The Two-Digit Rule and Winter’s Formula

To the Editor,

I recently wondered, “How does the “Two-digit rule” for determining the adequacy of respiratory compensation for metabolic acidosis relate to Winter’s formula?”  Many clinicians were taught this rule-of-thumb: the last two digits of the pH (those visible if you hold your thumb over the “7”) should provide an approximation of pCO₂ (in mm Hg) in the presence of normal respiratory compensation.  Although Winter’s formula is easy to remember and perform, the Two-digit rule is even easier.  Winter’s formula and the Two-digit rule have both been derived empirically from clinical data (1,2).  But the reason the Two-digit rule should work has never, to our knowledge, been adequately explained.  We wondered how the two rules were related.

We began with serum HCO₃ values ranging from 4 -18 mmol/L and used them to calculate the corresponding predicted pCO₂ values using Winter’s formula (3).  Next, we used the Henderson-Hasselbalch equation to calculate the corresponding pH for each [HCO₃^-]/pCO₂ pair and used the Two-digit rule to re-calculate the corresponding predicted pCO₂.  The predicted compensatory pCO2 calculated by the Two-digit rule and Winter’s formula were then compared. 

Table 1. Comparison of predicted compensatory respiratory response to metabolic acidosis by Winter’s formula and the Two-digit rule.  Results of the Two-digit rule in red font fall outside the 95% standard error range of Winter’s formula. (Click here to view Table 1 in a separate, enlarged window)

Estimates of pCO₂ by the Two-digit rule were then superimposed over Winter’s original graphical data, from which the Winter’s formula was derived (1).  See below. 

Figure 1.  Predicted pCO2 by the Two-digit rule (in red font) superimposed over the original graphic used to derive Winter’s formula (1). (Click here to view Figure 1 in a separate, enlarged window)

Note that the Two-digit rule provides pCO₂ estimates within two standard errors (+/- 2 mm Hg) of Winter’s formula, for most [HCO₃^-] values ranging from 5-18 mmol/L.  At a HCO₃ of 10 mmol/L, the Two-digit rule overestimates pCO₂ by 1mmHg compared to Winter’s formula.  At HCO₃ above 18 mmol/L and below 5 mmol/L, the Two-digit rule underestimates pCO₂ compared to Winter’s.

The apparently linear relationship between pH (the negative base-ten logarithm of [H+]) and related partial pressure of pCO2 in mm Hg is explained by the three relationships that link their association.

1) pH has a negative logarithmic association with [H⁺].  As most who have used the simplified form of the Henderson-Hasselbalch equation ([H+] = 24*pCO₂/HCO₃) will remember, this relationship is conveniently approximately linear over the narrow range of physiological pH values, such that [H+] values of 30, 40, 50 and 60 nmol/L approximately correspond to pHs of 7.50, 7.40, 7.30 and 7.20 respectively.  2) Central chemoreceptors in the ventral medulla (and other locations) respond to increasing brain interstitial [H+] by increasing ventilatory drive in a fashion that is also approximately linear in the physiological range of pH values (3).  See figure below.  3) Ventilatory drive is inversely linearly related to pCO₂.

(More precisely, Pa_CO2 = V_CO2*K/V_ALV , where V_CO2=the rate of CO₂ production, K, is a proportionality constant, and V_ALV=alveolar minute ventilation (total ventilation – dead space ventilation.)

Figure 2. The ventilatory response to changes in brain interstitial fluid pH as studied in conscious goats (3). (Click here to view Figure 2 in a separate, enlarged window)

Therefore, It's not surprising that the last two digits of the pH should have a positive, approximately linear correlation with pCO₂.  However, the convenience of the correlation (two digits of the pH equaling the pCO₂) is purely fortuitous. The Two-digit rule provides a good approximation of the expected compensatory pCO₂ as calculated by Winter’s formula for [HCO₃^-] ranging from 5-18 mmol/L.

Robert Raschke MD

Clinical Professor of Medicine, University of Arizona College of Medicine – Phoenix

Phoenix, AZ USA

References

1. Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med. 1967 Feb;66(2):312-22. [CrossRef] [PubMed]
2. Fulop M. A guide for predicting arterial CO2 tension in metabolic acidosis. Am J Nephrol. 1997;17(5):421-4. [CrossRef] [PubMed] (This shows empirical derivation of two-digit rule.)
3. Fencl V, Miller TB, Pappenheimer JR. Studies on the respiratory response to disturbances of acid-base balance, with deductions concerning the ionic composition of cerebral interstitial fluid. Am J Physiol. 1966 Mar;210(3):459-72. [CrossRef][PubMed] (This shows relationship between resp drive and [H].)

Cite as: Raschke RA. Letter to the Editor: The Two-Digit Rule and Winter’s Formula. Southwest J Pulm Crit Care Sleep. 2023;27(1):11-13. doi: https://doi.org/10.13175/swjpccs031-23 PDF

Epiglottic Calcification: The Unexplored Relationship with Increasing Rates of Renal Disease

To the Editor: In the September 2022 issue the Southwest Journal of Pulmonary Critical Care and Sleep published an interesting article authored by Punatar et al. detailing a case of severe dysphagia that was secondary to isolated epiglottic calcifications seen on computed tomography and flexible fiberoptic laryngoscopy (1). The epiglottis plays a critical role in the prevention of aspiration and coordination of swallowing. Calcifications can severely alter its flexibility and limit oral intake. Isolated calcifications of the epiglottis and sequential dysphagia is not a common entity. With the increasing rates of chronic and end-stage renal disease, this letter is focused on increasing the awareness of extra-osseous manifestations of secondary hyperparathyroidism.

Secondary hyperparathyroidism is characterized by adaptive parathyroid gland hyperplasia to increase the production of parathyroid hormone. Etiologies include vitamin D deficiency and chronic kidney disease. Vitamin D deficiency can be seen in about 50% of the world population and chronic kidney disease affects more than 37 million people in the United States (2-3). Manifestations of sustained increases in parathyroid hormone can cause high-turnover rates of osseous structures and extra-osseous manifestations. Among the extra-osseous manifestations, chondrocalcinosis is a known complication. Although there remains a higher risk of calcification within the larynx and trachea as opposed to the epiglottis, epiglottic calcifications should still be suspected in patients with dysphagia and chronic kidney disease (4-5). Early diagnosis and management may result in the prevention of worsening extra-osseous disease.

Given the lack of literature regarding the prevalence and characteristics of secondary hyperparathyroidism and epiglottic calcifications, all cases that identify epiglottic calcifications should note whether a secondary hyperparathyroidism work up or other causes of abnormal parathyroid hormone elevations was initiated, to aid the scientific community in identifying a potentially underdiagnosed phenomenon. My question to the authors of this study is if any further work up was completed, including biochemical serum testing for parathyroid hormone, vitamin D levels, calcium, or phosphate levels. This would be valuable for the audience of this journal and would allow providers to be increasingly aware of this clinical entity.

Ramzi Ibrahim MD

Department of Medicine – University of Arizona Tucson, Tucson, AZ USA

References

1. Punatar S, Song D, Zaman A, Jiao B, Spyratos T. September 2022 Medical Image of the Month: Epiglottic Calcification. Southwest J Pulm Crit Care Sleep. 2022;25(3):41-42. [CrossRef]
2. Bouillon R, Norman AW, Lips P. Vitamin D deficiency. N Engl J Med. 2007 Nov 8;357(19):1980-1; author reply 1981-2. [CrossRef] [PubMed]
3. Centers for Disease Control and Prevention. Chronic Kidney Disease in the United States, 2021. Atlanta, GA: US Department of Health and Human Services, Centers for Disease Control and Prevention; 2021.
4. Ajmani ML, Jain SP, Saxena SK. A metrical study of laryngeal cartilages and their ossification. Anat Anz. 1980;148(1):42-8. [PubMed]
5. Fernández-Rodríguez A, Benito-Orejas JI, Jiménez-Pérez AE, Morais-Pérez D. Calcificación de la epiglotis [Calcification of the epiglottis]. Acta Otorrinolaringol Esp. 2009 May-Jun;60(3):215-6. Spanish. [CrossRef] [PubMed]

The Author Replies: Dr. Ibrahim reflects on our contribution of a case of severe dysphagia secondary to epiglottic calcification. It is purported that cases of epiglottic calcification are not common, and that a workup for secondary hyperparathyroidism should be considered. This is suggested as secondary hyperparathyroidism from chronic kidney disease may cause extra-osseous manifestations such as calcifications of the larynx and trachea, and even epiglottis.

To confirm and collectively create a comprehensive understanding of our case of epiglottic calcification, we agree with the notion by Dr. Ibrahim that secondary hyperparathyroidism should be considered in causes of epiglottic calcification.

Upon further review with lab values included below, our patient had progressed from chronic kidney disease to end stage renal disease and was consistent with home peritoneal dialysis. It had been noted that the patient was undergoing care and monitoring for secondary hyperparathyroidism in the outpatient setting from nephrology services. While he was on calcitriol 0.5mcg daily in the outpatient, setting, we have included his pertinent lab values as follows:

• Calcium 9.3 mg/Dl( 8.6-10.3 mg/Dl)
• Corrected Calcium 10.1 mg/dL
• Albumin 3.0 g/dL (3.5-5.7 g/Dl)
• Phosphorus 3.6 mg/dL  (2.5-4.5mg/dL)
• Vitamin D 25 0H 37.5 ng/ML (30-100 ng/ml)

While controlled, it is possible that secondary hyperparathyroidism a contributory factor in leading to this patient’s epiglottic calcification and subsequent dysphagia.

Shil Punatar DO

Department of Internal Medicine- Franciscan Health Olympia Fields, Olympia Fields, Illinois USA

Cite as: Ibrahim R. Epiglottic Calcification: The Unexplored Relationship with Increasing Rates of Renal Disease. Southwest J Pulm Crit Care. 2022;25(4):50-51; author reply 51. doi: https://doi.org/10.13175/swjpccs043-22 PDF 

Steroids for Community-Acquired Pneumonia? Not in My House!

To the Editor:

In response to the paper by PR Bauer and VN Iyer (1) entitled “Corticosteroids and Influenza A Associated Acute Respiratory Distress Syndrome” published in the Southwest Journal of Pulmonary and Critical Care (SWJPCC) on November 18, 2016.  That paper presents a single case report of a patient with community-acquired pneumonia in Arizona attributed to influenza A.  The patient was treated with steroids and improved.  For a variety of reasons, a case report like this should not be published unless accompanied by a note pointing out the implications of such a report.  The audience of SWJPCC is generally going to be made up of two groups, mainly from Arizona.  Those with experience who would say that the treating physicians were lucky (but in the back of their minds this case might give them a reason to use steroids in similar circumstances) and those with little or no experience, who will say the next time I see a patient with a non-bacterial pneumonia who is not doing well, I am going to treat that patient with steroids.  The latter interpretation is the reason for this Letter to the Editor to point out the problems.

Why am I in a position to make judgments in this clinical situation? Because I was in private practice in Phoenix (“my house”) as a Board Certified Infectious Diseases specialist for over 25 years.  I estimate that I followed about 10,000 patients hospitalized with various types of pneumonia.  I have not published any papers on pneumonia in Arizona, but I have a lot of experience in treating pneumonias in Phoenix, the sixth largest city in the United States.  In addition, I was the Infectious Disease Society of America (IDSA) “Clinician of the Year in 2007” which suggests that I have some experience and knowledge with the infectious disease issues at hand.  There is a general clinical observation made by me over the years about the use of steroids in pneumonias of unknown cause - that is the steroid-treated patients initially seem to improve for a few days, irrespective of the cause.  Unfortunately those starting the steroids only remember how the patient seemed to improve with steroids, but forget that the patient dies about a week later.  The treating physicians only remember the initial improvement associated with the steroids and not the fact the patient ultimately died. 

A few years ago I reviewed the medical records of six patients with meningitis due to Coccidioides.  Of the six, two had been seen previously as outpatients for a pneumonia and given steroids (for unclear reasons), in addition to empirical antibiotics.  I knew the hospitalists who cared for those two patients.  They were good physicians, but new to Phoenix and had received their training outside of Arizona.  These observations would be difficult to make unless you had experience in this part of the world where there are lots of people and Coccidioides together in one place, more than anywhere else in the world.  I experienced similar issues myself of “occult” Coccidioides when I began practice in Phoenix in 1980.  It has been my idea that all physicians who get a license to practice in Arizona should show proficiency in coccidioidomycosis.  

The patient described in this Journal’s case report was felt to have influenza.  Please note however, that he had tested negative for influenza twice before a culture was positive for influenza A.   This supports the possibility that the influenza detection may have been incidental to some other underlying etiology.  In my opinion, to publish a single case report of influenza pneumonia treated with steroids there should be lung biopsy evidence consistent with influenza pneumonia.  Publishing a single case report, only perpetuates the idea that using steroids might be beneficial in influenza pneumonia.  In controlled studies on the use of steroids there has not been clear evidence that they are therapeutic in influenza pneumonia.  The authors prefer to call it a “controversy” to justify their use of steroids, but if this patent had died of coccidioidomycosis, what would be the controversy then?  How much to pay the plaintiff!  Please note the author’s affiliation is listed as Rochester, Minnesota an area not known to have endemic Coccidioides. 

There are three antiviral agents that can be used for serious influenza virus infections:  1) Oral oseltamivir (Tamiflu) which was used in this patient.  In critically ill patients a nasogastric tube may be needed to administer the oral agent.  Starting the drug within 72 hours of onset is optimal, but the drug can still have some effectiveness if started 4-5 days later; 2) Intravenous peramivir (Rapivab) was recently approved (12/2014) for use against influenza.  I prefer the intravenous formulation in critically ill patients; 3) There is an intravenous version of inhaled zanamivir (Relenza) which can be obtained on an investigational basis.  The sooner any of these agents are started the better the outcome.  In any patient critically ill with pneumonia during flu season, any of these agents should be started empirically even before the influenza studies are completed. 

It should be noted that the patient in the case report received both oseltamivir and methylprednisolone.  One could make the case that since steroids have not been shown in clinical studies to be effective in influenza pneumonia, that the clinical response may have been to the oseltamivir.  Often patients with influenza pneumonia will have rapid progression to respiratory failure before the antivirals are considered.  Starting oseltamivir or peramivir empirically on only the suspicion of a viral pneumonia is more likely to be beneficial than the empirical use of antibacterial antibiotics.

Young physicians recently out of training usually have little experience with the use of antivirals in critically ill patients.  In my opinion, the only benefit of publishing a single case of influenza A pneumonia is to have a companion rebuttal and discussion of the issues.  Hopefully these observations will give pause to the Arizona clinician’s next patient who appears to have a non-bacterial pneumonia – think of the early use of antivirals and the diagnosis of Coccidioides, not the use of steroids.

Tim Kuberski, MD, FIDSA

Maricopa Medical Center

Department of Medicine, Infectious Diseases

Phoenix, Arizona 

Reference

1. Bauer PR, Iyer VN. Corticosteroids and influenza A associated acute respiratory distress syndrome. Southwest J Pulm Crit Care. 2016;13(5):248-51. [CrossRef]

The Authors Reply:

We read with interest the letter to the Editor by Dr. Kuberski and acknowledge his concern. We intended to publish this case report for the exact same reason that triggered his worries. How can someone use corticosteroids in Influenza when their benefits are controversial (1,2)? Here are some elements of responses. First, Influenza affects Arizona like every other State so it is relevant to the readers in this part of the Country as well. Second, in spite of their controversial benefits, corticosteroids are commonly prescribed in Influenza-related illnesses (3). Third, due to its low sensitivity, albeit high specificity, diagnostic testing for influenza maybe negative in the upper airways (e.g. nasal swab) and positive in the lower airways (e.g. broncho-alveolar lavage) and therefore antiviral treatment can be delayed and outcome jeopardized like in our case. Fourth, the benefit of an anti-influenza agent is optimal if initiated within 48 hours after symptoms onset. Fifth, biopsy and electronic microscopy are not recommended to confirm the diagnosis of Influenza and the plan of care in this case assumed a high likelihood of severe Influenza with delayed diagnosis and therefore delayed treatment.

In spite of the severity of the presentation to our Institution, this patient’s condition improved dramatically, rapidly and definitively. We certainly cannot conclude that corticosteroids made the difference but the fact of the matter is that this patient did not need prolonged ventilation or extracorporeal membrane oxygenation. The use of corticosteroids in acute respiratory distress syndrome (ARDS) has been suggested long time ago but indeed was not associated with better long term outcome (4). That particular study was conducted between April 1997 and April 2002 that is before the era of lung volume protection strategy (published in 2000) and may have been confounded by the occurrence of ventilator associated lung injury and nosocomial infection (5). With the new Berlin definition of ARDS (6), not every ARDS is associated with diffuse alveolar damage for which corticosteroids have no known benefit; organizing pneumonia is also frequently encountered in ARDS which may be sensitive to corticosteroids (7). Lastly, the recent study on corticosteroids in community acquired pneumonia, which by the way included 27 cases of Influenza, demonstrated overall a shorter time to clinical stability without an increase in complications, like in our case (8).

At the end, this patient with moderate ARDS secondary to Influenza made a prompt and uncomplicated recovery, despite delayed treatment with antiviral agent and the adjunction of corticosteroids. We were surprised and thrilled by the patient’s fast and full recovery and wanted to share our experience and revisit the role of corticosteroids in this particular context.

Philippe R Bauer, MD, PhD, and Vivek N. Iyer, MD

Pulmonary and Critical Care Medicine

Mayo Clinic

Rochester, MN USA

References

1. Rodrigo C, Leonardi-Bee J, Nguyen-Van-Tam J, Lim WS. Corticosteroids as adjunctive therapy in the treatment of influenza. Cochrane Database Syst Rev. 2016 Mar 7;3:CD010406. [CrossRef] [PubMed]
2. Shafiq M, Mansoor MS, Khan AA, Sohail MR, Murad MH. Adjuvant steroid therapy in community-acquired pneumonia: a systematic review and meta-analysis. J Hosp Med. 2013 Feb;8(2):68-75. [CrossRef] [PubMed]
3. Delaney JW, Pinto R, Long J, et al. The influence of corticosteroid treatment on the outcome of influenza A(H1N1pdm09)-related critical illness. Crit Care. 2016 Mar 30;20:75. [CrossRef] [PubMed]
4. Meduri GU, Golden E, Freire AX, et al. Methylprednisolone infusion in early severe ARDS: results of a randomized controlled trial. Chest. 2007 Apr;131(4):954-63. [CrossRef] [PubMed]
5. The Acute Respiratory Distress Syndrome Network. Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome. N Engl J Med. 2000 May 4;342(18):1301-8. [CrossRef] [PubMed]
6. Ranieri VM, Rubenfeld GD, Thompson BT, et al. Acute respiratory distress syndrome: the Berlin Definition. JAMA. 2012 Jun 20;307(23):2526-33. [CrossRef] [PubMed]
7. Thille AW, Esteban A, Fernández-Segoviano P, et al. Comparison of the Berlin definition for acute respiratory distress syndrome with autopsy. Am J Respir Crit Care Med. 2013 Apr 1;187(7):761-7. [CrossRef] [PubMed]
8. Blum CA, Nigro N, Briel M, et al. Adjunct prednisone therapy for patients with community-acquired pneumonia: a multicentre, double-blind, randomised, placebo-controlled trial. Lancet. 2015;385(9977):1511-8. [CrossRef] [PubMed] 

Cite as: Kuberski T. Steroids for community-acquired pneumonia? not in my house! Southwest J Pulm Crit Care. 2016;13(5):257-60. doi: https://doi.org/10.13175/swjpcc124-16 PDF