Question

EXERCISE: Laser interstitial thermotherapy (LITT)is a minimally-invasive therapy procedure that uses heat to destroy or ablate tumor tissue. This heat is created by the absorption of near- infrared laser radiation emitted into the tumor site. The success of this treatment is dependent on the temperature distribution inside the target tissue area and the duration of treatment. Above 50 °C, the tissue exhibits coagulation, or the denaturation of proteins, and cell death within minutes, while at 60 °C, the tissue exhibits coagulation and cell death within seconds The amount of coagulation achieved during the laser irradiation process can be calculated using the Arrhenius equation, given by the following where Ea is the activation energy (J mol), A is the collision frequency (s), T(t) is the temperature as a function of time (°K), R is the universal gas constant (J mol °K), t is the time, ?(t) is the damage parameter as a function of time, Co is the concentration of non-coagulated tissue at time-0, and C is the concentration of non-coagulated tissue at time-t (Pearce and Thomsen 1995). Ea and A are constants. At the Biomedical Optics and Laser Laboratory, we are investigating the use of LITT as a minimally-invasive treatment for breast tumors. We use the Arrhenius equation and MATLAB to calculate the thermal damage, or coagulation, distribution within tissue both during and after laser irradiation as a function of the temperature and time. We use 15 thermocouples to measure the temperature throughout the tissue. These thermocouples record the temperature and send the information to a computer to be stored and analyzed. Problem: In this homework, you will create a MATLAB program that will calculate the amount of cell damage, or coagulation, as a function of the temperature distribution and time using the Arrhenius equation. This is given by the following 1-Ct/Co The constants required for the breast tissue are the following R-universal gas constant 8.32 J mol K Ea is the activation energy-5.09x 105 J mol1 As collision frequency-5.92 x 107

Answer 1

ANSWER

GIVEN BY

I comprise planned and developed the thermal blemish for the thermocouples by the Trapz Function.
I have built-in the observations for both part of the class and to end with further the output screenshot of the program.

Let me put in plain vocabulary you in a gradually manner:-

Step-1:

The original step is to accept the function with all the lone variables which position the limits of every one of the incorporation which are access for the mental picture purpose,

Step-2:

The next walk is to apply the numerical central of the trapezoid manner with the help of inveterate the unit spacing. The size of the size remains unmoved,

Step-3:

The concluding step is to reckon the integrates in the midst of the element dim which uses the specific length and apply the medium integrate (x,y,z) for every row.

Final Trapz Function;-

function trapz_ApprValue = trapz(f,I,m)

x=I(1):(I(2)-I(1))/(m-1):I(2);
for j=1:1:length(x)
y=subs(f,x);
end

trapz_ApprValue = trapz(x,y);
ezplot(f, [I(1), I(2)])
hold on
plot(x,y,'r')
for k=1:1:length(x)-1
rx = [x(k) x(k) x(k+1) x(k+1)];
ry = [y(k) 0 y(k+1) 0];
k = convhull(rx, ry);
fill (rx(k), ry(k), 'g','facealpha', 0.23);
end
stem(x,y,'r')