
Twoeqns.mFrom MathBioTwoEquations.mThe following code was used to set up the system of differential equations for a bacteria at starting position x. fourplots.m was used to graph these equations. function dxdt = twoeqns(t,x) r = 2e3; %mm r1 = 12.5; %radius of aorta = 12.5mm. radius of capillaries = .004 mm r3 = 1e3; %mm = radius of bacteria m = 1e12; %g k = 2.2e7; %N/m % r2 = r1  yd; v_m = 4250; %mm/s maximum velocity. 4.25e3 mm/s http://www.rwc.uc.edu/koehler/biophys/3e.html d = 1e3; %g/mm^3 density of fluid (water) % r1 = 0.125 mm. Large radius (of Aorta). http://www.answers.com/topic/bloodvessel % r2 = Distance from center of tube radius % r3 = 1e1 mm. Radius of Bacteria. http://physics.bu.edu/~redner/211sp06/class01/MKS.html Cd = 0.48; %drag coefficient for a sphere c = v_m/(r1^2); %Constant representing  1/4n * deltaP/deltax %v = c*(r1^2  r2^2); %Finding the velocity based on Poiseuille's equation %Fd = 0.5*d*(v^2)*Cd*(pi*r3^2); dxdt = zeros(5,1); dxdt(1) = x(2); dxdt(2) = (0.5*d*((c*(r1^2  (r1  x(3))^2))^2)*Cd*(pi*r3^2) cos(atan2(x(3),x(1)))*k*sqrt(x(1)^2 + x(3)^2))/m; dxdt(3) = x(4); dxdt(4) = (sin(atan2(x(3),x(1))*k*sqrt(x(1)^2 + x(3)^2)))/m; dxdt(5) = (x(1)^2 + x(3)^2)^(1/2); end 