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TEACHING WITH TECHNOLOGY
Division of Pulmonary Medicine, School of Medicine, Southern Illinois University, Springfield, Illinois
Address for reprint requests and other correspondence: K. S. Kapitan, Div. of Pulmonary Medicine, School of Medicine, Southern Illinois Univ., 751 N. Rutledge St., Rm. 1100, PO Box 19636, Springfield, IL 62794-9636 (e-mail: kkapitan{at}siumed.edu)
Abstract
Students often have difficulty understanding the relationship of O2 consumption, CO2 production, cardiac output, and distribution of ventilation-perfusion ratios in the lung to the final arterial blood gas composition. To overcome this difficulty, I have developed an interactive computer simulation of pulmonary gas exchange that is web based and allows the student to vary multiple factors simultaneously and observe the final effect on the arterial blood gas composition (available at www.siumed.edu/medicine/pulm/vqmodeling.htm). In this article, the underlying mathematics of the computer model is presented, as is the teaching strategy. The simulation is applied to a typical clinical case drawn from the intensive care unit to demonstrate the interdependence of the above factors as well as the less-appreciated importance of the Bohr and Haldane effects in clinical pulmonary medicine. The use of a computer to vary the many interacting factors involved in the arterial blood gas composition appeals to today's students and demonstrates the importance of basic physiology to the actual practice of medicine.
Key words: simulation; ventilation-perfusion distribution; arterial blood gas
UNDERSTANDING the physiology of pulmonary gas exchange is difficult for most students. Despite clear presentations in classic textbooks (9), many students leave medical training with only a qualitative grasp of the determinants of hypoxemia and hypercarbia. Although they may understand the relationship of shunt to hypoxemia and ventilation to PCO2, the more complicated dependence of the arterial blood composition on O2 consumption, CO2 production, cardiac output, and distribution ventilation-perfusion ratios in the lung is far more difficult. One reason for this difficulty is the fairly complex interrelationship of these factors to the final arterial blood gas, which makes it hard to guess the relative effects when several factors change simultaneously.
To overcome this difficulty, I have developed an interactive computer simulation of pulmonary gas exchange that is web based and allows the student to vary multiple factors simultaneously and observe the final effect on the arterial blood gas composition (available at www.siumed.edu/medicine/pulm/vqmodeling.htm). This gives the student an opportunity to literally play with the ventilation-perfusion distribution, O2 consumption, cardiac output, etc. until s/he is comfortable with the various interactions. I usually introduce my students to the simulation with a lecture covering the basic quantitative physiology of gas exchange in a single compartment and in a multicompartment model of the lung. I then have them use this simulation to work through several clinical cases taken from the pulmonary clinic and intensive care unit. Although interested senior medical students can take on this subject, it is more advanced than the introductory respiratory physiology to which they are usually exposed. The simulation therefore is intended more for senior medical residents and pulmonary fellows who have had some clinical experience to draw upon.
In the introductory lecture, I begin by focusing on a single gas exchange unit in the lung. This is the volume of lung within which gas composition is uniform due to diffusive mixing. In humans, the respiratory unit appears to be the distal alveolar duct (1, 2), which subtends 
1,000 alveoli. I then describe gas exchange across this unit by simply pointing out that in a steady state, the rate at which O2 enters the unit from the atmosphere is the same as the rate at which O2 leaves the unit in the capillary blood (Fig. 1). I write this down as an equation:
 | (1) |
where VI and VA are the inspired and alveolar ventilations, FI
and FA are the inspired and alveolar fractional O2 concentrations; Q is the blood flow to and from the unit; and CV and CC are the mixed venous and capillary O2 contents in the blood flowing into and out of the unit. It is important to pause and ensure that everyone understands that this equation is a satisfactory description of O2 flow across the unit.
|
 | (2) |
 | (3) |
 | (4) |
where FA
is the alveolar fractional CO2 concentration, CV and CC are the mixed venous and capillary CO2 contents, FI
and FA are the inspired and alveolar fractional N2 concentrations, and CV and CC are the mixed venous and capillary N2 contents. These equations are nonlinear, coupled, and simultaneous. Their complete solution requires a computer. However, for the purposes of discussion only, we can make the simplifying assumption that VI and VA are approximately the same (V) and then rearrange these equations algebraically to show O2 and CO2 contents in the blood flowing from the unit, as follows:
 | (5) |
 | (6) |
I point out that, consequently, the gas contents in the blood coming from the unit depend on only three things: the mixed venous composition entering the unit, the inspired O2 fraction, and the ratio of ventilation to perfusion of the unit. Of course, to then calculate the corresponding PO2 and PCO2, we must also know several additional details, namely, the blood hemoglobin concentration, the oxyhemoglobin dissociation curve, and the relationship between CO2 content and PCO2, which were discussed in a previous lecture. This mathematical approach explicitly reveals the fundamental importance of the mixed venous composition and the V-to-Q (V/Q) ratio to the final arterial blood gas.
To transfer these conclusions to the real lung, I note that there are about half a million respiratory units in the lung (8), each with its own V/Q ratio, but fortunately each receiving the same mixed venous blood and the same FIO2. Thus, all of the respiratory units in the lung share two of the three determinants of gas exchange. The blood from each unit drains ultimately into the left atrium, where the contributions from all of the units mix in proportion to their perfusion to form the final mixed arterial blood. So, the determinants of arterial blood gas composition in the lung are identical to those of the single unit, with the V/Q distribution taking the place of the V/Q ratio.
At this point I introduce the parallel multicompartment model of the lung (Fig. 2) and emphasize that it is just a number of single compartments each receiving the same mixed venous blood and inspiring the same FIO2 and each contributing to the final arterial mixture in proportion to its perfusion, just like the real lung. If we specify a different V/Q ratio for each compartment and know the distribution of perfusion to each compartment (the V/Q distribution), then we can calculate the mixed arterial contents by solving Eqs. 2–4 above exactly using a computer (10). The computer solution does not require the simplifying assumption we made in the algebraic solution. We can then use the hemoglobin dissociation curve and the CO2 solubility curve to transform the O2 and CO2 contents into the PO2 and PCO2 of the mixed arterial blood.
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To make the final jump to the bedside, I point out that although we have seen that the mixed venous composition is one of the fundamental determinants of arterial composition, in reality, the mixed venous composition is itself determined by the total O2 consumption and CO2 production of the body and by the mean and dispersion of the V/Q distribution. Consequently, the basic determinants of arterial composition are actually interdependent! This interdependence is a source of significant confusion among students, which can be relieved by having them interactively work through several case studies using the program. I encourage them to simply play around by varying aspects of the V/Q distribution, varying the O2 consumption and CO2 production requirements, introducing an anemia, etc., and to observe the final effect on the arterial blood gases, until they feel comfortable with their overall understanding of pulmonary gas exchange. By varying parameters stepwise, they can observe the effect of each parameter independently on the final blood gas values.
Here is a typical clinical case. An elderly man with underlying obstructive pulmonary disease and advanced congestive heart failure is admitted to the intensive care unit in respiratory failure. He is intubated, placed on mechanical ventilation, and is deeply sedated. He is found to have pneumonia and is wheezing diffusely. Based on these findings, one can assume his V/Q distribution is abnormal and is composed of a combination of shunt, low V/Q and high V/Q ratios (3). His arterial blood gas is pH 7.44, PCO2 = 36 mmHg, and PO2 = 65 mmHg on 30% inspired O2. Later that evening, he develops a fever (39°C), rigors, and hypoxemia. Reevaluation reveals his chest X-ray is unchanged, he remains sedated, and there is no evidence of any other complication. His arterial blood gas is now pH 7.25, PCO2 = 74 mmHg, and PO2 = 56 mmHg. What has happened? [Clue: what do fever and shivering do to the patient's O2 consumption and CO2 production (4, 11)?]
Here is the solution: using the program, the student creates an abnormal V/Q distribution containing perfusion of shunt, low V/Q and high V/Q ratios and sets the FIO2 at 0.30. Since the patient is sedated, default values of O2 consumption, CO2 production, and cardiac output are used, and the arterial blood gas is calculated. The V/Q distribution is varied until the initial blood gas values are approximated. At this point, body temperature is first raised from 37 to 39°C, and the arterial blood gas is computed. Paradoxically, the PO2 rises by 6 mmHg. Why? This is the Bohr effect, which is confirmed by noting that the total arterial O2 content has not increased, despite the higher PO2, implying a shift to the right of the hemoglobin dissociation curve. Next, O2 consumption and CO2 production are doubled to 500 ml/min and 400 ml/min, respectively. The arterial blood gas is recalculated and reveals the development of hypoxemia and hypercarbia. Why?
The output of the calculation (Table 2) shows that because of the higher O2 consumption, the mixed venous O2 content declines significantly. Since areas of shunt and low V/Q ratios are present, the lower mixed venous content, in turn, drives the mixed arterial O2 content lower, resulting in hypoxemia. The converse applies to CO2.
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Hands-on, interactive computer simulations appeal to today's students, many of whom don't recall a time when computer games didn't exist. The ability to step through a clinically relevant gas exchange problem taken from the intensive care unit and see how varying the many interacting factors involved affects the final arterial blood gas composition provides the opportunity to really understand the physiology of each piece. This observation is certainly not new. Computer simulations have a long history in the teaching of respiratory physiology, beginning with the many contributions of Dr. Harold Modell (5, 7). The present simulation is offered as an addition to the collection of software currently available (6). The differences between previous simulations and the present simulation are mainly in terms of presentation and format. The present simulation has the convenience of being web based and allows somewhat more interactive variation of parameters than past programs. It also explicitly includes N2 exchange in the output. The goal remains the same, however: namely, to promote an active learning experience for the individual student that demonstrates the essential importance of basic physiology to the actual practice of medicine.
Received for publication October 26, 2007. Accepted for publication November 19, 2007.
REFERENCES
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and FA
inspired and alveolar fractional O2 concentrations; CV
