One possible method for delivering pharmaceutical compound i

One possible method for delivering pharmaceutical compound? is transdermal delivery. The drug is impregnated within a patch. microneedle array, or similar device, which is then placed on the skin. Over time, the drug diffuses across the skin, where it enters the systemic circulation. This works well for drugs that are both potent and lipophilic (they diffuse through the skin well): for example, in the treatment of hypertension, estrogen replacement, birth control, pain, or smoking cessation. The concentration of drug within the body over time can be represented by the following equation: C(t) = C_ge^(-) + P_sc SC_drug/V_apparent (e^-(Psc/- e^-kect/k_tx - P_sc/delta_device) Where C_0 is the initial concentration of the drug in the obdy, k_tc is the first order elimination rate constant, P_SC is the permeability of the drug in the outer layer of skin, S is the total surface area of the transdermal patch, C_drug0 is the starting concentration of drug within the patch, V_apparent is the volume that the drug diffuses into, and delta_device is the thickness of the patch. Write a program to calculate the concentration of an experimental drug delivered via transdermal patch over a period of 24 hours given the values below. To accomplish this, create a vector with values of time from 0 to 24 hours in increments of 10 minutes. Then, use this in the above equation.

Solution

Note :

I am conveerting P_sc = 10^{-4} cm/hr = 10^{-4} cm/60 min = 10^{-5}/6 cm/min

and C is in mg/ml (milligram per milli litre)

this is the code:

k=0.1;
p=10^(-5)/6;
s=2.5;
c=10;
v=15000;
C(1)=0;
r=0.14;

i=1
for t=0:10:1440
   C(i+1)=C(i)*exp(-k*t)+((p*s*c)/v)*((exp(-((p*t)/r))- exp(-k*t))/(k-(p/r)));
   i=i+1;
end

0   0   1.75576879313719e-08   2.63908849484674e-08   2.77019510177698e-08   2.77664097206169e-08   2.77644547286279e-08   2.77612072805087e-08   2.77579256629511e-08   2.77546316995936e-08   2.77513322770196e-08   2.77480306570697e-08   2.77447283152546e-08   2.77414258966189e-08   2.77381236762036e-08   2.77348217690808e-08   2.77315202226776e-08   2.77282190562975e-08   2.77249182777059e-08   2.77216178899853e-08   2.77183178943337e-08   2.77150182911970e-08   2.77117190807223e-08   2.77084202629389e-08   2.77051218378296e-08   2.77018238053593e-08   2.76985261654858e-08   2.76952289181639e-08   2.76919320633478e-08   2.76886356009908e-08   2.76853395310464e-08   2.76820438534679e-08   2.76787485682086e-08   2.76754536752218e-08   2.76721591744608e-08   2.76688650658790e-08   2.76655713494296e-08   2.76622780250659e-08   2.76589850927414e-08   2.76556925524092e-08   2.76524004040229e-08   2.76491086475356e-08   2.76458172829008e-08   2.76425263100717e-08   2.76392357290019e-08   2.76359455396445e-08   2.76326557419531e-08   2.76293663358809e-08   2.76260773213814e-08   2.76227886984079e-08   2.76195004669138e-08   2.76162126268526e-08   2.76129251781776e-08   2.76096381208423e-08   2.76063514548000e-08   2.76030651800042e-08   2.75997792964083e-08   2.75964938039657e-08   2.75932087026299e-08   2.75899239923543e-08   2.75866396730924e-08   2.75833557447976e-08   2.75800722074234e-08   2.75767890609232e-08   2.75735063052505e-08   2.75702239403588e-08   2.75669419662016e-08   2.75636603827323e-08   2.75603791899045e-08   2.75570983876716e-08   2.75538179759871e-08   2.75505379548047e-08   2.75472583240776e-08   2.75439790837596e-08   2.75407002338041e-08   2.75374217741647e-08   2.75341437047948e-08   2.75308660256480e-08   2.75275887366780e-08   2.75243118378381e-08   2.75210353290820e-08   2.75177592103633e-08   2.75144834816355e-08   2.75112081428522e-08   2.75079331939670e-08   2.75046586349334e-08   2.75013844657051e-08   2.74981106862356e-08   2.74948372964786e-08   2.74915642963877e-08   2.74882916859164e-08   2.74850194650184e-08   2.74817476336474e-08   2.74784761917569e-08   2.74752051393006e-08   2.74719344762321e-08   2.74686642025051e-08   2.74653943180732e-08   2.74621248228901e-08   2.74588557169094e-08   2.74555870000849e-08   2.74523186723701e-08   2.74490507337189e-08   2.74457831840848e-08   2.74425160234215e-08   2.74392492516828e-08   2.74359828688224e-08   2.74327168747939e-08   2.74294512695510e-08   2.74261860530476e-08   2.74229212252373e-08   2.74196567860738e-08   2.74163927355109e-08   2.74131290735023e-08   2.74098658000018e-08   2.74066029149631e-08   2.74033404183399e-08   2.74000783100861e-08   2.73968165901554e-08   2.73935552585016e-08   2.73902943150785e-08   2.73870337598398e-08   2.73837735927393e-08   2.73805138137309e-08   2.73772544227683e-08   2.73739954198053e-08   2.73707368047958e-08   2.73674785776935e-08   2.73642207384524e-08   2.73609632870261e-08   2.73577062233686e-08   2.73544495474337e-08   2.73511932591753e-08   2.73479373585471e-08   2.73446818455031e-08   2.73414267199971e-08   2.73381719819830e-08   2.73349176314146e-08   2.73316636682458e-08   2.73284100924306e-08   2.73251569039227e-08   2.73219041026762e-08   2.73186516886448e-08   2.73153996617826e-08   2.73121480220433e-08   2.73088967693810e-08

these are the 146 values:

Let me know if you have any trouble.