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################################ FUNCTIONS #####################################
#' @title The Carcass (growth of beef cattle) model
#' @description \strong{Model description.}
#'
#'
#'
#' The model is defined by 20 equations, with a total of 19 parameters for the described process.
#' @param protcmax : amounts of protein in the carcass of the adult animal (kg)
#' @param protncmax : amounts of protein in the 5th district of the adult animal (kg)
#' @param alphac : maximum protein synthesis rate in the frame (excluding basal metabolism) (j-1)
#' @param alphanc : maximum rate of protein synthesis in the 5th district (except basal metabolism) (j-1)
#' @param gammac : Maximum rate of protein degradation in the frame (excluding basal metabolism) (j-1)
#' @param gammanc : maximum rate of protein degradation in the 5th district (except basal metabolism) (j-1)
#' @param lip0 : maximum lipid concentration to the theoretical physiological age (percent)
#' @param lipc1 : increase coefficient of the maximum lipid concentration with the physiological age of the carcase (percent)
#' @param lipnc1 : increase coefficient of the highest lipid concentration with physiological age area in the 5th (percent)
#' @param beta : lipid synthesis rate (j-1)
#' @param delta : lipid degradation rate (d-1)
#' @param k : Parameter coefficient between the half-saturation of the Michaelis-Menten equation of the metabolic weight (MJ.kg^0.75)
#' @param b0c : coefficient of the allometric equation linking mass and lipid-protein carcass
#' @param b1c : exponent allometric equation linking mass and defatted protein carcass
#' @param b0nc : coefficient of the allometric equation linking mass and lipid-protein 5th district
#' @param b1nc : exponent allometric equation linking mass and lipid-protein 5th district
#' @param c0 : coefficient of the allometric equation between live weight and live weight empty
#' @param c1 : exponent allometric equation linking body weight and live weight empty
#' @param cem :
#' @param duration : duration of simulation
#' @return data.frame with ProtC,LipC,ProtNC,LipNC,PV
#' @export
carcass.model <- function(protcmax,protncmax,alphac,alphanc,gammac,gammanc,lip0,lipc1,lipnc1,beta,delta,k,b0c,b1c,b0nc,b1nc,c0,c1,cem,duration)
{
#Intialize variables
# 5 states variables, as 5 vectors initialized to NA
#ProtC : Proteins in carcass tissues
ProtC=rep(NA,1,duration)
#LipC : Lipids in carcass tissues
LipC=rep(NA,1,duration)
#ProtNC : Proteins in non-carcass tissues
ProtNC=rep(NA,1,duration)
#LipNC : Lipids in non-carcass tissues
LipNC=rep(NA,1,duration)
#PV : body weight
PV=rep(NA,1,duration)
# Initialization of state variables
ProtC[1]=30
LipC[1]=15
ProtNC[1]=15
LipNC[1]=8
# Simulation loop
for (t in 1:duration)
{
#calcul of body weight PV
MDC=b0c*ProtC[t]^b1c
PoidsC=LipC[t]+MDC
MDNC=b0nc*ProtNC[t]^b1nc
PoidsNC=LipNC[t]+MDNC
PVV=PoidsC+PoidsNC
PV[t]=c0*PVV^c1
EMI=cem*(0.0157*(PV[t]^0.9)+3.3161)
CPM=k*PV[t]^0.75
#Carcass tissues
#Proteins
#Synthesis
ProtCSyn=alphac*ProtC[t]*log(protcmax/ProtC[t])*(EMI/(CPM+EMI))
#Degradation
ProtCDeg=gammac*ProtC[t]*log(protcmax/ProtC[t])
#Lipids
LipCmax=(lip0+lipc1*(ProtC[t]/protcmax))*PoidsC
#Synthesis
LipCSyn=beta*LipC[t]*log(LipCmax/LipC[t])*(EMI/(CPM+EMI))
#Degradation
LipCDeg=delta*LipC[t]*log(LipCmax/LipC[t])
#Non-carcass tissues
#Proteins
#Synthesis
ProtNCSyn=alphanc*ProtNC[t]*log(protncmax/ProtNC[t])*(EMI/(CPM+EMI))
#Degradation
ProtNCDeg=gammanc*ProtNC[t]*log(protncmax/ProtNC[t])
#Lipids
LipNCmax=(lip0+lipnc1*(ProtNC[t]/protncmax))*PoidsNC
#Synthesis
LipNCSyn=beta*LipNC[t]*log(LipNCmax/LipNC[t])*(EMI/(CPM+EMI))
#Degradation
LipNCDeg=delta*LipNC[t]*log(LipNCmax/LipNC[t])
# Calculate rates of change of state variables (dPC,dLC,dPNC,dLNC)
dPC=ProtCSyn-ProtCDeg
dLC=LipCSyn-LipCDeg
dPNC=ProtNCSyn-ProtNCDeg
dLNC=LipNCSyn-LipNCDeg
# Uptade state variables
ProtC[t+1]=ProtC[t]+dPC
LipC[t+1]=LipC[t]+dLC
ProtNC[t+1]=ProtNC[t]+dPNC
LipNC[t+1]=LipNC[t]+dLNC
}
# End simulation loop
results=data.frame(time=c(1:duration),ProtC=ProtC[1:duration],LipC=LipC[1:duration],ProtNC=ProtNC[1:duration],LipNC=LipNC[1:duration],PV=PV[1:duration])
return(results)
}
# End of file
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