Use quiver () function to plot vector field (xy plane) of O2 flux in lab5.

What I have currently:

rt= 50; % in micrometers

mu= 3.75*10.^8; %in mPa

delta_p= 1000; %delta p mmHg/um

l= 200; %length of the vessel (0-200 um)

v= ((rt.^2)/4.*u).*delta_p.*(1-(r/rt).^2); %velocity of vessel

x=linspace(0,200,20); % x points for the meshgrid

y=linspace(-rt,rt,-200); %y point for the meshgrid

%graph selection

[X, Y]=meshgrid (x,y);

vrx=blood(Y,rt,mu,delta_p);

U=Vrx;

V=U;

V(:,:)=0;

%vrx=v;

figure (1)

quiver(X,Y,u,v);

%part b graphing

%velocity of blood function

function [Vrx]=blood(r,rt,mu,delta_p)

Vrx=((rt^2)./(4*mu))*delta_p*(1-r/rt.^2);

end

What I had for Lab 5:

function[j]=lab05(x0,y0)

syms x y;

%muscle cell radius (R) - um - 1*10^-6m

R=25*(10^(-6));

%diffusion coeff(D) - cm^2*s^-1 - (1*10^-2m)^2*s^-1

D=(10^(-5))*(10^(-4));

%oxygen concentration outside cell (co2)0 - mol O2*mL^-1

co2=2.22*(10^(-7));

%oxygen consumption rate (sigma)- mole*mL^-1*s^-1

sigma=1.65*10^-8;

%oxygen concentration equation(phi)

phi=((sigma*(R^2))/4*D)*((((x^2)+(y^2))/(R^2))-1)+co2;

rtest= (x0^2)+(y0^2);

if rtest < (R)^2

disp('Will Work')

else

rtest > (R)^2; disp('Wont Work')

end

gradphi=gradient(phi,[x,y]);

%diffusing oxygen flux equation(j)

j=-D*gradphi;

jr0=subs(j,{x,y},{x0,y0});

divergence(j,[x,y])-phi;

disp('Flux of diffusing oxygen:') end

Answer 1

[Simran]

Hello @Joy Odigbo,

To plot the vector field “O2 flux” using the MATLAB’s “quiver()” function, you can follow these steps:

1.) Create a meshgrid of x and y points within the region of interest. I took it as "within the muscle cell radius(R)", where R = 25

x = linspace(-R, R, 20); 
y = linspace(-R, R, 20); 
[X, Y] = meshgrid(x, y);micrometers. 

2.) Now, use your "lab05" function logic to calculate the oxygen flux at each grid point.

% Calculating oxygen flux 
D = (10^(-5)) * (10^(-4)); % Diffusion coefficient 
sigma = 1.65e-8; % Oxygen consumption rate 
co2 = 2.22e-7; % Oxygen concentration outside cell 
R = 25e-6; % Muscle cell radius 
% Oxygen concentration equation 
phi = ((sigma * (R^2)) / (4 * D)) * (((X.^2 + Y.^2) / R^2) - 1) + co2; 
% Calculating gradient 
[phi_x, phi_y] = gradient(phi, x, y); 
% Calculating flux 
Jx = -D * phi_x; 
Jy = -D * phi_y; 

3.) Now, use the "quiver()" function to plot the flux vectors on the grid.

figure; 
quiver(X, Y, Jx, Jy); 
xlabel('x (um)'); 
ylabel('y (um)'); 
title('Oxygen Flux Vector Field'); 
axis equal; 

Following these steps I got this figure:

You can refer to these documentations for more information:

"quiver" : https://www.mathworks.com/help/releases/R2021a/matlab/ref/quiver.html

"linspace": https://www.mathworks.com/help/releases/R2021a/matlab/ref/linspace.html

"meshgrid": https://www.mathworks.com/help/releases/R2021a/matlab/ref/meshgrid.html 

"gradient": https://www.mathworks.com/help/releases/R2021a/matlab/ref/gradient.html