endpoints <- function(fit) {
# Calculate dissipation times DT50 and DT90 and, if necessary, formation
# fractions and SFORB eigenvalues from optimised parameters
# Additional DT50 values are calculated from the FOMC DT90 and k1 and k2 from HS and DFOP,
# as well as from Eigenvalues b1 and b2 of the SFORB model
ep <- list()
obs_vars <- fit$obs_vars
parms.all <- fit$bparms.ode
ep$distimes <- data.frame(DT50 = rep(NA, length(obs_vars)),
DT90 = rep(NA, length(obs_vars)),
row.names = obs_vars)
ep$ff <- vector()
ep$SFORB <- vector()
for (obs_var in obs_vars) {
type = names(fit$mkinmod$map[[obs_var]])[1]
# Get formation fractions if directly fitted, and calculate remaining fraction to sink
f_names = grep(paste("f", obs_var, sep = "_"), names(parms.all), value=TRUE)
f_values = parms.all[f_names]
f_to_sink = 1 - sum(f_values)
names(f_to_sink) = ifelse(type == "SFORB",
paste(obs_var, "free", "sink", sep = "_"),
paste(obs_var, "sink", sep = "_"))
for (f_name in f_names) {
ep$ff[[sub("f_", "", sub("_to_", "_", f_name))]] = f_values[[f_name]]
}
ep$ff = append(ep$ff, f_to_sink)
# Get the rest
if (type == "SFO") {
k_names = grep(paste("k", obs_var, sep="_"), names(parms.all), value=TRUE)
k_tot = sum(parms.all[k_names])
DT50 = log(2)/k_tot
DT90 = log(10)/k_tot
for (k_name in k_names)
{
ep$ff[[sub("k_", "", k_name)]] = parms.all[[k_name]] / k_tot
}
}
if (type == "FOMC") {
alpha = parms.all["alpha"]
beta = parms.all["beta"]
DT50 = beta * (2^(1/alpha) - 1)
DT90 = beta * (10^(1/alpha) - 1)
DT50_back = DT90 / (log(10)/log(2)) # Backcalculated DT50 as recommended in FOCUS 2011
ep$distimes[obs_var, c("DT50back")] = DT50_back
}
if (type == "DFOP") {
k1 = parms.all["k1"]
k2 = parms.all["k2"]
g = parms.all["g"]
f <- function(t, x) {
fraction <- g * exp( - k1 * t) + (1 - g) * exp( - k2 * t)
(fraction - (1 - x/100))^2
}
DTmax <- 1000
DT50.o <- optimize(f, c(0.001, DTmax), x=50)$minimum
DT50 = ifelse(DTmax - DT50.o < 0.1, NA, DT50.o)
DT90.o <- optimize(f, c(0.001, DTmax), x=90)$minimum
DT90 = ifelse(DTmax - DT90.o < 0.1, NA, DT90.o)
DT50_k1 = log(2)/k1
DT50_k2 = log(2)/k2
ep$distimes[obs_var, c("DT50_k1")] = DT50_k1
ep$distimes[obs_var, c("DT50_k2")] = DT50_k2
}
if (type == "HS") {
k1 = parms.all["k1"]
k2 = parms.all["k2"]
tb = parms.all["tb"]
DTx <- function(x) {
DTx.a <- (log(100/(100 - x)))/k1
DTx.b <- tb + (log(100/(100 - x)) - k1 * tb)/k2
if (DTx.a < tb) DTx <- DTx.a
else DTx <- DTx.b
return(DTx)
}
DT50 <- DTx(50)
DT90 <- DTx(90)
DT50_k1 = log(2)/k1
DT50_k2 = log(2)/k2
ep$distimes[obs_var, c("DT50_k1")] = DT50_k1
ep$distimes[obs_var, c("DT50_k2")] = DT50_k2
}
if (type == "SFORB") {
# FOCUS kinetics (2006), p. 60 f
k_out_names = grep(paste("k", obs_var, "free", sep="_"), names(parms.all), value=TRUE)
k_out_names = setdiff(k_out_names, paste("k", obs_var, "free", "bound", sep="_"))
k_1output = sum(parms.all[k_out_names])
k_12 = parms.all[paste("k", obs_var, "free", "bound", sep="_")]
k_21 = parms.all[paste("k", obs_var, "bound", "free", sep="_")]
sqrt_exp = sqrt(1/4 * (k_12 + k_21 + k_1output)^2 + k_12 * k_21 - (k_12 + k_1output) * k_21)
b1 = 0.5 * (k_12 + k_21 + k_1output) + sqrt_exp
b2 = 0.5 * (k_12 + k_21 + k_1output) - sqrt_exp
SFORB_fraction = function(t) {
((k_12 + k_21 - b1)/(b2 - b1)) * exp(-b1 * t) +
((k_12 + k_21 - b2)/(b1 - b2)) * exp(-b2 * t)
}
f_50 <- function(t) (SFORB_fraction(t) - 0.5)^2
max_DT <- 1000
DT50.o <- optimize(f_50, c(0.01, max_DT))$minimum
if (abs(DT50.o - max_DT) < 0.01) DT50 = NA else DT50 = DT50.o
f_90 <- function(t) (SFORB_fraction(t) - 0.1)^2
DT90.o <- optimize(f_90, c(0.01, max_DT))$minimum
if (abs(DT90.o - max_DT) < 0.01) DT90 = NA else DT90 = DT90.o
for (k_out_name in k_out_names)
{
ep$ff[[sub("k_", "", k_out_name)]] = parms.all[[k_out_name]] / k_1output
}
DT50_b1 = log(2)/b1
DT50_b2 = log(2)/b2
# Return the eigenvalues for comparison with DFOP rate constants
ep$SFORB[[paste(obs_var, "b1", sep="_")]] = b1
ep$SFORB[[paste(obs_var, "b2", sep="_")]] = b2
ep$distimes[obs_var, c(paste("DT50", obs_var, "b1", sep = "_"))] = DT50_b1
ep$distimes[obs_var, c(paste("DT50", obs_var, "b2", sep = "_"))] = DT50_b2
}
ep$distimes[obs_var, c("DT50", "DT90")] = c(DT50, DT90)
}
return(ep)
}
