Mucus Distribution Model in a Lung with Cystic Fibrosis

Cystic fibrosis (CF) is the most common autosomal recessive disease in Caucasians with a reported incidence of 1 in every 3200 live births. Most strikingly, CF is associated with early mortality. Host in flammatory responses result in airway mucus plugging, airway wall edema, and eventual destruction of airway wall support structure. Despite aggressive treatment, the median age of survival is approximately 38 years. This work is the first attempt to parameterize the distributions of mucus in a CF lung as a function of time. By default, the model makes arbitrary choices at each stage of the construction process, whereby the simplest choice is made. The model is sophisticated enough to fit the average CF patients' spirometric data over time and to identify several interesting parameters: probability of colonization, mucus volume growth rate, and scarring rate. Extensions of the model appropriate for describing the dynamics of single patient MRI data are also discussed.

[1]  Federico Marchetti,et al.  Early antibiotic treatment of pseudomonas aeruginosa colonisation in cystic fibrosis: a critical review of the literature , 2004, European Journal of Clinical Pharmacology.

[2]  Ruy M Ribeiro,et al.  Hepatitis B virus kinetics and mathematical modeling. , 2004, Seminars in liver disease.

[3]  Douglas W. MacEwan,et al.  Roentgenologic Anatomy of the Lung. , 1979 .

[4]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[5]  Richard B Buxton,et al.  Quantitative MRI measurement of lung density must account for the change in T  2* with lung inflation , 2009, Journal of magnetic resonance imaging : JMRI.

[6]  A P Yoganathan,et al.  Dynamics of systolic pulmonary venous flow in mitral regurgitation: mathematical modeling of the pulmonary venous system and atrium. , 1995, Journal of the American Society of Echocardiography : official publication of the American Society of Echocardiography.

[7]  B Suki,et al.  Branching design of the bronchial tree based on a diameter-flow relationship. , 1997, Journal of applied physiology.

[8]  Maynard Thompson,et al.  Mathematical Modeling and Computer Simulation , 2005 .

[9]  J. Ardell,et al.  Vascular tree structure affects lung blood flow heterogeneity simulated in three dimensions. , 1997, Journal of applied physiology.

[10]  Avner Friedman,et al.  Mathematical framework for human SLE Nephritis: disease dynamics and urine biomarkers , 2010, Theoretical Biology and Medical Modelling.

[11]  Alissa M. Weaver,et al.  Mathematical modeling of cancer: the future of prognosis and treatment. , 2005, Clinica chimica acta; international journal of clinical chemistry.

[12]  J L Hankinson,et al.  Spirometric reference values from a sample of the general U.S. population. , 1999, American journal of respiratory and critical care medicine.

[13]  H. Fuchs,et al.  Effect of aerosolized recombinant human DNase on exacerbations of respiratory symptoms and on pulmonary function in patients with cystic fibrosis. The Pulmozyme Study Group. , 1994, The New England journal of medicine.