pbpk organs¶

Organs, blood pools and the parts of an organ: the topology of the body.

PORTAL_ORGANS = frozenset(
    {
        Organ.STOMACH,
        Organ.SMALL_INTESTINE,
        Organ.LARGE_INTESTINE,
        Organ.SPLEEN,
        Organ.PANCREAS,
    }
)

SYSTEMIC_ORGANS = (
    frozenset(Organ)
    - PORTAL_ORGANS
    - {Organ.LUNG, Organ.LIVER}
)

inflow(organ)

outflow(organ)

as_member(enum, value, name)

as_organ_keys(mapping, name)

as_organs(organs, name)

The collapsing of the parts of a substance in an organ.

Parts(blood_cells, flow_carrier, tissue)

parts_for(substance, organ, chemistry)

The organ components: their interface and the standard organ.

An organ component builds the comp model definition of one organ and its boundary to the body. The standard organ (PK-Sim 4-compartment structure, Willmann 2005, Schmitt 2008) has the parts

plasma          V*f_vas*(1-HCT)    Cpl
blood cells     V*f_vas*HCT        Cbc   (kinetic erythrocytes)
interstitial    V*f_int            Cis   (full form)
intracellular   V*(1-f_vas-f_int)  Cic   (full form)
tissue          V*(1-f_vas)        Cti   (merged tissue)
organ           V                  Cor   (flow-limited)

of which only the parts a substance needs are built (parts_for). Every species is a concentration, every reaction an amount per time. The organ owns its inflow from the arterial pool (and the portal vein for the liver) and its outflow into the venous pool (the portal vein for the portal organs, the arterial pool for the lung); it reads every element of the body (volumes, flows, hematocrit, fractions, substance parameters, pool and sink species) through a port, and Boundary.replacements names the element of the body which replaces it. The Kp of a substance is the whole-tissue (interstitial + intracellular) to plasma coefficient in every form.

The liver has a portosystemic shunt, the fraction f_shunt of its arterial and portal inflow which flows past it into the venous pool, and a functional fraction f_functional of its tissue, which scales the tissue volumes and the capacity of its processes (both inputs of the top model, healthy 0 and 1). The kidney filters the unbound afferent (arterial) plasma concentration of a substance with urinary excretion into the urine, J_gfr = fu*GFR*Car*(1 - f_reabsorbed); the plasma leaving the kidney lacks the net filtrate at the outflow concentration, Qki*(1-HCT)*Cout - fu*GFR*(1 - f_reabsorbed)*Cout, so the filtration clearance of the arterial plasma is fu*GFR*(1 - f_reabsorbed) and a secretion clears the plasma flow less the filtrate. A saturable reabsorption (ThresholdReabsorption) replaces the constant fraction by the fraction 1/(1 + (fu*C/reab_threshold)^reab_n)^(1/reab_n) at the concentration of each term (Car in the filtration, Cout in the outflow). Its metabolism and transport (the tubular processes) run with the tubular capacity 1 - f_tubular + f_tubular*f_renal_function, which follows the renal function (the intact nephron hypothesis, f_tubular 1). The kidney exposes the urinary excretion rate Rurine_<s>, the sum of its fluxes into the urine, as an output.

The volumes of the parts, the coefficients and the exchanges depend on parameters only and are constants with initial assignments (they follow a change of the body before a simulation, not during it); only what reads a species is an assignment rule: the outflow concentrations and the unbound concentrations of the tissue parts Cu_<part>_<s> (observers).

The elements (inputs with their ports, compartments, species, rules, constants) are collected by pkpdsim.pbpk.organ_builder.OrganBuilder, which the variants reuse. The standard organ is one well-stirred zone; the zonated liver (pkpdsim.pbpk.variants.liver_zonated) builds the same parts, flows and exchanges in each of its zones, which the blood flows through in series.

OrganContext(
    organ,
    substances,
    parts,
    chemistry,
    inhibitions,
    inductions,
    sex,
    routes=(),
    top=dict(),
    slow_pools=(),
    steady=None,
)

Boundary(replacements, outputs)

name

build(ctx)

replaces

body_objects(definition)

StandardOrgan(name='standard')

build(ctx)

StandardBuilder(ctx, name)

build()

The elements of an organ component: the base of the standard organ and its variants.

An organ component builds a comp model definition whose elements of the body (volumes, flows, hematocrit, fractions, substance parameters, pool and sink species) are inputs with a port, which the body replaces (replacements), and whose outputs replace parameters of the top model (outputs). OrganBuilder collects the elements of one organ by id and creates each element once: the inputs, the compartments and species of the organ, the rules (for what reads a species), the initial assignments (for what depends on parameters only), the constants with their provenance, the reactions and the activity of the proteins of its processes. The standard organ and the variants derive from it and add their kinetics.

A protein of a process of the organ has the base activity f_<protein>, a constant of the organ (1, set by genotype and the experiments); in the liver the impairment multiplies it by the input fimp_<protein> (pkpdsim.pbpk.impairment). When a substance of the definition inactivates it (mechanism-based) or induces it, the organ has the turnover state E_<protein>, the amount of the protein relative to its baseline (initially 1),

dE/dt = kdeg*(1 + sum Emax*I/(EC50 + I)) - kdeg*E - sum kinact*I/(KI + I)*E

(Mayhew 2000, Almond 2009, Fahmi 2008), with the unbound concentration I of the inhibitor or inducer in the cell (intracellular, else the equivalent tissue part, else plasma) and the degradation rate kdeg_<protein> of the organ; the rates of the protein are multiplied by E_<protein>. The constants of the interactions (Ki, Kiu, kinact, Emax, EC50) are parameters of the body, read through a port.

ONE = '1 dimensionless'

CAPACITY = "Not a physical volume: the plasma-equivalent capacity of the blood of a substance with erythrocytes in equilibrium, the vascular volume times the blood to plasma ratio, so that the plasma concentration in it gives the amount in the blood."

COMPARTMENT_KINDS = {
    Part.PLASMA: "plasma",
    Part.BLOOD_CELLS: "blood_cells",
    Part.INTERSTITIAL: "interstitial",
    Part.INTRACELLULAR: "intracellular",
    Part.TISSUE: "tissue",
    Part.ORGAN: "organ",
}

OrganBuilder(ctx, name)

v

hct

f_vas

f_int

model_definition(notes)

stationary_ids(p)

label(organ)

The placement of the chemistry in the parts of the standard organ.

A process of the chemistry acts in one part of the organ: a metabolism in the part which holds the tissue of its substrate (intracellular in the full form, the merged tissue, the whole organ when flow-limited, the plasma without tissue), a transport across the membrane of the cell (basolateral between interstitium and cell, apical between cell and the sink of the organ: bile, urine or the intestinal lumen; the standard kidney has no uptake from the cumulative urine), a custom reaction in the part it names.

Every rate acts on the unbound concentration of its part and is an amount per time: the Vmax of a process is per litre of organ, so the whole organ has the capacity Vmax * V<o>; the clearance k of a first order process is per litre of organ as well (FirstOrder.per_volume, the default, 1/min), so the whole organ has k * V<o> as with a Vmax; with per_volume=False it is the clearance of the whole organ (l/min). The activity f_<protein> of its protein multiplies the rate (times the turnover state E_<protein> when a substance of the definition inactivates or induces the protein). The organ may give a factor of its capacity, which multiplies the rate of every metabolism and transport as well: the functional fraction f_functional of the liver, the share of the capacity in the functional tissue, and the tubular capacity of the kidney, which follows the renal function f_renal_function (the intact nephron hypothesis); a custom reaction states its rate itself and is not scaled.

The reversible inhibitors of the protein enter the rate of every process of the protein with their unbound concentration I in the compartment from which the process takes its substrate (the part of the substrate of a metabolism, the interstitium of a basolateral influx, the cell of an efflux, the sink of an apical influx): the inhibitor species of the same part, else of the equivalent tissue part, else plasma. With the competitive sum c = sum I/Ki (competitive, mixed with its competitive constant, noncompetitive, and mechanism-based inhibition with Ki = KI) and the uncompetitive sum u = sum I/Kiu (uncompetitive, mixed, noncompetitive), the rate laws of mutually exclusive inhibitors (Segel 1975) are

MM           Vmax*V*C / (Km*(1 + c) + C*(1 + u))
Hill         Vmax*V/(1 + u) * x^n / (1 + x^n),  x = C/(Km*(1 + c)/(1 + u))
first order  k*C / (1 + c), per volume k*V*C / (1 + c)

i.e. Vmax_app = Vmax/(1 + u) and Km_app = Km*(1 + c)/(1 + u); the first order rate is the limit C << Km, which an uncompetitive inhibitor does not change.

A zonated organ (pkpdsim.pbpk.variants.liver_zonated) places every metabolism and transport into the parts of each of its zones (zone), with the ids of the zone (Cti_z1_<s>, DRG2M_z1) and the share of the zone of the capacity of the organ (capacity); the apical sink is that of the organ.

A constant of a process given as RateOf is the initial assignment <p>_Vmax = <p>_Vmax_ratio * <other>_Vmax over local ids of the organ (OrganFormulaParameter). A metabolism whose product fractions are values or the remainder REST has them as the constants f_<p>_<s> of the organ: its reaction consumes the substrate, and one reaction per product forms the product with its fraction of the rate (<p>_to_<s>, rate f_<p>_<s> * <p>), so the products are formed by the fractions which a fit or an experiment sets; numbers which sum to 1 are the stoichiometry of the one reaction.

A variant with a lumen of its own on the apical side of the cell gives it (Apical): the nephron kidney (pkpdsim.pbpk.variants.kidney_nephron) places the apical transport between the cells of the kidney and the lumen of the proximal tubule, an efflux secretes into it, an influx reabsorbs from it (with the inhibitors of its protein in the lumen).

ONE = '1 dimensionless'

Sink(species, compartment, amount)

Apical(name, species)

Inhibitors(
    competitive=None, uncompetitive=None, modifiers=()
)

FormulaParameter(pid, formula, name, sbo, notes)

OrganFormulaParameter(
    pid, expression, reads, unit, name, sbo, notes
)

apical_sink(organ, s)

built_parts(parts)

metabolism_part(parts)

species_compartment(part, s, parts, zone=None)

start_formula(substance, coefficient=None)

species_start(sid, formula, name)

kp_id(substance, organ)

unbound(part, substance, organ, zone=None)

process_source(process, parts)

inhibitor_unbound(
    source, inhibitor, organ, parts, zone=None
)

has_turnover(protein, ctx)

inhibitor_terms(process, ctx, site)

inhibition_parameters(sid, inh)

formula_ids(expression)

formula_problems(where, expression, top)

formula_assignment(p)

value_parameter(pid, q, unit, name, sbo, text='')

place(
    process,
    ctx,
    parts,
    capacity=None,
    zone=None,
    apical=None,
)

rate_law(process, ctx, cu, capacity, inhibitors)

fractions_are_constants(process)

fraction_parameters(process, organ)

product_reaction(
    process,
    product,
    species,
    compartment,
    zone,
    organ,
    segment=None,
)

process_kind(process, organ)

with_modifiers(equation, modifiers)

stoichiometry(fraction, species)

in_zone(text, zone)

The coefficients of the distribution between plasma and tissue in the standard organ.

The Kp of a substance is the whole-tissue (interstitial + intracellular) to plasma coefficient in every form of the organ:

• full form: the interstitial to plasma coefficient follows from fu (Schmitt 2008), K_int_pls = (f_water_int + r_protein_int_pls*(1/fu - f_water_pls))*fu, and the intracellular one is derived so that both together have the Kp, K_cell_pls = (Kp*(f_int + f_cell) - f_int*K_int_pls)/f_cell. A Kp at or below the interstitial share f_int*K_int_pls/(f_int + f_cell) has no positive K_cell_pls: the build refuses it for the reference individual of its sex, and the rule floors K_cell_pls at K_CELL_FLOOR should a fit or another individual reach it (the interstitial share is the lower bound of a fitted Kp). The fu of chronic kidney disease raises the share at a fixed Kp: the build warns (KCellFloorWarning) when the share exceeds the Kp at the fu of a CKD stage (kp_floor_stages), where the floor holds;
• flow-limited organ: K_or = (Vpl + Vbc*Kbc + Vti*Kp)/V, the organ to plasma coefficient of the well-stirred organ.

The interstitial share f_int*K_int_pls/(1 - f_vas) of the reference individual of the sex of the build (interstitial_share) is the Kp of an extracellular substance, Kp(interstitial=...) scales it in every organ.

Every formula is written once as a template, which gives the SBML rule (with ids) and the number (with values) alike.

INTERSTITIAL = (
    "f_water_int",
    "f_water_pls",
    "r_protein_int_pls",
)

K_VAS = 'k_vas'

K_CELL_FLOOR = 1e-06

constants()

constant(key)

number(q)

k_int_pls(fu)

k_int_pls_value(fu)

interstitial_share(organ, fu, sex)

kp_of_organ(substance, organ, sex)

k_cell_pls(kp, k_int, f_vas, f_int)

k_cell_pls_value(kp, fu, f_vas, f_int)

k_organ(f_vas, vascular, kp)

kp_floor_stages(substance, organ, sex)

warn_kp_floor(substance, organ, sex)

kp_floor_notes(substance, organ, sex)

check_kp(substance, organ, sex)

The tissue to plasma coefficients of the Kp methods.

A Kp method computes the whole-tissue (interstitial + intracellular) to plasma coefficient of every organ when the model is built (KpMethod of a substance). The builder writes one Kp_<o>_<s> per organ, an initial assignment fKp_<s> * value with the factor fKp_<s> of the method, so that a fit scales every coefficient at once.

Rodgers & Rowland (Rodgers, Leahy & Rowland 2005 for moderate-to-strong bases, Rodgers & Rowland 2006 for acids, very weak bases, neutrals and zwitterions) predict the tissue to unbound plasma coefficient Kpu (Kp = Kpu * fu) in the form stated by Yau 2020 (eqs. 1 to 5), from the composition of data/tissue_composition.toml:

• moderate-to-strong bases (a basic pKa >= 7), electrostatic binding to the acidic phospholipids AP of the tissue (eq. 1), Kpu = X*f_iw/Y + f_ew + (P*f_nl + (0.3*P + 0.7)*f_np)/Y + Ka_AP*AP*(X - 1)/Y, with the affinity from the erythrocytes (eqs. 3, 5), Kpu_bc = (HCT - 1 + BP)/(fu*HCT), `Ka_AP = (Kpu_bc - X_bcf_iw_bc/Y - (Pf_nl_bc + (0.3*P + 0.7)*f_np_bc)/Y)
• Y/(AP_bc*(X_bc - 1))`;
• acids, very weak bases and zwitterions (albumin) and neutrals (lipoproteins), binding to the extracellular protein PR (eqs. 2, 4), Kpu = X*f_iw/Y + f_ew + (P*f_nl + (0.3*P + 0.7)*f_np)/Y + Ka_PR*[PR]_T, Ka_PR*[PR]_T = (1/fu - 1 - (P*f_nl_p + (0.3*P + 0.7)*f_np_p)/Y) * [PR]_T/[PR]_P;
• P is the octanol:water partition coefficient, the vegetable oil:water one log P_vo:w = 1.115*log P - 1.35 in the lipid terms of adipose; X and Y are the ionisation terms of intracellular water and plasma, 1 + 10^(pKa - pH) for a base, 1 + 10^(pH - pKa) for an acid, 1 for a neutral; a negative affinity is set to zero (Yau 2020, citing Rodgers & Rowland 2006).

Choices of the library (not verified against the 2005/2006 papers, which were not accessible): several pKa of an acid or a base give the ionisation of successive dissociation, 1 + 10^(pH - pKa1) + 10^(2*pH - pKa1 - pKa2) for an acid (pKa ascending) and 1 + 10^(pKa1 - pH) + 10^(pKa1 + pKa2 - 2*pH) for a base (pKa descending); a zwitterion (pka = (acidic, basic)) has 1 + 10^(pH - pKa_acid) + 10^(pKa_base - pH) and binds to the acidic phospholipids if its basic pKa is >= 7, to albumin otherwise.

The method applies the rat tissue composition to human tissues (Rodgers & Rowland 2007, Coutinho 2024; the acidic phospholipids and the erythrocytes of Utsey 2020); the inputs are the substance's reference fu (Binding.fu), its blood to plasma ratio (Erythrocytes.bp, or 1 - HCT + HCT*kbc) and the reference hematocrit of the sex. The coefficients are numbers of the build: a change of fu by an impairment (the binding factor of pkpdsim.pbpk.impairment) or of the hematocrit does not recompute them.

A limitation of the full form (Mode.PERMEABILITY): its interstitium binds the substance as K_int_pls of Schmitt 2008 (pkpdsim.pbpk.distribution), not as the albumin ratio of Rodgers & Rowland. For a highly bound, hydrophilic acid (e.g. fu 0.01, pKa 4, logP 1) the Kp of adipose (albumin ratio 0.049) lies below the interstitial share, the full form would need K_cell_pls <= 0 and the build refuses it (distribution.check_kp); such a substance uses the merged tissue or the perfusion-limited organ.

AP_PKA = 7.0

Composition(
    tissue,
    f_ew,
    f_iw,
    f_nl,
    f_np,
    albumin,
    lipoprotein,
    ap,
    sources=(),
)

composition(organ)

kp_sources(organ)

binds_phospholipids(method)

rodgers_rowland(
    substance, organ, fu, bp, hct, *, tissue=None
)

blood_to_plasma(substance, hct)

kp_values(substance, sex)

check_kp_method(substance)

The registry of the organ variants.

A variant is an OrganComponent registered under a name for an organ; a definition selects it by name (Variants(organs={Organ.LIVER: "zonated"})) or gives a component (ZonatedLiver(n_zones=4, profiles=...)). Every organ has the standard organ (standard); the liver has the zonated liver (zonated, 8 zones placed by volume); the kidney has the nephron kidney (nephron, filtration into the segments of the tubule); the intestine has the segmented intestine (segmented, the default) and the single lumen (single_lumen), which replace small and large intestine with one submodel GU.

DEFAULTS = {Organ.SMALL_INTESTINE: 'segmented'}

register(organ, name, component)

names(organ)

lookup(organ, name)

The zonated liver: the sinusoid from periportal to pericentral in zones.

ZonatedLiver builds the liver as n zones in series along the sinusoid, from the periportal zone z1 to the pericentral zone z<n>, the pattern of the sinusoidal unit of the zonation models of pkdb_models (misc/zonation): a chain of the same compartments, the chemistry placed into the cells of every zone. Its boundary is that of the standard liver (StandardOrgan): the same inputs (volumes, flows, HCT, fractions, substance parameters, pool and sink species) and the same outputs, the concentrations of the plasma (and the kinetic blood cells) leaving the liver Cout_<s>, so the hepatic and the arm vein observers are those of the standard liver.

Every zone has the parts of the standard liver which a substance needs (pkpdsim.pbpk.parts), with the share f_zone = 1/n of their volumes and of the passive exchanges of the liver and the coefficients of the liver (Kp, K_int_pls, K_cell_pls, K_or), so the zones together have the capacity and the exchange of the standard liver. The blood (plasma and kinetic blood cells) flows from the hepatic artery and the portal vein into the first zone, from each zone into the next (J_sin_<zone>_<part>_<s>) and from the last one into the venous pool; the portosystemic shunt f_shunt bypasses all zones and the functional fraction f_functional scales the tissue of every zone and the capacity of every process, as in the standard liver. The species, compartments, unbound concentrations (observers), exchanges and processes of a zone carry the zone in their ids: Cpl_z1_<s>, Vti_z1, Cu_ti_z1_<s>, J_ti_z1_<s>, DRG2M_z1.

Every metabolism and transport of the liver is placed into every zone (pkpdsim.pbpk.placement.place), with the share w_<zone> of the capacity of the liver: by volume f_zone, or by the profile of its protein (profiles, the relative abundance p_<key>_<zone> per zone, e.g. a pericentral CYP3A4), w = p*V_zone/sum(p*V_zone) = p/sum(p), so that the total capacity Vmax*V (k of a first order process) is that of the standard liver. A metabolism with a profile takes the profile of that name, any other process the profile of its protein, if there is one. The inhibitors act inline in every zone with their unbound concentration in the zone; the bile is the sink of all zones. A protein which a substance inactivates or induces has one turnover state E_<protein> for the liver (as the intestine), driven by the unbound concentration in the cells of the zones weighted by the placement of the protein: exact for the same concentration in every zone, the mean of the zones along a gradient. A custom reaction states its rate for the whole liver and is not split over the zones: the zonated liver refuses it.

The zones are well-stirred tanks in series. With one zone the zonated liver is the standard liver. With n zones and linear kinetics the availability of a flow-limited liver at steady state is (1 + x/n)^-n with x = fu*CLint/(Q*BP) instead of the well-stirred 1/(1 + x): with the same intrinsic clearance the zonated liver extracts more, the difference of the extraction is about x/2*(1 - 1/n) of it (second order in x), and for large n it approaches the parallel tube, exp(-x).

ZonatedLiver(n_zones=8, profiles=dict(), name='zonated')

build(ctx)

ZonatedBuilder(ctx, liver)

The nephron kidney: glomerular filtration into the tubule and its segments.

NephronKidney builds the kidney with the tubule of the nephron. The unbound afferent (arterial) plasma concentration is filtered into the lumen of the proximal tubule, fu*GFR*Car, and the tubular fluid flows through the lumens of the segments in series, proximal tubule pt, loop of Henle lh, distal tubule dt and collecting duct cd; the collecting duct drains into the urine Aurine_<s>. Every segment reabsorbs water: the flow leaving a segment is the fraction f_tub_<seg> of the GFR (Scotcher 2016), so the tubular flows follow the GFR of the individual and the renal function. The drug moves with the fluid, GFR*f_tub_<seg>*Ctub_<seg>_<s> out of a segment, and concentrates as the water is reabsorbed (the filtrate has no proteins, the lumen concentration is unbound).

The lumens are well-stirred compartments of constant volume (Vtub_<seg>, Huang 2018, both kidneys). They are lumen, not tissue: they are not carved out of the kidney volume, the blood and the tissue of the kidney keep the volumes of the standard kidney and the tubule adds its fluid (about 0.12 l) to the kidney.

Without secretion and reabsorption every filtered molecule reaches the urine: at steady state the flow out of every segment equals the flow into it, so the urinary excretion is the filtration fu*GFR*Car of the standard kidney, whatever the volumes and the flows of the segments; the tubule delays the excretion by minutes. The glomerulus filters the afferent (arterial) plasma and the plasma leaving the kidney lacks the net filtrate, as in the standard kidney: at steady state the reabsorption from the collecting duct returns the fraction reabsorbed, so the circulation sees the standard kidney.

The fraction reabsorbed of a filtered substance (f_reabsorbed_<s> of Excretion.fraction_reabsorbed) is an empirical passive reabsorption at the end of the collecting duct: that fraction of the drug leaving it returns into the plasma of the kidney (J_reab_<s>), the rest is urine, so the renal clearance without transport is fu*GFR*(1 - f_reabsorbed) as in the standard kidney. With secretion the fraction acts on the secreted drug as well, the lumped (fu*GFR + CL_sec)*(1 - F_reabs) of the literature. A threshold reabsorption (Excretion.reabsorption, ThresholdReabsorption) returns the fraction of the standard kidney at the afferent plasma of the flow out of the collecting duct, up to the filtered load: min(GFR*f_tub_cd*Ctub_cd, fu*GFR*Car)*f(Car) with f(Car) = 1/(1 + (fu*|Car|/reab_threshold)^reab_n)^(1/reab_n) (Car_<s> a modifier). It never exceeds the filtration, also with a secretion into the tubule (the secreted drug leaves into the urine), and at steady state without a secretion the circulation sees the standard kidney. A reabsorption by a transporter is an apical influx instead.

The chemistry of the kidney is placed by membrane: a metabolism in the cells of the kidney and a basolateral transport between interstitium and cells as in the standard kidney; an apical transport between the cells and the lumen of the proximal tubule, an efflux secretes into it, an influx reabsorbs from it on the lumen concentration (the inhibitors of its protein act from the lumen of the proximal tubule). A custom reaction states its rate for a part of the standard kidney: the nephron kidney refuses it. Every metabolism and transport runs with the tubular capacity of the standard kidney, 1 - f_tubular + f_tubular*f_renal_function. A substance has the species of the tubule when it is filtered, transported apically in the kidney or inhibits the protein of an apical influx of the kidney.

The blood side (perfusion, tissue distribution, blood cells, the unbound observers, the outflow concentrations Cout_<s>) is the code of the standard kidney (StandardBuilder), and the boundary is that of the standard kidney: the same inputs replaced by the same elements of the body and the same outputs. A substance which is secreted but not filtered reads the GFR in addition, for the flow of the tubule.

NephronKidney(name='nephron')

build(ctx)

NephronBuilder(ctx, name)

The intestine variants: the segmented intestine and the single lumen.

Both replace small and large intestine with one submodel (GU, the id of the small intestine for every intestine variant, ids.submodel) with the boundary of the standard organs on the blood side: the arterial inflow of both organs, Qgu = Qsi + Qla, drains into the portal vein. The output Cout_si_<s> is the plasma leaving the wall; the venous blood of the mucosa enters the portal vein directly. Their parts:

• the intestinal wall, the standard organ (StandardBuilder) of the volume Vgu = Vsi + Vla with the volume-weighted vascular and interstitial fractions, the distribution of the small intestine (its Kp) and the share of ftissue of its tissue volume;
• the lumen segments: stomach, duodenum, upper and lower jejunum, upper and lower ileum, caecum, colon ascendens, transversum, descendens, sigmoid and rectum (segmented, Thelen 2011), or one lumen, the fluid of the small intestine (single_lumen); a substance which reaches the lumen (oral route, biliary excretion, transport into the lumen) has the dissolved concentration Clumen_<seg>_<s> per segment, which moves on with the transit V*C/T_<seg> and from the last segment into the feces Afeces_<s>; an oral tablet has the undissolved amount Asolid_<seg>_<s> (in the first segment the dose state PODOSE_<s>), which dissolves with the dissolution of its formulation (pkpdsim.pbpk.routes) and moves with the transit too; the bile drains into the duodenum (the single lumen); the fed state FED = 1 slows the gastric emptying (the stomach transit time of the fed state);
• the absorption: ka_<s> (1/hr) is the absorption rate constant of the small intestine, a segment absorbs with ka_<s> * f_area_<seg> (the mucosal surface per lumen volume relative to the small intestine; the stomach does not absorb), a segment of the large intestine optionally times f_ka_colon_<s> (SegmentedIntestine.f_ka_colon, a substance with an oral route), a segment of the regional absorption profile of a substance times f_ka_<seg>_<s> (RegionalAbsorption); the single lumen absorbs with ka_<s>; of the absorbed flux the fraction fabs_<s> enters the body and the rest the feces (the single lumen for every substance, the segments with SegmentedIntestine.fabs for a substance with an oral route);
• the mucosa (enterocytes) per intestinal segment, Cmu_<seg>_<s>, only for a substance with chemistry of the intestine (substrate, product, transported substance, inhibitor or inducer of a protein of a process of the small intestine): flow-limited with the mucosa to plasma coefficient K_mu_<s> (the Kp of the small intestine, 1 without), perfused by arterial blood with its flow Qmu_<seg> = f_mucosa_flow * Q<region> * share (the mucosa fraction of the blood flow of its region, small or large intestine, times the transit share of the segment in the region; the wall gets the rest) and draining into the portal vein; the absorbed drug enters it; its volume Vmu_<seg> is carved out of the tissue of the wall of that substance (V<part>_wall), so wall and mucosa together have the capacity of the wall of a substance without mucosa; the unbound concentration Cu_mu_<seg>_<s> is an observer. Without such chemistry the substance has no mucosa species and is absorbed into the plasma of the wall.

The chemistry of the small intestine is placed into the mucosa segments by the relative expression of its protein (CYP3A4 of the data) times the mucosa volume, the sum kept: the Vmax of a process stays per litre of small intestine (Vmax * Vsi for the whole intestine, as in the standard organ), a segment has the weight w_<protein>_<seg>; a protein without expression data (or a process without protein) is placed by mucosa volume over the segments of the small intestine, the organ of the process. Apical efflux moves the drug from the mucosa into the lumen of the segment, apical influx back. A protein which a substance inactivates or induces has one turnover state E_<protein> for the intestine, driven by the unbound mucosa concentration weighted by the placement weights of the protein.

The bile of every substance drains: of a substance with lumen species into the duodenum (the single lumen), of any other into the feces.

A conversion in the lumen (LumenConversion, the segmented intestine) converts a dissolved substance into another in chosen segments, first order with kconv_<s>_<m> (1/hr); the product gets lumen species.

PerSubstance = Q | Mapping[str, Q]

SegmentedIntestine(
    name="segmented",
    ka=None,
    fabs=None,
    f_ka_colon=None,
    regional=None,
    conversions=(),
)

replaces

absorption(definition)

body_objects(definition)

build(ctx)

SingleLumen(
    name="single_lumen",
    ka=None,
    fabs=None,
    regional=None,
    conversions=(),
)

replaces

absorption(definition)

body_objects(definition)

build(ctx)

absorbed_substances(definition, ka)

The options of the lumen of the segmented intestine: regional absorption and conversions.

RegionalAbsorption is the regional absorption profile of a substance, a factor of the absorption ka_<s>*f_area_<seg> per segment or per group of segments (colon, caecum to rectum, the parameter f_ka_colon_<s>, of which SegmentedIntestine.f_ka_colon is the shorthand); LumenConversion converts a substance into another in chosen lumen segments, first order. Both are options of pkpdsim.pbpk.variants.intestine.SegmentedIntestine; the builders of the intestine (gut, gut_lumen) read them here.

ABSORBING = tuple(
    t for t in ids.GUT_SEGMENTS if t != "st"
)

LARGE = tuple(t for t in ABSORBING if t not in SMALL)

COLON = 'colon'

GROUPS = {COLON: LARGE}

RegionalAbsorption(factors)

segments

covers(tokens)

LumenConversion(substrate, product, k, segments)