########## NAME
alcoholmodel
########## METADATA
time_unit = m
########## MACROS
########## STATES
d/dt(Vol_Stomach) = + vol_drink_per_time*10 - r2            // dL
d/dt(Kcal_Liquid) = + vol_drink_per_time*kcal_liquid_per_vol - rKcal_clearance         // kcal [ L * kcal/L = kcal]

d/dt(max_Kcal_Solid) = 0
d/dt(Kcal_Solid)     = r_Kcal_Solid

d/dt(EtOH_Pool) = + r_poolIn*Vol_Stomach - r_poolOut                    //mg

d/dt(Conc_EtOH_Stomach) = r_drinkEtOH  - r_poolIn + r_poolOut/Vol_Stomach // mg/dL
d/dt(Mass_EtOH_Intestines) = + r2*Conc_EtOH_Stomach - r3  - r4          // mg

d/dt(Blood_Conc) =  + (r3/V_Blood) - r5*(V_Liver/V_Blood)               //mg/dL 

d/dt(Plasma_acetate) = + r5 - r6                  //mg/dL  

d/dt(PEth)       = rPEth - rPEth_bound + rPEth_release - rPEth_clearance 
d/dt(PEth_Bound) = rPEth_bound - rPEth_release

d/dt(Kcal_remain) = + vol_drink_per_time*kcal_liquid_per_vol - r2*kcal_liquid_per_vol/10          // kcal [ L * kcal/L = kcal]

d/dt(time_elapsed) = 1

Vol_Stomach(0)          = 0.001
Kcal_Liquid(0)          = 0
max_Kcal_Solid(0)       = 0
Kcal_Solid(0)           = 0
EtOH_Pool(0)            = 0
Conc_EtOH_Stomach(0)    = 0
Mass_EtOH_Intestines(0) = 0
Blood_Conc(0)           = 0
Plasma_acetate(0)       = 0
PEth(0)                 = 0
PEth_Bound(0)           = 0
Kcal_remain(0)          = 0
time_elapsed(0)         = 0

########## PARAMETERS
kPEth            = 14824.3201129844
kPEth_out        = 155.700230807449
kPEth_bind       = 16899.8070912636
kPEth_release    = 0.00567465407687899
k_poolIn         = 8.51709430245296
k_poolOut        = 0.346199847345036
Vmax             = 2018.19466075863
km               = 16336.3631792709
k_kcal           = 154.363454312840
k3               = 84.3794789018948
k4               = 852.816905367382
k6               = 0.127255213814248
VmaxADH          = 0.935326859734748
VmaxCYP2E1       = 0.177371543132190
KmADH            = 8.97358830896085  
KmCYP2E1         = 40.9840079864542  
k_Kcal_clearance = 0.00570193833670537

########## VARIABLES
SS_vol = 0.001

V_Liver = 15
V_Blood = ((1-sex)*(0.3561 * height^3 + 0.03308 * weight + 0.1833) + sex*(0.3669 * height^3 + 0.03219 * weight + 0.6041))*10 // dL     Nadler's Equation for total blood volume

conc_drink = (EtOH_conc*789.1) //mg/dL

vADH    = (VmaxADH*Blood_Conc/( KmADH + Blood_Conc))           
vCYP2E1 = (VmaxCYP2E1*Blood_Conc/( KmCYP2E1 + Blood_Conc))  

kcal_solid_vol = max(1,Kcal_Solid)/(4*100) // 4kcal/g assumes 1g/ml, 100 scales ml--> dL 

// Model reactions
r2 = Vmax*( (Vol_Stomach-SS_vol)/((Vol_Stomach-SS_vol) + km) ) * exp( - max(0, Kcal_Liquid)/k_kcal )

r_Kcal_Solid = (max_Kcal_Solid * -1.88 * 0.010* (0.010*max(0, time_elapsed))^0.86  * exp(-(0.010*max(0, time_elapsed))^1.86))    // doi: 10.1016/S0002-9270(00)00868-6

r_poolIn  = gt(Kcal_Solid, 1e-3) * max(0, (Conc_EtOH_Stomach - EtOH_Pool/kcal_solid_vol) * k_poolIn)
r_poolOut =  gt(Kcal_Solid, 1e-3) * EtOH_Pool * k_poolOut

r_drinkEtOH     = (conc_drink - Conc_EtOH_Stomach)*(vol_drink_per_time*10/Vol_Stomach)
rKcal_clearance = Kcal_Liquid*k_Kcal_clearance

r3 = Mass_EtOH_Intestines*k3 
r4 = Mass_EtOH_Intestines*k4

r5  = vADH + vCYP2E1

r6 = Plasma_acetate*k6

rPEth           = kPEth*Blood_Conc
rPEth_clearance = kPEth_out*PEth
rPEth_bound     = kPEth_bind*PEth
rPEth_release = max(0, kPEth_release*( PEth_Bound - PEth ))

########## FUNCTIONS

########## EVENTS
new_drink = gt(vol_drink_per_time,0), Kcal_Liquid, Kcal_remain, Kcal_remain, 0
new_meal  = gt(kcal_solid,0), max_Kcal_Solid, kcal_solid+Kcal_Solid, Kcal_Solid, kcal_solid+Kcal_Solid, time_elapsed, 0 

########## OUTPUTS

########## INPUTS
EtOH_conc           = EtOH_conc           @ 0
vol_drink_per_time  = vol_drink_per_time  @ 0
kcal_liquid_per_vol = kcal_liquid_per_vol @ 0
kcal_solid          = kcal_solid          @ 0
drink_length        = drink_length        @ 0

sex                 = sex                 @ 1       // male=1 , female=0
weight              = weight              @ 104     // Kg
height              = height              @ 1.85    // m

########## FEATURES

Blood alcohol concentration = Blood_Conc    [mg/dL]
Acetate in plasma = Plasma_acetate/10.2     [mM]
Breath alcohol concentration (g/210L) = 0.840*(Blood_Conc/1000) + 0.00367 [g/210L]
Blood BrAC concentration (g/dL) = Blood_Conc/1000 [g/dL]

Gastric volume = Vol_Stomach*100 [mL]
PEth = PEth [ng/mL]