Diffusion of carbon dioxide gas through the skin
Diffusion of carbon dioxide gas
through the skin
Richard Rivers, M.D., Ph.D
Johns Hopkins University
Summary: This paper discusses the process of diffusion of carbon dioxide passing through the skin and into the tissue. It offers evidence of this diffusion and quantitates that amount of gas that is expected to transfer during an episode of transdermal treatment.
Carbon dioxide is a natural substance that is generated by every living organism that uses oxygen as its source of energy. Oxygen transfers into the organism through the cell wall for multicellular organisms, through the skin in insects and very small animals, and transfers into the body through lungs or gills for larger animals. Regardless of how it gets into the cells, it reacts with enzymes and proteins in the mitochondria to generate transferable energy molecules and then discharges carbon dioxide as a byproduct. The carbon dioxide leaves the organism using the same pathway that the oxygen entered.
Oxygen is very a very reactive substance that will oxidize and destroy tissues. The concentration inside the body is tightly controlled and the danger of reactive oxygen species are balanced by anti-oxidant molecules. Carbon dioxide is critical in maintaining the anti-oxidant milieu1. The tissue concentration of carbon dioxide in the tissue is closely maintained around 40mmHg; although, levels as high as 100 are reported during extreme exercise. Elevations in the concentration of carbon dioxide in the tissue have been shown to decrease the size of metastatic tumors, decrease inflammation, generate new blood vessels, and improve circulation in patients with peripheral vascular disease.
A new device on the market allows for portable treatment of various lesions and ailments with transdermal carbon dioxide. To be effective, the carbon dioxide gas must diffuse through the skin to reach the affected tissues.
Diffusion through the skin
The target tissue for carbon dioxide therapy may be the skin for wound healing or it may be the soft tissue, or even the joints. The gas must penetrate the skin and diffuse further into the tissue as desired. Diffusion of CO2 in the muscle is 14 times faster than it is through the skin2. Nonetheless, diffusion through the skin is adequate to obtain a therapeutic response in the deeper tissues.
Respiration of gases through the skin was described as long ago as 18723. The passage of oxygen and carbon dioxide through the skin has been demonstrated by isolating the body, or an arm, within an enclosure and measuring the amount of gases that pass either out of the skin or is absorbed in through the skin, based on the gas concentrations within the enclosure4,5. The average rate of passive diffusion of CO2 through the skin to the atmosphere at 27°C is 120ml/m2/hr.
According to Fick’s law, diffusion through the skin will depend on the surface area, diffusion coefficient, and the concentration gradient. As noted above, the average passive transfer is 120ml/m2/hr going from inside to outside the body. The concentration gradient is assumed to be 40mmHg in the tissue to 0.3 mmHg in the atmosphere. Thus, the gradient produces 120/(40-0.3) = 3.0 ml/mmHg.
With transdermal therapy 100% CO2 is applied to the skin. So the concentration gradient is 760mmHg at the skin and 40mmHg in the tissue giving a driving force of 720mmHg. Given the surface area and diffusion coefficients are not affected by the direction of the gradient we estimate the diffusion of CO2 through the skin to be equal to 720 x 3 = 2176 ml/m2/hr. This is roughly 2 liters per hour per square meter. If we look at a typical adult arm as a cone with 3.25cm radius1; 4.45cm radius2; and 28cm length, the surface area = Π*28*(3.24 + 4.45) = 677cm2 = 0.067m2. Volume = 1/3 * Π* (3.252 + 4.452 + 3.25*4.45) * 28 = 1274ml. 2.17 l/hr/m2 * 0.067 m2 = 145 ml/hr of CO2 diffusing into the arm, or about 48 ml in a twenty minute treatment.
Modifying the diffusion through the skin
Data show the rate of transfer through the skin increases with the temperature of the skin6, diseases of the skin7, and the water content of the skin.
Moist skin accelerates carbon dioxide diffusion
Bull frogs moderate skin transfer of gases when in the dry air8.
Human in a box measuring transfer from inside to outside. Wetting skin with a sponge doubles transfer CO2 transfer9.
Arm in a box measuring CO2 transfer from in to out. CO2 transfer tripled4.
Pig ear skin studied in-vitro. Resistance to diffusion decreased over 10 fold when the humidity was increased10.
Study compares bath containing CO2, to a bag over body with moist or dry CO2 gas. Only moist gas mimicked activity of water bath11.
Rats skin studied in vitro. Skin kept moist with a gel showed highly significant increases in diffusion of CO2 compared to diffusion though dry skin12.
Analysis of multiple studies show the diffusion coefficient of CO2 through various tissue, including skin, increases exponentially depending on the water content12.14. In Fact, the diffusion coefficient in very moist tissue approximates diffusion in water itself13, essentially abolishing the diffusion barrier of dry skin.
Deep penetration to the tissues
How far will CO2 transfer into tissue? CO2 is highly soluble in soft tissue so it continues to move towards lower concentrations. It is also carried away by blood flowing through the tissue.
What is the concentration gradient? According to the Fick equation four variables control the depth of penetration into the tissue: 1) the mass of tissue available for absorbing the gas, 2) the transport of gas away from the tissue by the blood, 3) the concentration of CO2 at the skin (the diffusion coefficient CO2 in the skin), and 4) the time allotted for diffusion. Given that these many variables will change based on the environment, the anatomy and the disease, a precise calculation of the concentration in the tissues is almost impossible. All we know is that (i) CO2 does penetrate the skin, (ii) the diffusion rate is increased 2 to 4 fold when wet (approaching diffusion in water) and (iii) CO2 is very soluble in the soft tissues. It is comforting to know that the target tissue is reported to generate a response with CO2 increases as little as 5%15, so the amount of CO2 needed to reach the tissue is not very high.
Bolevich S, Kogan A, Zivkovic V, et al. Protective role of carbon dioxide (CO2) in generation of reactive oxygen species. Mol Cell Biochem. 2016;411(1):317-330. http://www.ncbi.nlm.nih.gov/pubmed/26541754. doi: 10.1007/s11010-015-2594-9.
Shaw LA, Messer AC, Weiss S. Cutaneous respiration in manned : I. factors affecting the rate of carbon dioxide elimination and oxygen absorption. American Journal of Physiology-Legacy Content. 1929;90(1):107-118. doi: 10.1152/ajplegacy.19188.8.131.52.
Aubert H. Untersuchungen über die menge der durch die haut des menschen ausgeschiedenen kohlensäure. Archiv für die gesamte Physiologie des Menschen und der Tiere. 1872;6(1):539-552. https://doi.org/10.1007/BF01612264. doi: 10.1007/BF01612264.
Shaw LA, Messer AC. Cutaneous respiration in man ii the effect of temperature and of relative humidity upon the rate of carbon dioxide elimination and oxygen absorption. American Journal of Physiology-Legacy Content. 1930;95(1):13-19. doi: 10.1152/ajplegacy.19184.108.40.206.
R. A. Klocke, G. H. Gurtner, L. E. Farhi. Gas transfer across the skin in man. Journal of Applied Physiology. 1963;18(2):311-316. http://jap.physiology.org/content/18/2/311.
Wimberley PD, Gronlund Pedersen K, Olsson J, Siggaard-Andersen O. Transcutaneous carbon dioxide and oxygen tension measured at different temperatures in healthy adults. Clinical Chemistry. 1985;31(10):1611. http://www.clinchem.org/cgi/content/abstract/31/10/1611.
Ernstene AC, Volk MC. Cutaneous respiration in man: V. the rate of carbon dioxide elimination and oxygen absorption in subjects with diseases of the skin. The Journal of clinical investigation. 1932;11(2):377-382. https://www.ncbi.nlm.nih.gov/pubmed/16694046.
Feder ME, Burggren WW. Cutaneous gas exchange in vertebrates: Design, patterns, control and implications. Biological Reviews. 1985;60(1):1-45. doi: 10.1111/j.1469-185X.1985.tb00416.x.
Alkalay I, Suetsugu S, Constantine H, Stein M. Carbon dioxide elimination across human skin. The American journal of physiology. 1971;220(5):1434. http://www.ncbi.nlm.nih.gov/pubmed/5574662
Björklund S, Ruzgas T, Nowacka A, et al. Skin membrane electrical impedance properties under the influence of a varying water gradient. Biophysical Journal. 2013;104(12):2639-2650. https://www.sciencedirect.com/science/article/pii/S000634951300533X. doi:10.1016/j.bpj.2013.05.008.
Bedu M, Cheynel J, Gascard J, and Coudert J. Transcutaneous CO2 diffusion comparison between CO2 spa water and dry gas in Royal thermal spa. In: Advances n Vascular Pathology, edited by Strano A, and Novo S. Elsevier Science Publishers B. V. (Biomedical Division); 1989:1109-1113.
Sakai Y, Miwa M, Oe K, et al. A novel system for transcutaneous application of carbon dioxide causing an "artificial Bohr effect" in the human body. PloS one. 2011;6(9):e24137. http://www.ncbi.nlm.nih.gov/pubmed/21931656. doi: 10.1371/journal.pone.0024137.
Akgerman A, Gainer JL. Diffusion of gases in liquids. Ind Eng Chem Fund. 1972;11(3):373-379. https://doi.org/10.1021/i160043a016. doi: 10.1021/i160043a016.
Vaupel P. Effect of percentual water content in tissues and liquids on the diffusion coefficients of O2, CO2, N2, and H2. Pflugers Archiv: European journal of physiology. 1976;361(2):201-204. https://www.ncbi.nlm.nih.gov/pubmed/943095. doi: 10.1007/BF00583467.
Duling BR. Changes in microvascular diameter and oxygen tension induced by carbon dioxide. Circulation Research. 1973;32(3):370-376. http://circres.ahajournals.org/cgi/content/abstract/32/3/370. doi: 10.1161/01.RES.32.3.370.