How to calculate and morph an iAUC argument into an argument that will run on multiple columns?

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I am looking for help in turning my code into a ‘loop’. I have code that can calculate iAUC for my x (time) and y (one participant). I have almost 40+ participants (all in separate columns) and am hoping to get some help turning this into a loop so I don’t have to do this individually for each participant column! Thanks in advance! This is my data:

 [Picture for formatting][1]
 
  t<- 0, 30, 37.5,45,60,90,120,150
 P01<- 4.631,4.764,6.784,9.799,7.452,6.673,6.584,7.25
 P02<- 5.23,7.965,10.67,12.3,12.53,12.83,11.14,8.478
 P04<- 5.84,5.661,7.57,7.615,8.868,8.734,8.6,8.003

 [Image of data][2]

I have the following code. It works for one single instance but get errors if I try the ncols function to try to move the ‘v’ argument from participant to participant in each column (keeping the ‘t’ time the same):

t<- data1$Time
v<- data1$`P01-C`
(AUC<-data.frame(t,v))

i_auc.fn <- sapply(TheR_Glucose_SherbrookeHIIT[-1], function(x,y) {
auc <- ifelse(y[2] > y[1], (y[2]-y[1])*(x[2]-x[1])/2, 0)
seg.type <- 0
for (i in 3:length(x)) {
if (y[i] >= y[1] & y[i-1] >= y[1]) { 
  auc[i-1] <- (((y[i]-y[1])/2) + (y[i-1]-y[1])/2) * (x[i]-x[i-1]) 
  seg.type[i-1] <- 1
} else if (y[i] >= y[1] & y[i-1] < y[1]) { 
  auc[i-1] <- ((y[i]-y[1])^2/(y[i]-y[i-1])) * (x[i]-x[i-1])/2 
  seg.type[i-1] <- 2 
} else if (y[i] < y[1] & y[i-1] >= y[1]) {  
  auc[i-1] <- ((y[i-1]-y[1])^2/(y[i-1]-y[i])) * (x[i]-x[i-1])/2
  seg.type[i-1] <- 3
} else if (y[i] < y[1] & y[i-1] < y[1]) { 
  auc[i-1] <- 0             
  seg.type[i-1] <- 4
  break
} else {
 
  return(cat("i:", i, "Error: No condition met\n"))
 }
 }
 return(list(auc=sum(auc), segments=auc, seg.type=seg.type))
}

Compute positive iAUC

iAUC <- i_auc.fn(AUC$t, AUC$v)
iAUC$auc

This returns:

> iAUC$auc
[1] 299.3887

Which works great for P01. But hoping to turn this into a loop!

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