Acid-base imbalance: interpretation

The interpretation of acid-base imbalances requires the understanding of some basic principles of physiology, biochemistry and inorganic chemistry, as well as interest for medical attention and calculations. Whenever the severity or the emergency of a case imposes an immediate and proper interpretation, such as in critical patients who cannot tolerate mistakes, the preparation of the veterinarian becomes fundamental in order to start with the correct therapy and life-saving procedures.

Whenever a blood sample is taken to analyse the acid-base status of the animal it is necessary to:

• avoid prolonged blood stasis and conflicts in containing the patient as these may cause stress, alterations of pH, partial oxygen pressure (O₂), carbon dioxide (CO_2),  glucose, haemolysis and may even cause the death of the patient;
• know the origin of the sample, be it arterial, venous or mixed; in case of doubt repeat the blood withdrawal from a sure venous source (e.g. from the cephalic vein of the forearm) and compare the results;
• analyse the blood sample immediately, especially when dealing with an arterial sample (necessary to assess the function of the respiratory system);
• to assess metabolic alterations the sample must be analysed within 6 hours and preserved in test tubes with lithium heparin, avoiding contact with air._¹

PHYSIOLOGY

The acid-base balance is determined by two main molecules: water (H₂O) and carbon dioxide (CO₂). In the presence of the enzyme carbonic anhydrase (ubiquitary within the organism) these two chemical species give rise to the formation of carbonic acid (H₂CO₃), by means of the following reaction: 

CO₂ + H₂O → H₂CO₃                                                    Formula n. 1  

Carbonic anhydrase shifts the reaction (formula n. 1) to the right, making it quantitative and forming carbonic acid (H₂CO₃), thanks to the availability of carbon dioxide (CO₂). L’H₂CO₃ is an acid species and as such possesses its own pKa (dissociation constant), which indicates its propensity to dissociate into H^₊ (hydrogen ions) and  HCO_3^- (bicarbonate ions):   

H₂CO_{3 ↔} H⁺ + HCO₃^-                                  Formula n. 2

Based on the law of mass action, in the organism the balance described in the two previous formulas must be maintained both on the right side and on the left side, as indicated in the formula:

CO₂ + H₂O  ↔ H₂CO₃ ↔  H⁺ + HCO₃^-            Formula n. 3   

For this reason when sodium bicarbonate is administered there is an excess of  CO₂ production (shift to the left of formula n. 3) which must be eliminated with ventilation; in fact its administration in patients with ventilatory failure (e.g. pleural space diseases) may cause a paradoxical metabolic acidosis as the subjects are not capable of rapidly eliminating the CO₂ in excess. When the patient has instead a retention of CO₂ there is an increased  production of  H^₊ hydrogen ions (deviation to the right of formula n. 3) with a reduction of bicarbonate. Bicarbonate decreases as it is consumed by fixed acids produced by the organism (e.g. chloridric acid of gastric origin) while hydrogen ions (H^₊) must be buffered by an increase in the retention of bicarbonate at renal level, which requires at least 24-48 hours and which is completed in around 4-5 days. In normal conditions, the increase in the frequency and depth of ventilation rapidly reduces the concentration of CO₂ in the blood; the stimulus which causes the change in the respiratory pattern is consequent to the activation of central and peripheral chemoreceptors which are activated by the increase in paCO₂, of H^₊ and by the reduction of paO₂.

The increase in the concentration of H_⁺ causes a decrease of blood pH, while an increase in bicarbonate causes an increase of pH (see formula n. 4). pH is the logarithmic measurement of the concentration of  H⁺ and is calculated as indicated in the Henderson-Hasselbach formula:

pH = 6,1 + log  [HCO₃^-] / 0,03 pCO₂                                      Formula n. 4   

Observing the formula, it is clear that an increase in carbon dioxide is linked to a reduction of pH, while an increase in bicarbonate is linked to an increase in pH.

All metabolic processes of the organism and of the cell require a neutral and stable pH; an alteration of the acid-base balance causes an altered enzymatic activity which can hinder cell activity. In the presence of a pathological process which is capable of altering the acid-base balance, by modifying the composition of extracellular liquid (e.g. vomiting and diarrhoea) or respiration (e.g. pleural effusion, gastric dilatation and torsion),  the organism, via a series of compensatory mechanisms (compensation), tries to correct the unbalance, however never compensating in excess. When compensation is not successful in  correcting the acid-base imbalance, the vital functions of the organism may be compromised and it is therefore necessary to intervene with a suitable treatment, with modalities and timings which must be decided case by case. Compensation takes place thanks to a buffer system composed by intra- and extra-cellular chemical species which buffer the H_⁺ excess or deficit, by neutralizing the H_⁺ in excess or by releasing them, depending on the specific need. 

BLOOD GAS ANALYSIS (BGA) AND ITS INTERPRETATION

Blood gas analysis is the measurement of pH, of the gasses dissolved in the blood and of the chemical species which are mostly involved in the acid-base balance. To simplify calculations, pH is measured with a logarithmic scale (fomula n. 4), while dissolved gasses are measured as a partial pressure expressed in millimetres of mercury (mmHg) or in Kilopascals (kPa); the conversion factor from mHg to kPa is 0.133. The partial pressure of oxygen in arterial blood is indicated as paO₂, while the partial pressure of CO₂ in arterial blood is indicated as paCO₂. Blood gas analysis is useful to diagnose an acid-base imbalance, a deficit in oxygenation or ventilation and to identify some electrolytic imbalances which may have an impact on the acid-base balance. An example of the usefulness of blood gas analysis is represented by the assessment of a tachipnoic, tachicardic and cyanotic patient; such patient could have two entirely different problems, requiring a totally different therapeutic intervention. There could be an increase of blood pH, a reduction of paCO₂ and a reduction of paO₂, caused by the presence of an acute ventilatory failure (e.g. a pneumonia), or there could be a decrease of blood pH, an increase of paCO₂ and a mild reduction of paO₂ (e.g. a pneumothorax). In the first case the patient suffers from hypoxia and requires oxygen supplementation and supportive care, while in the second case the patient is affected primarily by a ventilatory problem and requires a thoracic drainage. Thanks to blood gas analysis in the first case it was possible to document an insufficient oxygenation, to specify that the main problem was caused by hypoxia, to identify the primary disorder (decreased paO₂) and to quantify the severity of the abnormality by measuring the gasses dissolved in the arterial blood.^₂ In the second case it was possible to document the presence of a ventilatory failure, to specify that the main problem was caused by ventilation (elevated paCO₂) and to quantify the severity of the disorder. Patients affected by respiratory problems require an arterial blood gas analysis, while in patients with metabolic disorders a venous blood gas analysis can be done. The arterial sample is usually taken from the metatarsal artery, and less frequently from the femoral artery (more painful and at risk of haematoma), while the venous samples may be peripheral or central (e.g. the cephalic vein of the forearm, saphenous vein and jugular vein).

Blood gas analysis is useful to differentiate if acid-base disorders are of metabolic or of respiratory origin and if the respiratory deficits are mostly ventilatory or due to problems in oxygenation. Since BGA is also useful to diagnose and to quantify metabolic imbalances it should be done in all patients affected by a severe pathological disorder, the goal being to treat the acid-base imbalance which may put the life of the patient at risk, as well as to determine the capacity of the lungs to oxygenate blood.

From the Henderson-Hasselbach fomula (formula n. 4) it has been shown that H_⁺ and CO₂ are part of the bicarbonate buffering system; by measuring the first two, bicarbonate may be calculated, and by measuring the concentration of haemoglobin,  the base excess (BE) may be calculated. By determining and calculating these components all the data necessary to interpret the acid-base status of the patient are available.

The normal values measured in the dog and cat are shown in Table 1 (different laboratories may have different ranges).

Table 1. Normal values of BGA in the dog and cat (Legend: pH= hydrogen ion concentration, CO₂= bicarbonate, HCO_3^-= bicarbonate, O₂= oxygen, BE= base excess, AG= anion gap, TCO₂= total carbon dioxide, SO₂= haemoglobin saturation, A-a= alveolar-arterial gradient).

The interpretation of BGA must always be correlated to the existing pathological condition and to the clinical history. At times radiography may be necessary to confirm a diagnostic suspicion, while it is always necessary to assess the values measured with the vital parameters found in the patient (heart and respiratory rate, body temperature, capillary filling time and measurement of arterial pressure). When acid-base balance alterations are found, it is necessary to repeat the BGA until stabilisation of the patient and control of the imbalance. The frequency with which the test is to be repeated depends on the severity of the imbalance and on the treatment used. In some cases it may be necessary to repeat the blood gas analysis at intervals of just a few hours (e.g. for respiratory problems and electrolyte imbalance), or daily (e.g. for metabolic imbalances). The interpretation of the blood gas analysis starts with the recognition of the origin of the sample, meaning if it is arterial, venous or mixed (artero-venous); arterial samples have a haemoglobin saturation percentage greater than 90%. Samples with a haemoglobin saturation equal or inferior to 75% are of venous or mixed origin. Blood gas analysis measurements are read in the following chronological order: 

1. pH: when it is under 7.35 there is acidaemia, when it is over 7.45 there is alkalaemia; the terms acidosis and alkalosis indicate the tendency of a process to cause the disorder, while the suffix –aemia indicates that the disorder is present;
2. paCO₂: when it is over 45 a respiratory acidosis is present, when it is under 35 a respiratory alkalosis is present;
3. HCO₃^-:when it is under 20 with a BE equal or under 5 a metabolic acidosis is present, if it is >20 with a BE > 5 a metabolic alkalosis is present.

Having assessed the first three components (pH, paCO₂, HCO₃^-) it is then necessary to identify the primary disorder. The primary disorder indicates which parameter measured with BGA is responsible for the acid-base imbalance. To be able to recognise it, it is necessary to specify the type of pH alteration present, specifically if it’s a case of acidosis or of alkalosis, by comparing the result obtained with normal values (see Table 1). The next step is to assess the paCO_2;  if it is altered in the same direction of pH and if bicarbonate is within the norm or within the compensation range then the primary disorder is of respiratory type. As an example, if the pH of a patient is under the normal range (acidaemia) and there is an icrease in paCO₂, the primary disorder will be caused by ventilatory failure, with the presence of a respiratory acidosis. The amplitude of variation of BGA results allow to quantify the severity of the disorder, while the subsequent BGA results allow to verify the eventual success of the treatments adopted. If in the presence of acidaemia there is a reduction of bicarbonate, with a normal paCO₂, or within the range of compensation, the primary disorder is metabolic (metabolic acidosis). The same interpretation methodology is to be used for pH values greater than normal (alkalosis): if the bicarbonate is increased the primary disorder is of metabolic origin, if instead the paCO₂ is decreased, the primary disorder is of respiratory origin. 

As a summary, in the case of acidosis (reduction of pH) it is necessary to determine if the origin of the imbalance is respiratory or metabolic; in the first case there is going to be an increase of CO₂, in the second a decrease of HCO_3^-. Vice versa, in the presence of alkalosis (increase of pH) the primary disorder is respiratory in the case of a decrease of carbon dioxide, or metabolic in the case of an increase of bicarbonate. 

Once identified the primary disorder, it is then necessary to verify if the compensatory reaction of the organism is within expectations and if it is sufficient to correct the acid-base imbalance. Whenever the compensation is within expectations but not capable of correcting the acid-base imbalance it is necessary to intervene, as some imbalances are incompatible with survival. Non-compensated imbalances are easy to identify, as the altered value concerns a single parameter, bicarbonate for the metabolic component and carbon dioxide for the respiratory component. Normal compensatory reactions are presented in Table 2.

Table 2. Compensation (Legend: paCO₂ =  partial pressure of carbon dioxide, HCO_3^- = concentration of bicarbonate ions).

When a metabolic acidosis is diagnoses and the compensation has been calculated, the next step is to calculate the anion gap (AG); if increased, it is necessary to verify the eventual presence of metabolites in circulation which can alter the acid-base status. Following is a list of some of the metabolites and pathologic entities which are responsible for an increase of the anion gap:

• lactic acidosis (e.g. convulsions);
• ketoacidosis (e.g. diabetic ketoacidosis);
• renal failure (e.g. uraemia);
• increase of sulphates and phosphates (e.g. renal failure);
• rhabdomyolysis (e.g. hyperthermia, hypothermia, severe traumas);
• sepsis (e.g. pyometra, parvovirosis);
• poisonings (e.g. ethylene glycol, methylene glycol, alcohol, salicylates, paraldehyde, iron).

For reasons of electroneutrality cations and anions present in the blood must be in equal amount. Cations are distinguished in: measured cations, such as sodium (Na_⁺) and potassium (K_⁺),  and unmeasured cations (UC), which are present in an inferior amount (e.g. magnesium (Mg_⁺⁺)). Anions are also distinguished in  measured anions, such al chloride (Cl^-) and bicarbonate (HCO_3^-), and unmeasured anions (UA), such as proteins, phosphates and sulphates. Their balance is regulated by the following formula:

 (Na⁺+ K⁺) + UC⁺  =  (Cl^- + HCO₃^-) + UA^-                            Formula n. 5

To measure the difference between cations and anions the calculation can be done with the following formula:

AG  = [(Na⁺+ K⁺) + UC⁺] -  [(Cl^- + HCO₃^-) + UA^-]             Formula n. 6                                

Simplifying the formula, and removing  the unmeasured anions from the calculation, the AG can be calculated by subtracting the measured anions from the measured cations:

AG =  (Na⁺+ K⁺) - (Cl^- + HCO₃^-)                Formula n. 7                                                                       

In normal conditions, if the calculation is made in the absence of unmeasured ions, cations are more numerous than anions, and hence the normal AG is included within an interval of values between 12 and 20 mmol/L. When minor anions (UA) increase, major anions (Cl^- and HCO_3^-) must decrease in order to maintain the electrolytic balance, causing an increase of the AG. A metabolic acidosis with a normal AG is typical in renal failure and in diarrhoea. During these disorders there is often a loss of bicarbonate with a compensatory increase of the chloride ion (as the electrolytic balance must remain unchanged), to the extent of being defined as hyperchloraemic acidosis. The calculation of the AG is therefore helpful in identifying the cause of metabolic acidosis.

Apart from assessing the acid-base status, blood gas analysis allows to measure the alveolar-arterial oxygen gradient (A-a). A-a measures the capacity of the lungs to transport oxygen from inhaled air to the blood, and it allows to assess the ventilation/perfusion ratio (V-Q). A-a is calculated by subtracting the partial pressure of oxygen measured in the arterial bed from the partial pressure of alveolar oxygen; the following formula can be used:

A-a = PAO₂ - paO₂                   Formula n. 8                                                                                                      

The alveolar partial pressure of oxygen ((PAO₂) is calculated with the following formula:

PA= (atmospheric pressure - 47) FiO₂ – (paCO₂ /0,8)                 Formula n. 9                                   

The first part of the formula used to calculate A-a, identified as formula n. 9, is useful to calculate the alveolar pressure of oxygen; the calculation starts by measuring the atmospheric pressure with the subtraction of water vapour (atmospheric pressure – 47) and multiplying it by FiO₂ (percentage of oxygen in inspired gas); from the result obtained it is then necessary to subtract the fraction of air which still contains carbon dioxide divided by the respiratory quotient. Values of A-a greater than 15 mmHg indicate an increase of the V-Q ratio, as is the case during parenchymal pulmonary diseases (e.g. pneuomonia). The greater the V-Q ratio, the more severe the hypoxaemia. When the difference existing between alveolar oxygen and arterial blood oxygen is increased, the diffusion of oxygen through the lung parenchyma is hindered. The A-a gradient may increase also during diffusion hypoxia and a right-to-left pulmonary shunt. A-a is important in order to understand the severity of some pulmonary diseases, to assess the efficacy of the treatment chosen and to identify which patients require positive pressure pulmonary ventilation as they are not capable of ensuring a sufficient oxygenation in spite of oxygen therapy. To assess the capacity of a patient to oxygenate blood during oxygen therapy it may be useful and simple to calculate the shunt fraction using the following formula:

PaO₂/FiO₂             Formula n. 10                                                 

Normal values are of around 500; values between 300 and 500 are suggestive of a mild hypoxaemia; values between 200 and 300 indicate a severe or moderate hyoxaemia and values under 200 indicate an extremely severe hypoxaemia and possibly ARDS (Acute respiratory distress syndrome).

Blood gas analysis also allows to calculate the base excess or deficit (commonly abbreviated BE, Base Excess). Apart from bicarbonate, blood contains other bases, among which haemoglobin is the one found in greater quantity. In the presence of an increase of acids, fixed or volatile, the amount of total bases and of bicarbonate present in the blood decreases, while in a state of metabolic alkalosis bicarbonate increases. In other words it’s as if we could say that for each increase or decrease of bicarbonate there is an increase or a decrease of all the bases present in the blood. The measurement of the bases present in the blood requires a more accurate calculation as against the only determination of the ion bicarbonate. To calculate it, it is necessary to know the concentration of haemoglobin: if we consider 15 g/dl as the normal value for the amount of haemoglobin present in the blood and 20 ± 4 mEq/L the normal concentration of bicarbonate, it is then possible to determine the base excess or deficit with the following formula:

BE = BB measured - BB normal           Formula n.  11                                                                        

BB is the buffer base, the normal value of which is of around 20 ± 4 mEq/L, if normal haemoglobin is considered equal to 15 g/dl. The normal values of BE (Base Excess) are included between -2 and +2 mEq/L; when the BE is over 2 it means that there is a base excess, vice versa a negative value under -2 indicates a base deficit. Bicarbonate accounts for about half the value of total BE. The value of BE may vary depending on the laboratory, and this depends on if the BE is calculated in the blood or in the extracellular liquid. In some cases a value outside of the reference range may be normal, and might even indicate a positive response from the organism. As an example a patient which suffers from a chronic respiratory acidosis (e.g. asthma) may have a BE above normal values, to buffer the increase of CO₂ present in the blood: in such case a high BE is not a pathological finding and is instead the natural response to an altered acid-base balance. Increases of BE may be due to an increase in bases or to a decrease in acids; a decrease of BE may be due to a reduction of bases or to an increase of acids. BE is useful, in the presence of metabolic acidosis, in order to understand if the disorder is compensated by the bases present within the circulatory stream or if they must be reintegrated. In such cases if the BE is under the normal values it is necessary to decide on whether the disorder must be corrected with the addition of bases, or of their precursors (balanced solutions such as Lactated Ringer’s, ES or Normosol R), or if it is instead necessary to control the excess in the production of acids; the final decision will depend on the pathological process present and on the examination of the blood gas analysis in toto.

ACID-BASE IMBALANCES

Acid-base imbalances are defined as simple when the primary disorder alters the pH in a direction while at the same time the compensatory mechanisms try to correct the alteration in the opposite direction, bringing the pH back within the normal range._³To be able to recognise a simple disorder it is necessary to characterise the pH alteration: acidosis or alkalosis. When the imbalance is instead characterised by two or more pathophysiological processes which tend to alter the pH in the same direction, or in opposite directions, the disorder is defined as mixed. In the first case there can for example be a metabolic acidosis consequent to a hypovolaemic shock of traumatic origin, which compromises tissue perfusion and promotes lactic acidosis, while at the same time the patient may suffer from a respiratory acidosis consequent to a pneumothorax; in such a case acidaemia is severe and it must be immediately recognised and treated. In the second case it is for example possible to find patients with vomiting with a metabolic alkalosis produced by the loss of chloridric acid with emesis with at the same time  a metabolic acidosis from hypoperfusion produced by hypovolaemia consequent to severe dehydration. The treatment of mixed disorders consists in the aetiological treatment of the primary condition;_³   a new blood gas analysis is subsequently done to verify if the imbalance has resolved or if it’s necessary to cotinue with the correction of the acid-base and electrolytic imbalances.

Metabolic acidosis

The most frequent causes of metabolic acidosis are:

• trauma;
• diabetic chetoacidosis;
• renal failure;
• diarrhoea;
• drugs;
• haemorrhages._⁴

In these pathological processes a metabolic acidosis may develop due to an excessive production of acids, a reduced elimination of acids via the renal emunctory function, or an excessive loss of bicarbonate (e.g. from the bowel with diarrhoea). The excess of  H⁺ ions determines a shift of the reaction to the right with a consequent increase of CO₂.

H⁺ + HCO₃^-  Û  H₂O + CO₂

When metabolic acidosis is correlated to a loss of bicarbonate there is an increase of the AG, which may be consequent to an increase of UC (e.g. lactate, acetoacetate). The treatment of metabolic acidosis requires the treatment of the cause of the pathological process together with the intravenous use of fluids containing precursors of bicarbonate (Lactated Ringer’s, ES or Normosol R), in order to restore an effective circulation or to restore the fluids lost with dehydration. In general, if one is successful in treating the cause of the imbalance and if solutions with precursors of bicarbonate are administered, it is not necessary to administer sodium bicarbonate (NaHCO₃); vice versa when the pH is < 7,0 and bicarbonate is under 14 mEq/L a therapy with NaHCO₃ may be considered. The dose of  NaHCO₃ is calculated with the following formula:

NaHCO₃ = 0,3 x body weight (Kg) x (ideal bicarbonate – measured bicarbonate)     Formula n. 12  

NaHCO₃ must be administered very slowly (15-20 minutes) intravenously at the dose of  1/4 to 1/8 of the calculated one. The next blood gas analysis is to be carried out after around 30 minutes.

Respiratory acidosis

Acidosis of respiratory origin is usually caused by an insufficiency in pulmonary ventilation, which may result from:

•  pleural space diseases (e.g. pneumothorax, GDV);
•  drugs (e.g. pain therapy with opiates);
•  pulmonary diseases (e.g. pneumonia, severe oedema);
•  traumas (e.g. effusions, costal fractures);
•  airway obstructions (e.g. asthma, herniae);
•  central or peripheral nervous system diseases (e.g. poisonings, tetanus).

The above mentioned pathological processes may for example cause a reduction in CO² elimination with a consequent accumulation of carbonic acid in the blood (see formula n. 1). The cause of  ventilatory failure must be readily recognised as it does not respond to oxygen therapy and it must be treated as early as possible (e.g. chest drainage in the case of pneumothorax). In any case, patients with ventilatory failure must undergo oxygen therap in order to reduce the risk of a concomitant hypoxia which, if combined with hypercapnia, may compromise vital functions. In these patients the  fluid therapy strategy requires a small-volume fluid  resuscitation with solutions containing bicarbonate precursors (e.g. LRS, ES or Normosol R) and chloride.

Metabolic alkalosis

The most common causes of metabolic alkalosis are  medical conditions which cause a loss of fixed and volatile acids:

• vomiting;
• diarrhoea;
• administration of antacids;
• therapy with alkalising agents;
• administration of furosemide.

Apart from the loss of acids, in some patients it is also possible to find a iatrogenic base excess caused by an exaggerated alkalising therapy (e.g. LRS, ES or Normosol R). In normal conditions kidneys are successful in rapidly eliminating  the HCO₃  in excess, correcting the acid-base imbalance, so in the case of iatrogenic alkalosis following the administration of a balanced solution it is always advisable to check the renal function. During a metabolic alkalosis there is a shift to the left of the reaction indicated in formula n. 3, with an increase in the production of  CO₂, which must be eliminated with ventilation. As for the other imbalances, the treatment is to be centred on the underlying pathological contidion, combined with fluid therapy with NaCl 0,9% and a close monitoring of the pH and its variables, while allowing the organism to adapt itself better to acidosis rather than to alkalosis.

Respiratory alkalosis

The most frequent causes of respiratory alkalosis are those forms which, by producing an increase in ventilation, cause a decrease in CO₂:

•  hypoxiaemia, anaemia
•  traumas;
•  pain
•  fever;
•  hyperthyroidism;
•  pregnancy;
•  pneumonia;
•  drugs._⁵

The reduction in CO₂ causes a compensatory reaction of HCO₃^-. Also for respiratory alkalosis the principal therapy consists in the treatment of the pathological condition which has caused the disorder; in general an acidifying therapy is not necessary, however the aetiological therapy (hypoxemia in particular must be corrected) may be combined with fluid therapy with NaCl 0,9%.

References

1. Viganò F. Equilibrio acido base. In: Terapia intensiva del cane e del gatto. Milano: Elsevier; 20011.pp 99-118.
2. Rose BD, Post TW. Introduction to simple and mixed acid-base disorders. In: Rose BD, Post TW, editors. Clinical physiology of acid-base and electrolyte disorders, 5th ed. New York: McGraw Hill;2001.p.535-50.
3. Shapiro BA, Cane RD, Chomka CM, et al: Preliminary evaluation of intrarterial blood gas system in dogs and humans. Crit Care Med, (17), 1989 pagg 57-67
4. Sirker AA, Rhodes A, Grounde RM, et al. Acid-base physiology: the traditional and the modern approaches. Anestesia 2002;57:348-56.
5. Di Bartola S. In Fluid electrolyte and acid base disorders in small animal practice.  S. Louis Elsevier 2006 pp 292-294