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tumor-growth.R
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tumor-growth.R
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# {α1, α2, β1, β2} = {1.07, 1.31, 1.47, 6.51} / assuming cell size = 0.001 mm
set.seed(4)
intervals <- seq(1,20)
vol = function(t, k){ 128 / (1 + ((128/.001)^.25 - .001) * exp(-.25*k*t))^4}
generate_K <- function(α1, α2) {
#https://msalganik.wordpress.com/2017/01/21/making-sense-of-the-rlnorm-function-in-r/
m <- α1
s <- α2
location <- log(m^2 / sqrt(s^2 + m^2))
shape <- sqrt(log(1 + (s^2 / m^2)))
k_Values <- rlnorm(n=1, location, shape)
return(k_Values)
}
generate_tumor <- function(α1, α2, interval) {
k <- generate_K(α1, α2)
tumor_year <- sample(0:interval, 1, replace = FALSE)
tumor_time_upper <-30
while (TRUE) {
size <- vol(tumor_year, k)
if (size >= 5 | tumor_year >= tumor_time_upper)
break;
tumor_year <- tumor_year + 1
}
if (tumor_year >= tumor_time_upper){
generate_tumor(α1, α2, interval) #search for another tumor
}
else
return(size)
#return( c(tumor_year=tumor_year, size= size , vol(tumor_year+1, k), vol(tumor_year+2, k),vol(tumor_year+3, k), k=k))
#return( c(α1=α1, α2=α2,tumor_year=tumor_year, k=k))
}
pCA <- 0.02
gen_Ca <- function(age) { sample(c('Benign', 'CA'), size = 1, replace = TRUE, c(1 - pCA, pCA))}
apply_genTumor <- function(cancerStatus, interval, α1, α2) {
if (cancerStatus != 'CA')
return (NA)
else
return (generate_tumor(α1, α2,interval))
}
intervalApply <- function(interval, α1, α2, seed){
print(interval)
n <- 100000
set.seed(seed)
ages <-sample(40:70, n, replace = TRUE)
data = data.frame(ages)
data$BenignVsCA <- mapply(gen_Ca, ages)
data$Tumors<- mapply(apply_genTumor, interval=interval, α1 = α1 , α2 = α2, data$BenignVsCA)
m <- mean(data[data$BenignVsCA == "CA",]$Tumors)
sd <- sd(data[data$BenignVsCA == "CA",]$Tumors)
q99 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .99)
q95 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .95)
q90 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .90)
q85 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .85)
q80 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .80)
q75 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .75)
q50 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .50)
q25 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .25)
q10 <- quantile(data[data$BenignVsCA == "CA",]$Tumors, .10)
return(list(mean=m, sd=sd, q99=q99, q95=q95, q90=q90,q85=q85,q80=q80,q75=q75, q50=q50, q25=q25, q10=q10))
}
generateData <- function(α1, α2, title){
results <- mapply(intervalApply, intervals, α1 = α1 , α2 = α2, 5)
results <- sapply(results, function(x)unlist(x))
mean_volume <- results[c(TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE)]
sd_volume <- results[c(FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE)]
p99 <- results[c(FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE)]
p95 <- results[c(FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE)]
p90 <- results[c(FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE)]
p85 <- results[c(FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE)]
p80 <- results[c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE)]
p75 <- results[c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE)]
p50 <- results[c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE)]
p25 <- results[c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE)]
p10 <- results[c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE)]
png(filename=paste0("/Users/akshaygoel/Desktop/α1-", α1,"-α2-",α2,"-mean.png"), width = 4, height = 5, units = 'in', res = 150)
plot(p99, cex = 0.30, ylim=c(0,50), col = "white", main="tumor volume percentiles", xlab="MRI interval length (years)", ylab="mean tumor volume (mm diameter)")
grid()
lines(p99, lty = 1)
lines(p95, lty = 2)
lines(p90, lty = 3)
lines(p85, lty = 4)
lines(p80, lty = 5)
lines(p75, lty = 6)
lines(p50, lty = 7)
lines(p25, lty = 8)
# lines(p10, lty = 9)
mtext(paste0(title))
text(intervals[c(TRUE, TRUE)], p99[c(TRUE, TRUE)]+.5, paste(round(p99[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p95[c(TRUE, TRUE)]+.5, paste(round(p95[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p90[c(TRUE, TRUE)]+.5, paste(round(p90[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p85[c(TRUE, TRUE)]+.5, paste(round(p85[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p80[c(TRUE, TRUE)]+.5, paste(round(p80[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p75[c(TRUE, TRUE)]+.5, paste(round(p75[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p50[c(TRUE, TRUE)]+.5, paste(round(p50[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
text(intervals[c(TRUE, TRUE)], p25[c(TRUE, TRUE)]+.5, paste(round(p25[c(TRUE, TRUE)], digits = 1)), cex=0.40, font=4)
legend(16, 25, legend=c("99th %", "95th %", "90th %", "85th %", "80th %", "75th %", "50th %", "25th %"), lty=c(1:8), cex=0.45)
dev.off()
# png(filename=paste0("/Users/akshaygoel/Desktop/α1-", α1,"-α2-",α2,"-sd.png"),, width = 4, height = 5, units = 'in', res = 150)
# plot(sd_volume, ylim=c(0,50), xlim=c(0,20), cex = 0.30, main="σ of tumor volumes on detection", xlab="MRI interval length (years)", ylab="σ tumor volume (mm diameter)")
# mtext(paste0(title))
# text(intervals, sd_volume + 1.2, paste(round(sd_volume, digits = 1)), cex=0.30)
# dev.off()
return(list(mean_volume,sd_volume))
}
x <- seq(1,10)
plot(x)
grid()
dev.off()
generateTumorGraph <- function(α1, α2, title){
apply_gen = function(x){generate_tumor(α1, α2,1)}
sample <-seq(1, 1000)
r <- mapply(apply_gen, sample)
png(filename=paste0("/Users/akshaygoel/Desktop/tumors-visual-",α1,"-α2-",α2,".png"),, width = 8, height = 10, units = 'in', res = 300)
plot(r, main="individual tumor volumes", xlab="patient index", ylab="volume (mm diameter)")
mtext(paste0(title, " (300 patients, α1 ", α1, " α2 ", α2,")"))
dev.off()
}
all <- generateData(1.07, 1.31, "all patients")
young <- generateData(1.38, 1.36, "age group 50 to 59")
old <- generateData(0.70, 1.18, "age group 60 to 69")
young_vs_old_mean <- unlist(young[1])-unlist(old[1])
young_vs_old_sd <- unlist(young[2])-unlist(old[2])
png(filename=paste0("/Users/akshaygoel/Desktop/young-mean-vs-old-mean.png"), width = 4, height = 5, units = 'in', res = 150)
plot(young_vs_old_mean, main="difference in mean tumor volume", ylim=c(0,50), xlim=c(0,20), xlab="MRI interval of screening (years)", ylab="50-to-59 yrs - 60-to-69 yrs")
text(intervals, young_vs_old_mean + 1.2, paste(round(young_vs_old_mean, digits = 1)), cex=0.35)
dev.off()
png(filename=paste0("/Users/akshaygoel/Desktop/young-mean-vs-old-sd.png"), width = 4, height = 5, units = 'in', res = 150)
plot(young_vs_old_sd, main="difference in σ tumor volume", ylim=c(0,50), xlim=c(0,20), xlab="MRI interval of screening (years)", ylab="50 to 59 yrs - 60-to-69 yrs")
text(intervals, young_vs_old_sd + 1.2, paste(round(young_vs_old_sd, digits = 1)), cex=0.35)
dev.off()
generateTumorGraph(1.07, 1.31, "all patients")
generateTumorGraph(1.38, 1.36, "age group 50 to 59")
generateTumorGraph(0.70, 1.18, "age group 60 to 69")
results <- mapply(intervalApply, intervals, α1 = α1 , α2 = α2, seed = 3)
results <- sapply(results, function(x) unlist(x))
mean_volume <- results[c(TRUE, FALSE, FALSE, FALSE)]
sd_volume <- results[c(FALSE, TRUE, FALSE, FALSE)]
plot(sd_volume, ylim=c(0,50), main="σ of tumor volumes on MRI detection", xlab="MRI interval of screening (years)", ylab="sd tumor volume mm")
intervalApply3 <- function(interval, α1, α2){
n <- 1000
set.seed(4)
ages <-sample(40:70, n, replace = TRUE)
data = data.frame(ages)
data$BenignVsCA <- mapply(gen_Ca, ages)
data$Tumors<- mapply(apply_genTumor, interval=interval, data$BenignVsCA, α1, α2)
return(data[data$BenignVsCA == "CA",]$Tumors)
}
# For all age groups combined, model parameters were estimated as
# {α1, α2, β1, β2} = {1.07, 1.31, 1.47, 6.51}, while the two age
# groups 50 to 59 years and 60 to 69 years gave estimates of
# {1.38, 1.36, 1.50, 6.33} and {0.70, 1.18, 1.46, 6.65}, respectively.
#lapply(results, function(x) write.table( data.frame(x), 'test.csv' , append= T, sep=',' ))
write.table(
data$BenignVsCA,
na = "",
file = "tumorSizes.csv",
sep = ",",
col.names = NA,
qmethod = "double"
)
vol = function(t, k){ 128 / (1 + ((128/.001)^.25 - 1) * exp(-.25*k*t))^4}
volumes <-mapply(vol, t=3, k_Values)
mean(volumes)
plot(volumes, ylim=c(0,128))
mriDetect <- function(k, t_0, t_1){vol(3,k) < t_0 & vol(4,k) > t_1 }
filter <- mapply(mriDetect, k_Values, t_0 = 3, t_1 = 4)
plot(volumes[filter], ylim=c(0,128))
#check change in tumor after 1.7 years
ratio = function(k) {vol(2.7,k)/vol(1, k)}
ratio_Values <- mapply(ratio,k_Values)
mean(ratio_Values)
Vmax <- 128
cell <- .01
t <- 0
denominator <- (1 + ((Vmax/cell)^.25 - 1) * exp(-.25*k*t))^4
Vi_0 <- Vmax / denominator
Vi_0
t <- 1.7
denominator <- (1 + ((Vmax/cell)^.25 - 1) * exp(-.25*k*t))^4
Vi_1 <- Vmax / denominator
Vi_1
#Overall, the mean time taken to grow from 10 mm to 20 mm was estimated as 1.7 years
#curve(eq, from=0, to=1.5, xlab="time", ylab="growth")