Part II: The Lethal Corner
Authored by: Gary Grist, BS, RN, CCP, LCP
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The Lethal Corner
The Krogh cylinder predicts a wide range of tissue pO2 values called an oxygen pressure field surrounding individual capillaries. As the relationship between the capillary and its surrounding tissue changes, the oxygen pressure field also changes. The level of oxygen consumption, the intracapillary velocity and the length of the cylinder are variables which affect the oxygen concentration at any particular area within the pressure field.
However, these changes, at most, result in fractional changes in tissue pO2 concentrations.
Suppose that an increased O2 consumption drops the median tissue pO2 from 20 mmHg to 10 mmHg at the arterial end of the cylinder. With an arterial pO2 of 80 mmHg, the capillary-to-tissue gradient would increase fractionally from 60 to 70 mmHg (a 17% increase). Similarly, at the venous end the median tissue pO2 dropping from 10 mmHg to 5 mmHg would increase the gradient from 30 mmHg to 35 mmHg (also a 17% increase). Both these are fractional increases of a factor that maintains the oxygen transfer to the cells, the radial vectors. If cardiac output remains unchanged, then intracapillary velocity would not be fast enough to prevent the reduction of the capillary pO2 as increased amounts of oxygen are transferred into the tissue.
The result would be desaturation of the intracapillary blood (what we see as a reduced mixed venous saturation). Desaturation of the capillary blood obviously reduces the capillary-to-tissue-gradient, which in turn reduces the magnitude of the radial vectors. Less oxygen is transferred to the tissues.
Those tissues farthest from the capillary and nearest the venous end of the tissue cylinder, because they already have the lowest pO2 concentration, would be particularly vulnerable to this reduced transfer of oxygen. Potentially, to prevent this, the body can increase the cardiac output by approximately 17% to maintain the normal capillary pO2 values. The 17% increase in intracapillary velocity represents another fractional factor change.
The interplay of most of the variables described by the Krogh cylinder structure and oxygen pressure field are easily compensated by making fractional changes. However, when changes are exponential in magnitude the situation becomes life threatening at the capillary level because the compensation mechanisms are inadequate.
In Part 1, the relationship between the capillary X-section and the cylinder X-section was 1/4. This ratio was a major factor in predicting the mean tissue pO2 along the length of the cylinder. If the capillary radius remains the same (r = 5 microns) but the cylinder radius has doubles from 10 to 20 microns the X-section of the cylinder will increase from 314 to 1256 square microns. The ratio becomes 1/16, an exponential increase.
By doubling the cylinder radius the volume of tissue served by this single capillary has increased by a factor of 4. Under these circumstances, at the arterial end of the cylinder the capillary pO2 of 80 mmHg would sustain an average cylinder pO2 of only 5 mmHg. It is true that the capillary-to-tissue gradient would increase from 60 to 75 mmHg but this represents only a 25% increase in the magnitude of the radial vectors.
The passive transfer of gas in this situation is dependent upon two main variables; the gradient and the distance.
An increase of 25% in the driving gradient would only increase the volume of gas transferred by 25%. However, by increasing the cylinder radius to 20 microns the volume of tissue needing oxygen has increased by a factor of 4. In addition, the distance that the oxygen must diffuse in order to reach the most distant cells at the periphery of the cylinder has doubled. This situation predicts that tissue farthest from the capillary and nearest the venous end will receive little or no oxygen.
Even if cardiac output remains high in order to sustain intracapillary pO2 values there would still not be enough of a driving gradient to supply all of the tissues needing oxygen around this capillary. In addition, the mixed venous saturation (a key indicator of oxygen extraction ) would remain normal.
“The areas farthest from the capillary and nearest the venous end which
do not receive adequate oxygenation have been called the “Lethal Corner”
because, conceptually, they exist is the distal corners of the Krogh
cylinder. The size of the lethal corner is determined, for the most part,
upon the size of the tissue cylinder. The bigger the tissue cylinder in
relation to its need for oxygen, the bigger the lethal corner will be. In
this situation some of the cells within the tissue cylinder will receive
adequate oxygen and some will not, allowing normoxic, hypoxic and anoxic
cells to exist within the same capillary bed !!! “
This situation is well known to perfusionists and other health care professionals in the acute caresetting.
Only the term used is “shock” rather than lethal corner.
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All kinds of shock (cardiogenic, hypovolemic, septic, and others) represent a change in the reationship between the capillary X-section and the tissue cylinder X-section, whatever the cause. If the shock is occult in nature, the usual clinical parameters will be normal. This is sometimes seen during a routine pump run. Oxygen delivery, blood pressure, mixed venous saturation are all kept within normal limits by the perfusionist but an insidious increase in base deficit occurs, sometimes necessitating the need to give a buffer base. Since the size of the lethal corner is dependent upon the size of the tissue cylinder, the ability to change the Krogh cylinder size is of extreme importance. The next posting will discuss this issue by describing “Perfused Capillary Density”.
Although the Krogh cylinder is the original and simplest model for studying the oxygen pressure field it is by no means the only model.
One model suggests that each tissue cylinder is solid and very large with oxygen being transferred by multiple capillaries at the periphery of the cylinders but running parallel to the cylinder’s axis. This would result in the lowest tissue pO2 being at the center of the cylinder rather than at the periphery. The lethal corner would be more like a lethal apple core.
The idea suggests that if one or two capillaries at the periphery fail to supply oxygen the others will pick-up the slack to minimize the lethal apple core.
Another model suggests that the Krogh cylinder is shaped like a cone which tapers towards the venous end of the capillary bed where the capillaries increasingly branch prior to becoming venules. The concept here is that as the intracapillary pO2 drops near the venous end and the magnitude of the radial vectors falls, the cone tapers to compensate. This model predicts a more uniform oxygen pressure field, however, tests have shown this not to be the case.
Another model suggests that since the capillaries are completely random the concept of a cylinder or cone is not applicable. Instead the oxygen pressure field is delineated by the presence of mitochondria. Theoretically, in areas of the highest tissue pO2 there would be more mitochondria and in the lowest areas there would be fewer mitochondia. This concept seems to be plausable in muscle tissue. However, in other tissues like the liver and brain where mitochonria distribution is more or less uniform but variations in the oxygen pressure field still exist this model doesn’t work well. Other models describe regions and sub-regions, constants for diffusion of O2 which varies from tissue to tissue and even augmented diffusion over great distances at low concentrations mediated by the presence of myoglobin in the cells.
All of these ideas have merit and all have faults. None of them answers all the questions about oxygen distribution at the cellular level, but the Krogh concept seems to be the most useful in helping people understand oxygen pressure field theory.