A Generalized Mathematical Study of Two Phase Pulmonary Blood Flow in Lungs with Special Reference to Asthma

Abstract

In the present paper, we formulate the pulmonary blood flow in Lungs. Keeping in view the nature of pulmonary circulatory system in human body, the viscosity increases in the arterioles due to formation of roulex along axis by red blood cells, as we know the Lungs are remote from heart and proximate to the Asthma. P.N. Pandey and V. Upadhyay have considered the blood flow of two phased, one of which is that of red blood cells and other is Plasma. They have also applied the Herschel Bulkley non-Newtonian Model in bio-fluid mechanical set-up. We have collected a clinical data in case of Asthma for Hematocrit v/s Blood Pressure. The graphical presentation for particular parametric value is much closer to the clinical observation. The overall presentation is in tensorial form and solution technique adapted is analytical as well as numerical. The role of Hematocrit is explicit in the determination of blood pressure in case of pulmonary disease-Asthma. I. Introduction (Description of Bio-Physical Problem) Blood is a complex fluid consisting of particulate solids suspended in a non-Newtonian fluid . The particulate solids are red blood cells (RBCs), white blood cells (WBCs) and platelets. The fluid is plasma, which itself is a complex mixture of proteins and other intergradient in an aqueous base. 50% of the plasma and 45% of the blood cells and in 45% of the blood is RBCs and there is a few part of the other cells. Which are ignorable, so one phase of the blood is plasma and 2nd phase of the blood is RBCs. Two phase pulmonary blood flow is a study of measuring the blood pressure if the hemoglobin is known. The percentage of volume covered by blood cells in the whole blood is called hematocrit. This work will focus on two phase pulmonary blood flow in Lungs with special reference to Asthma. A lot of work is available, but P.N. Pandey and V. Upadhyay (5) discussed some phenomena in two phase blood flow gave an idea on the two phase pulmonary blood flow in Lungs with a pulmonary disease Asthma. The work of P.N. Pandey and V. Upadhyay is in whole circulatory system but our work will focus on pulmonary circulatory system, and pulmonary circulatory system which is a sub system of whole circulatory system. In this work, we apply the Herschel Bulkley non-Newtonian model. Here, pulmonary blood flow means blood flow in Lungs tissue. We present an improvement on the previous work in the field and this is discussed separately below. The ultimate use of this model is to predict normal reference levels of two phase blood flow in Lungs for individual patients undergoing to Asthma disease. Recent research estimates that the number of people diagnosed with Asthma will rise from 23.7 million to 44.1 million between 2009 and 2034. The Centers for Disease Control and Prevention (CDCP) further predict that up to one-third of U.S. adults could have Asthma by 2050 if Americans continue to gain weight and avoid exercise. According to recent estimates, approximately 285 million people worldwide (6.6%) in the 20-79 year age group have Asthma in 2010 and by 2030, 438 million people (7.8%) of the adults population, is expected to have Asthma. According to A.C. Guyton (11 ) the pulmonary circulation occurs due to blood pressure gradient, the high pressure of glomerular capillaries about 60 mm Hg causes rapid fluid filtration, whereas much lower hydrostatic pressure in the particular capillaries about 13 mm Hg permits rapid re-absorption. Pulmonary blood flow is not a linear function of the blood pressure gradient. The efferent Lungs are blood vessels that are part of the urinary tract of organisms. The efferent Lungs form from a convergence of the capillaries of the glomerular. They play an important role in maintaining the glomerular filtration rate despite fluctuations in blood pressure.