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A simple, closed-form, mathematical model for gas exchange in microchannel artificial lungs

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Abstract

Microfabrication techniques are attractive for constructing artificial lungs due to the ability to create features similar in size to those in the natural lung. However, a simple and intuitive mathematical model capable of accurately predicting the gas exchange performance of microchannel artificial lungs does not currently exist. Such a model is critical to understanding and optimizing these devices. Here, we describe a simple, closed-form mathematical model for gas exchange in microchannel artificial lungs and qualify it through application to experimental data from several research groups. We utilize lumped parameters and several assumptions to obtain a closed-form set of equations that describe gas exchange. This work is intended to augment computational models by providing a more intuitive, albeit potentially less accurate, understanding of the operation and trade-offs inherent in microchannel artificial lung devices.

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References

  • J.C. Anderson, A.L. Babb, M.P. Hlastala, Modeling soluble gas exchange in the airways and alveoli. Ann. Biomed. Eng. 31(11), 1402–1422 (2003)

    Article  Google Scholar 

  • J.C. Anderson, M.P. Hlastala, Breath tests and airway gas exchange. Pulm. Pharmacol. Therapeut. 20, 112–117 (2007)

    Article  Google Scholar 

  • K.A. Burgess, H.H. Hu, W.R. Wagner, W.J. Federspiel, Towards microfabricated biohybrid artificial lung modules for chronic respiratory support. Biomed. Microdevices 11, 117–127 (2009)

    Article  Google Scholar 

  • W.J. Federspiel, K.A. Henchir, Lung, artificial: Basic principles and current applications, in Encyclopedia of Biomaterials and Biomedical Engineering, ed. by G.L. Bowlin, G. Wnek, 1st edn. (Marcel Dekker, New York, 2004), pp. 910–921

    Google Scholar 

  • B. Florchinger, A. Philipp, A. Klose, M. Hilker, R. Kobuch, L. Rupprecht, A. Keyser, T. Puhler, S. Hirt, K. Wiebe, Pumpless extracorporeal lung assist: a 10-year institutional experience. Ann. Thorac. Surg. 86(2), 410 (2008)

    Article  Google Scholar 

  • S. Fischer, A.R. Simon, T. Welte, M.M. Hoeper, A. Meyer, R. Tessmann, B. Gohrbandt, J. Gottlieb, A. Haverich, M. Strueber, Bridge to lung transplantation with the novel pumpless interventional lung assist device NovaLung. J. Thorac. Cardiovasc. Surg. 131, 719–723 (2006)

    Article  Google Scholar 

  • G. Gros, W. Moll, The diffusion of carbon dioxide in erythrocytes and hemoglobin solutions. Pflügers Arch. 324, 249–266 (1971)

    Article  Google Scholar 

  • T.J. Hewitt, B.G. Hattler, W.J. Federspiel, A mathematical model of gas exchange in an intravenous membrane oxygenator. Ann. Biomed. Eng. 26, 166–178 (1998)

    Article  Google Scholar 

  • A.V. Hill, The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J. Physiol. 40, 4–7 (1910)

    Google Scholar 

  • D.M. Hoganson, J.L. Anderson, E.F. Weinberg, E.J. Swart, B.K. Orrick, J.T. Borenstein, J.P. Vacanti, Branched vascular network architecture: a new approach to lung assist device technology. J. Thorac. Cardiovasc. Surg. 140(5), 990–995 (2010)

    Article  Google Scholar 

  • D.M. Hoganson, H.I. Pryor II, E.K. Bassett, I.D. Spool, J.P. Vacanti, Lung assist device technology with physiologic blood flow developed on a tissue engineered scaffold platform. Lab on a Chip (2011). doi:10.1039/c0lc00158a

  • T.-K. Hung, H.S. Borovetz, M.H. Weissman, Transport and flow phenomena in a microchannel membrane oxygenator. Ann. Biomed. Eng. 5, 343–361 (1977)

    Article  Google Scholar 

  • S. Kawahito, T. Maeda, T. Motomura, T. Takano, K. Nonaka, J. Linneweber, M. Mikami, S. Ichikawa, M. Kawamura, J. Glueck, K. Sato, Y. Nosé, Development of a new hollow fiber silicone membrane oxygenator: in vitro study. Artif. Organs 25(6), 494–498 (2001)

    Article  Google Scholar 

  • T. Kniazeva, J.C. Hsiao, J.L. Charest, J.T. Borenstein, A microfluidic respiratory assist device with high gas permeance for artificial lung applications. Biomed. Microdevices (2010). doi:10.1007/s10544-010-9495-1

  • T. Kniazeva, A.A. Epshteyn, J.C. Hsiao, E.S. Kim, V.B. Kolachalama, J.L. Charest, J.T. Borenstein, Performance and scaling effects in a multilayer microfluidic extracorporeal lung oxygenation device. Lab Chip 12, 1686–1695 (2012)

    Article  Google Scholar 

  • J.K. Lee, H.H. Kung, L.F. Mockros, Microchannel technologies for artificial lungs: (1) theory. ASAIO Journal 54, 372–382 (2008a)

    Google Scholar 

  • J.K. Lee, M.C. Kung, H.H. Kung, L.F. Mockros, Microchannel technologies for artificial lungs: (3) open rectangular channels. ASAIO Journal 54, 390–395 (2008b)

    Article  Google Scholar 

  • G. Meschia, A. Hellegers, H. Prystowsky, W. Huckabee, J. Metcalfe, D.H. Barron, Oxygen dissociation curves of the bloods of adult and fetal sheep at high altitude. Exp. Physiol. 46, 156–160 (1961)

    Google Scholar 

  • M. Mochizuki, H. Tazawa, M. Tamura, Mathematical formulation of CO2 dissociation curve and buffer line of human blood at rest. Jpn J Physiol. 32(2), 231–44 (1982)

    Article  Google Scholar 

  • M. Mochizuki, H. Takiwaki, T. Kagawa, H. Tazawa, Derivation of theoretical equations of the CO2 dissociation curve and the carbamate fraction in the Haldane effect. Jpn J Physiol. 33(4), 579–99 (1983)

    Article  Google Scholar 

  • J.T. Ottesen, M.S. Olufsen, J.K. Larsen, Applied Mathematical Models in Human Physiology, 1st edn. (Society for Industrial Mathematics, Philidelphia, 2004), pp. 155–190

    Book  MATH  Google Scholar 

  • G.J. Peek, M. Mugford, R. Tiruvoipati, A. Wilson, E. Allen, M.M. Thalanany, C.L. Hibbert, A. Truesdale, F. Clemens, N. Cooper, Efficacy and economic assessment of conventional ventilatory support versus extracorporeal membrane oxygenation for severe adult respiratory failure (CESAR): a multicentre randomised controlled trial. Lancet 374, 1351–1363 (2009)

    Article  Google Scholar 

  • J.A. Potkay, M. Magnetta, A. Vinson, B. Cmolik, Bio-inspired, efficient, artificial lung employing air as the ventilating gas. Lab on a Chip 11(17), 2901–2909 (2011)

    Article  Google Scholar 

  • S.N. Vaslef, R.W. Anderson, R.J. Leonard, Use of a mathematical model to predict oxygen transfer rates in hollow fiber membrane oxygenators. ASAIO J. 40, 990–996 (1994)

    Google Scholar 

  • M.H. Weisman, T.-K. Hung, Numerical simulation of convective diffusion in blood flowing in a channel with a steady, three-dimensional velocity field. Am. Inst. Chem. Eng. J 17(1), 25–30 (1971)

    Article  Google Scholar 

  • M.H. Weissman, L.F. Mockros, Oxygen and carbon dioxide transfer membrane oxygenators. Med. Biol. Engng. 7, 169–184 (1969)

    Article  Google Scholar 

  • A. White, Principles of Biochemistry, 1st edn. (McGraw-Hill, 1978), pp. 960–962

  • World Health Organization (WHO), Chronic Respiratory Disease, (WHO Media Centre, 2011), http://www.who.int/mediacentre/factsheets/fs315/en/index.html. Accessed 13 Jan 2011.

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Acknowledgments

We thank Dr. Ronald Triolo for facilities used to complete this work. This work was supported by Department of Veterans Affairs Rehabilitation Research and Development (VA RR&D) Grant F7404-R and VA RR&D Grant C3819C, The Advanced Platform Technology Research Center of Excellence.

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Authors and Affiliations

  1. Advanced Platform Technology Center, VA Ann Arbor Healthcare System, Ann Arbor, MI, 48105, USA

    Joseph A. Potkay

  2. Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH, 44106, USA

    Joseph A. Potkay

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  1. Joseph A. Potkay
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Correspondence to Joseph A. Potkay.

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Potkay, J.A. A simple, closed-form, mathematical model for gas exchange in microchannel artificial lungs. Biomed Microdevices 15, 397–406 (2013). https://doi.org/10.1007/s10544-013-9736-1

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