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bronchisA.m
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bronchisA.m
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clear all
%load BT_2CM3CM4CMdTraq81.mat % Tubs matrix contiaing the branches leading to the lobe
load BT_model1_2.mat;
load xarxa.mat % matrix Xarxa
% To generate the bronchis at each bifrucation it is followed the same
% process.
% The direction of each bronchi is to follow the mass center of
% the irrigated volume.
% To distinguish terminal / already bifrucated / to be bifurcated branches
% the following totation for the natality column is used:
% Natality:
% - 0: terminal branch
% - 1: can bifrucate but has not done it yet
% - 2: has been bifurcated
% There is an exception for those branches with only one daughter, this are
% stored and removed from the set of branches that will bifrucate next.
% Each time a new branch emerges, the volume that it irrigates is saved in
% the fourth column of the matrix Xn with the integer of its row in Tubs.
index = find(Tubs(:,11) == 1); % Branches that have to be bifurcated
oneD = []; % Matrix of branches that have only one daughter
Xn = Xarxa(:,1:4);
Xn(:,4) = Xarxa(:,5); % First iteration computs first lobe bifurcation
M = 3; n = 3;
tic
count = 1; % to keep track of the number of iterations
while ~isempty(index) % while there are branches to be bifurcated
for k = 1:length(index)
j = index(k); % Is the row of the branch being bifurcated, but also
% it is the integer defining the volume that the branch irrigates
xf = Tubs(j,8:10); % final point
d0 = Tubs(j,3); % diameter
v = Tubs(j,8:10) - Tubs(j,5:7); v = v/norm(v); % mother vector
va = Tubs(j,12:14); % 'grandmother' vector
vs = cross(v,va); vs = vs/norm(vs); % separation vector
if count == 1
vol = Xn(:,4) == Tubs(j,end);
else
vol = Xn(:,4) == j; % logical indexes for the volume being irrigated
end
Xnn = Xn(vol,:); % reduced matrix to lower the dimensions of the
% calculations, thus the computational cost
% Find the two subvolumes
vS = repmat(vs,[sum(vol),1]);
class = dot([Xnn(:,1)-xf(1), Xnn(:,2)-xf(2), Xnn(:,3)-xf(3)]', vS');
% Make sure that both sub-volumes exist, if one of them is 0 it
% means that that part is already irrigated so there is only
% one duaghter branch. In that case the index of the mother branch
% is save so it does not bifurcate again, even if its natality is
% 1.
right = class > 0;
N1 = sum(right);
N2 = sum(~right);
if N1 == 0 || N2 == 0 % One volume is 0
diam = d0; % Diameter of the daughter = mother's diameter
long = d0*M; % Length of the daughter = mother's length
% Update the integer defining the volume
t = size(Tubs,1);
if N1 == 0
Xnn(~right,4) = t+1;
else
Xnn(right,4) = t+1;
end
% The direction changes:
cm = [0 0 0] + mean(Xn(Xn(:,4)==j,1:3));
dir = (cm-xf)/norm(cm-xf);
% Save the integers in the whole matrix
Xn(vol,4) = Xnn(:,4);
Tubs = [Tubs;
Tubs(j,1)+1 j diam long xf xf+dir*long 1 v acosd(dot(v,dir)) Tubs(j,16)];
% Natality of mother branch stays 1, however this branch has to
% be disntiguish from the non bifurcated yet, so the index j
% will be stored in this matrix of one-daughter branches:
oneD = [oneD j];
else
% The number asigned to the segment irrigated for each daughter branch
% will be the row of the branch in the matrix Tubs:
t = size(Tubs,1);
Xnn(right,4) = t+1;
Xnn(~right,4) = t+2;
% Save the integers in the whole matrix
Xn(vol,4) = Xnn(:,4);
% Diameters and lengths of the daughter branches
d1 = d0 * (N1/(N1+N2))^(1/3); l1 = M*d1;
d2 = d0 * (N2/(N1+N2))^(1/3); l2 = M*d2;
u = cross(v,vs);
[cos1,sin1,cos2,sin2] = Angle(t+1,t+2,Xnn,xf,n,u,v);
dir1 = v*cos1+vs*sin1; dir1 = dir1/norm(dir1); % direcction daugther 1
dir2 = v*cos2-vs*sin2; dir2 = dir2/norm(dir2); % direcction daugther 2
Tubs(j,11) = 2; % As j has bifuracted, its natality changes
% A bronchi is termial if the diameter is smaller than 0.5mm
if d1 > 0.5
nat1 = 1;
else
nat1 = 0;
end
if d2 > 0.5
nat2 = 1;
else
nat2 = 0;
end
Tubs = [Tubs;
Tubs(j,1)+1 j d1 l1 xf xf+dir1*l1 nat1 v acosd(dot(v,dir1)) Tubs(j,16);
Tubs(j,1)+1 j d2 l2 xf xf+dir2*l2 nat2 v acosd(dot(v,dir2)) Tubs(j,16)];
end
end
index = find(Tubs(:,11) == 1);
index(ismember(index,oneD)) = []; % Take out of the index list the branches that have only one daugther
count = count + 1;
end
toc
save('bronchis_model1_2.mat','Tubs','-mat')