Winters's formula

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Winters's formula, [1] named after R. W. Winters, [2] is a formula used to evaluate respiratory compensation when analyzing acid-base disorders in the presence of metabolic acidosis. [3] [4] It can be given as:

Contents

,

where HCO3 is given in units of mEq/L and PCO2 will be in units of mmHg.

History

Dr. R. W. Winters was an American physician and graduate from Yale Medical School. He was a professor of pediatrics at Columbia University College of Physicians and Surgeons. In 1974 he was awarded the Borden Award gold medal by the American Academy of Pediatrics. [5]

Dr. R. W. Winters conducted an experiment in the 1960s on 60 patients with varying degrees of metabolic acidosis. He aimed to empirically determine a mathematical expression representing the effect of respiratory compensation during metabolic acidosis. He measured the blood pH, plasma PCO2, blood base excess, and plasma bicarbonate concentrations. He focused on the relationship between plasma PCO2 and plasma bicarbonate. Winter's Formula was derived from a linear regression of this relationship between plasma PCO2 and plasma bicarbonate. [6]

Physiology

There are four primary acid-base derangements that can occur in the human body - metabolic acidosis, metabolic alkalosis, respiratory acidosis, and respiratory alkalosis. These are characterized by a serum pH below 7.4 (acidosis) or above 7.4 (alkalosis), and whether the cause is from a metabolic process or respiratory process. If the body experiences one of these derangements, the body will try to compensate by inducing an opposite process (e.g. induced respiratory alkalosis for a primary metabolic acidosis). [7]

Respiratory compensation is one of three major processes the body uses to react to derangements in acid-base status (above or below pH 7.4). It is slower than the initial bicarbonate buffer system in the blood, but faster than renal compensation. Respiratory compensation usually begins within minutes to hours, but alone will not completely return arterial pH to a normal value (7.4). Winter's Formula quantifies the amount of respiratory compensation during metabolic acidosis. [8]

During metabolic acidosis, a decrease in pH stimulates chemoreceptors. Peripheral chemoreceptors are found in the aortic and carotid bodies and respond to changes in the PaCO2, the arterial partial pressure of carbon dioxide. Central chemoreceptors are found in the brainstem and respond primarily to decreased pH in the cerebrospinal fluid. In response to decreased pH, these chemoreceptors lead to an increase in minute ventilation and increased elimination of carbon dioxide. A decrease in carbon dioxide lowers PaCO2 and pushes arterial pH towards normal. [8]

Clinical use

One difficulty in evaluation acid-base derangements is the presence of multiple pathologies. A patient may present with a metabolic acidosis process alone, but they may also have a concomitant respiratory acidosis. Winters's formula gives an expected value for the patient's PCO2; the patient's actual (measured) PCO2 is then compared to this. Using this information, physicians may elucidate additional causes of the acid-base derangement and identify different treatment options which may not have otherwise been considered. [9]

If the two values correspond, respiratory compensation is considered to be adequate.

If the measured PCO2 is higher than the calculated value, there is also a primary respiratory acidosis.

If the measured PCO2 is lower than the calculated value, there is also a primary respiratory alkalosis.

Related Research Articles

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An arterial blood gas (ABG) test, or arterial blood gas analysis (ABGA) measures the amounts of arterial gases, such as oxygen and carbon dioxide. An ABG test requires that a small volume of blood be drawn from the radial artery with a syringe and a thin needle, but sometimes the femoral artery in the groin or another site is used. The blood can also be drawn from an arterial catheter.

A blood gas test or blood gas analysis tests blood to measure blood gas tension values, it also measures blood pH, and the level and base excess of bicarbonate. The source of the blood is reflected in the name of each test; arterial blood gases come from arteries, venous blood gases come from veins and capillary blood gases come from capillaries. The blood gas tension levels of partial pressures can be used as indicators of ventilation, respiration and oxygenation. Analysis of paired arterial and venous specimens can give insights into the aetiology of acidosis in the newborn.

Acidosis is a biological process producing hydrogen ions and increasing their concentration in blood or body fluids. pH is the negative log of hydrogen ion concentration and so it is decreased by a process of acidosis.

Alkalosis is the result of a process reducing hydrogen ion concentration of arterial blood plasma (alkalemia). In contrast to acidemia, alkalemia occurs when the serum pH is higher than normal. Alkalosis is usually divided into the categories of respiratory alkalosis and metabolic alkalosis or a combined respiratory/metabolic alkalosis.

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Metabolic acidosis is a serious electrolyte disorder characterized by an imbalance in the body's acid-base balance. Metabolic acidosis has three main root causes: increased acid production, loss of bicarbonate, and a reduced ability of the kidneys to excrete excess acids. Metabolic acidosis can lead to acidemia, which is defined as arterial blood pH that is lower than 7.35. Acidemia and acidosis are not mutually exclusive – pH and hydrogen ion concentrations also depend on the coexistence of other acid-base disorders; therefore, pH levels in people with metabolic acidosis can range from low to high.

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Blood gas tension refers to the partial pressure of gases in blood. There are several significant purposes for measuring gas tension. The most common gas tensions measured are oxygen tension (PxO2), carbon dioxide tension (PxCO2) and carbon monoxide tension (PxCO). The subscript x in each symbol represents the source of the gas being measured: "a" meaning arterial, "A" being alveolar, "v" being venous, and "c" being capillary. Blood gas tests (such as arterial blood gas tests) measure these partial pressures.

In nephrology, the delta ratio, or "delta-delta", is a formula that can be used to evaluate whether a mixed acid–base disorder is present, and if so, assess its severity. The anion gap (AG) without potassium is calculated first and if a metabolic acidosis is present, results in either a high anion gap metabolic acidosis (HAGMA) or a normal anion gap acidosis (NAGMA). A low anion gap is usually an oddity of measurement, rather than a clinical concern.

References

  1. Albert, Morris S.; Dell, R. B.; Winters, R. W. (1967). "Quantitative Displacement of Acid-Base Equilibrium in Metabolic Acidosis". Annals of Internal Medicine. 66 (2): 312–322. doi:10.7326/0003-4819-66-2-312. PMID   6016545.
  2. Asch, M. J.; Dell, R. B.; Williams, G. S.; Cohen, M.; Winters, R. W. (1969). "Time course for development of respiratory compensation in metabolic acidosis". The Journal of Laboratory and Clinical Medicine. 73 (4): 610–615. PMID   5775132.
  3. "Case 1: Acid Base Tutorial, University of Connecticut Health Center" . Retrieved 2009-05-09.
  4. "Acid-Base Disorders: Acid-Base Regulation and Disorders: Merck Manual Professional" . Retrieved 2009-05-09.
  5. "Yale Medicine: Alumni Bulletin of the School of Medicine, 1973-1975" (PDF). 1975. Retrieved 17 December 2023.
  6. Albert, M. S.; Dell, R. B.; Winters, R. W. (1967). "Quantitative displacement of acid-base equilibrium in metabolic acidosis". Annals of Internal Medicine. 66 (2): 312–322. doi:10.7326/0003-4819-66-2-312. ISSN   0003-4819. PMID   6016545.
  7. Pocock, Gillian; Richards, Christopher D.; Richards, David A. (2017-12-07), "Acid–base balance", Human Physiology, Oxford University Press, doi:10.1093/hesc/9780198737223.003.0050, ISBN   978-0-19-873722-3 , retrieved 2023-12-17
  8. 1 2 DiLorenzo, Amy N.; Schell, Randall M. (2014). "Morgan & Mikhail's Clinical Anesthesiology, 5th Edition". Anesthesia & Analgesia. 119 (2): 495–496. doi: 10.1213/ane.0000000000000298 . ISSN   0003-2999.
  9. Kopel J, Berdine G. Winters's formula revisited. The Southwest Respiratory and Critical Care Chronicles 2019;7(27):43–49.