality is corrected completely when a balance is restored.

This principle is well illustrated in Figure 10.5 . In this model system, water enters the tank from a faucet at the top, and leaves the tank through a hole at the bottom. The input is independently regulated, but the water output depends on two factors, the size of the outlet hole and the hydrostatic pressure. The hydrostatic pressure in turn depends on the water level, which is determined by the balance between the water input and water output. At equilibrium, the water input is equal to the water output. What would happen if the capacity of the tank is suddenly altered at this point by, for example, placing a brick in the tank, without a change in the water input or the size of outlet hole (i.e., output function)? Initially, the water level would rise and hydrostatic pressure at the bottom of the tank would be increased. The higher pressure with the same size outlet hole would cause the output of water to exceed water input. The consequent imbalance between the input and output would cause a gradual decline in the water level. But, as long as the water level is higher, even slightly, than the baseline value, the water output will exceed the water input. Only when the water level decreases to the original level, will the water input equal the water output. A sudden increase in the capacity of the tank, for example by creating a pouch on the tank, would cause an imbalance between the water input and the water output because of the initial reduction in the water level and the hydrostatic pressure, but the discrepancy would be only transient. At equilibrium, the water level will return to the original level.

This type of compensation mechanism is ubiquitous in various physiological and pathological states in the human body, but the importance of this mechanism was first recognized by Guyton, who presented the concept in his discussion of the regulation of arterial blood pressure. He boldly predicted that in the absence of an altered function of renal excretion of salt, no abnormality will sustain hypertension chronically. This prediction was made on the basis of the observation that the arterial blood pressure is normally a powerful regulator of renal salt excretion, and that a minute increase in blood pressure results in a large increase in salt excretion, and salt excretion in excess of salt intake will continue until the blood pressure returns to normal .

Suppose hypertension develops as a result of increased systemic vascular resistance, while the responsiveness of the kidney to changes in blood pressure to influence salt output (i.e., renal function curve in response to blood pressure) remains unchanged; the higher the pressure, the higher the renal salt output. Increased salt output caused by a higher blood pressure in the absence of commensurate increase in salt intake would lead to a negative salt balance. The negative salt balance would reduce effective vascular volume, circulating blood volume, and eventually cardiac output. A lower cardiac output will reduce blood pressure to a lower level, but as long as the blood pressure is still higher than the baseline, salt output will remain greater than the basal salt output. The salt output in excess of salt intake progressively reduces the salt content of the body. Only when blood pressure returns to the original value will the renal salt output return to the baseline value. At this point, balance is restored between salt intake and salt output, and the abnormality in blood pressure is completely dissipated.

In Guyton’s use, the term “gain” is defined as the fraction of abnormality that has been corrected divided by the fraction yet to be corrected. For example, if an abnormality causes an increase in blood pressure, and a control system brings it back halfway to the original value, the feedback gain is one (0.5/0.5=1). Gain is zero if a control system does not correct at all (0/1=0). Gain is infinite if the abnormality is almost all corrected completely with virtually nothing left to be corrected, because division of a number with an infinitely small number results in an infinitely large number.

What is the reason why an abnormality disappears completely in the infinite gain control mechanism, but not in other control mechanisms? The main difference is in the nature of the influence that causes disturbances in the system. When the disturbance affects either input or responsiveness of the system to change in a parameter for the output (i.e., output function), the abnormality will not be corrected completely, and the compensation mechanism does not involve the infinite gain control mechanism. On the other hand, when the disturbance introduced is not one of these two kinds, the compensation mechanism is an infinite gain control mechanism.

Common Misconceptions and New Insights

A series of topics discussed in the following section deals with widespread misconceptions regarding principles related to restoration of balance states.