Physiology¶

The standard human physiology is a set of SBML parameters of the top model: the covariates of the individual, the reference values of the sex of the build (ICRP 89), and everything which follows from them, the organ masses and volumes, the blood volume, the cardiac output, the blood flows and the GFR. An experiment changes the covariates (BW, HEIGHT) and the factors of organ function (f_renal_function, f_cardiac_function, the impairment severities) before the simulation, as it changes BW in the hand-written models, and the organs follow.

Topology¶

The circulation of Jones & Rowland-Yeo 2013 and PK-Sim (Kuepfer 2016): an arterial and a venous blood pool, the lung in series (its flow is the cardiac output), the other organs in parallel between the arterial and the venous pool. Stomach, small intestine, large intestine, spleen and pancreas drain into the portal vein, which feeds the liver together with the hepatic artery; the liver drains into the venous pool. The organs (pkpdsim.pbpk.Organ, their two-letter tokens are the prefixes of their ids) are lung lu, heart he, brain br, liver li, kidney ki, stomach st, small intestine si, large intestine la, spleen sp, pancreas pa, muscle mu, skin sk, adipose ad, bone bo and gonads go; the blood pools (Pool) are arterial ar, venous ve and portal po.

Every organ owns its blood flows: it reads the plasma (and blood cell) species of the pool which supplies it and writes into the pool it drains into, through its ports (see Standard organ). The pools have no reactions of their own besides the exchange with kinetic blood cells and the intravenous dose. The intestine variants replace small and large intestine with one submodel GU with the inflow of both.

Reference values¶

The organ masses, densities, blood contents and blood flows are those of the ICRP 89 reference individuals (Valentin 2002), taken directly from its tables; the interstitial fractions are those of Schmitt 2008 as tabulated by httk 2.7.4 (tissue.data, MIT), where they were read. The data file data/physiology_human.toml compares the male values with Jones & Rowland-Yeo 2013 in the notes of every value. The conventions of the data:

• mass is the mass of the organ without its blood (the blood is counted on its own); density is the specific gravity (1 kg/l where ICRP 89 states none); blood is the blood content of the organ as fraction of the blood volume.
• The organ volume of the model is the volume of its tissue and its blood, V<o> = M<o>/density + blood*Vblood; the vascular fraction is its blood, f_vas_<o> = blood*Vblood/V<o>, so that the vascular spaces of the organs and the pools are the blood volume for every individual.
• f_int is the interstitial fraction of the organ volume, the interstitial fraction of the tissue without blood of Schmitt 2008 (as tabulated by httk) times 1 - f_vas; the intracellular fraction is 1 - f_vas - f_int.
• flow is the blood flow as fraction of the cardiac output (ICRP 89 Table 2.40); the liver states its arterial flow (Qli is the hepatic artery, Qha), the portal organs feed it in addition. ICRP 89 gives about 8 % of the cardiac output to tissues which are no organ of the model ([unmapped] of the data): the flow fractions of the model, fQ<o>, are renormalised over the organs, so they sum to the cardiac output.
• The portal vein pool is the anatomical portal vein (Chau 2023, 4.4 ml); the splanchnic venous blood stays in the vascular volume of the portal organs. The blood of the unmapped tissues is part of the venous pool.
• Adipose closes the body weight: its mass is the remainder, Mad = BW - Mlean - Vblood*rho_blood; the ICRP adipose mass in the data is a reference value only.

Generated from data/physiology_human.toml by scripts/pbpk_tables.py; the notes of every number are in the data file.

The numbers of the reference individuals are public, so that a model which states a value of a hand-written model per kg of body weight or per litre of an organ converts it with them and copies none: reference_individual(Sex.MALE) has the body weight bw (73 kg), the height height (176 cm), the healthy GFR gfr (0.125 l/min, 0.109 l/min of a woman: GFR_base of the default individual, the GFR at renal function 1 which healthy_gfr of the build of the sex gives in ml/min; the GFR of a component a model keeps outside the library, the fluid model of hctz, reads it), the organ volumes with their blood volumes (V<o>, the liver 2.33 l), the tissue volumes without blood tissue_volumes, the volumes of the cells intracellular_volumes (V<o>*(1 - f_vas_<o> - f_int_<o>), the intracellular space Vic of the full form, the hepatocytes 1.3859 l) and the fluid volumes of the lumen segments lumen_volumes (Vlumen_<seg> by the tokens of ids.GUT_SEGMENTS, the same for both sexes), the values of the default individual of a male build (ICRP 89). A model writes no copy of these numbers (73.0, 2.33, 1.3859, 0.125) into its definition or its fit parameters, it imports them.

from pkpdsim.pbpk import Organ, Sex, reference_individual

man = reference_individual(Sex.MALE)
print(man.bw, man.height, round(man.volumes[Organ.LIVER], 3))
small = sum(man.lumen_volumes[seg] for seg in ("du", "jej1", "jej2", "ile1", "ile2"))
print(round(man.intracellular_volumes[Organ.LIVER], 4), round(small, 5))
print(man.gfr, round(reference_individual(Sex.FEMALE).gfr, 4))

73.0 176.0 2.33
1.3859 0.105
0.125 0.109

Male reference individual¶

Generated from data/physiology_human.toml by scripts/pbpk_tables.py; the notes of every number are in the data file.

Sources of the columns: mass, density, blood, f_vas, flow: ICRP89; f_int: httk.

Female reference individual¶

Generated from data/physiology_human.toml by scripts/pbpk_tables.py; the notes of every number are in the data file.

Sources of the columns: mass, density, blood, f_vas, flow: ICRP89; f_int: httk.

Blood and plasma¶

Every vascular space has plasma V_vas*(1 - HCT) and blood cells V_vas*HCT, and the blood flows carry plasma, Q*(1 - HCT)*C_p, and blood cells, Q*HCT*C_bc. The hematocrit is that of the sex (0.43 male, 0.38 female, ICRP 89), not the uncited 0.51 of some hand-written models. The blood concentration and the blood to plasma ratio are observers, never a conversion written by hand; how a substance enters the erythrocytes is its erythrocytes flag (see Substances).

HCT = HCT_ref * fimp_HCT
Vve = fVve * Vblood
Vve_pl = Vve * (1 - HCT)
Vve_bc = Vve * HCT

Scaling to the individual¶

The covariates are the body weight BW (kg), the height HEIGHT (cm) and the age AGE (yr, no rule reads it yet); their defaults are the reference individual of the sex of the population of the build. The chain follows Huisinga 2012: body mass index, body surface area (Du Bois 1916) and fat-free mass (Janmahasatian 2005); brain is constant, skin scales with the body surface area, the other lean organs and the blood with the fat-free mass less brain and skin (SV_tis, Huisinga 2012 eqs. 9, 10 and 12), adipose is the remainder of the body weight. The cardiac output scales as the tissues (eq. 13), the organ flows are fractions of it, and the GFR scales with the body surface area. This replaces the ftissue*BW/BW_ref scaling of the hand-written models.

BMI = BW / 1 kg / (HEIGHT / 100 cm)^2 * 1 kg_per_m2
BSA = 0.007184 m2 * (BW / 1 kg)^0.425 * (HEIGHT / 1 cm)^0.725
FFM = BW * 9270 / (6680 + 216 * BMI / 1 kg_per_m2)
SV_tis = (FFM - Mbr - Msk) / (FFM_ref - Mbr_ref - Msk_ref)

Mbr = Mbr_ref
Msk = Msk_ref * BSA / BSA_ref
M<o> = M<o>_ref * SV_tis
Vblood = Vblood_ref * SV_tis
Mad = BW - Mlean - Vblood * 1.06 kg_per_l
Vli = Mli / 1 kg_per_l + 0.1 * Vblood
f_vas_li = 0.1 * Vblood / Vli
f_int_lu = 0.2 * (1 - f_vas_lu)

CO_base = CO_ref * SV_tis * f_cardiac_function
CO = CO_base * fimp_CO
Qlu = CO
Q<o> = fQ<o> * CO_base * fimp_Q<o>
Qha = Qli
Qpo = Qst + Qsi + Qla + Qsp + Qpa
Qh = Qha + Qpo
GFR_base = GFR_ref * BSA / BSA_ref * fimp_GFR
GFR = GFR_base * f_renal_function

GFR_base is the GFR of the individual at renal function 1, with the body surface area and the other impairments: a model which needs the GFR of the kidney without chronic kidney disease (a PD model whose effect scales with the filtration relative to it, a measured clearance converted into a renal function) reads it, and it is defined at renal function 0, where the GFR is 0.

The factors fimp_<id> are those of the impairment, 1 for the healthy individual; f_cardiac_function and f_renal_function are the factors of organ function of the hand-written models, with the same ids. All of these are initial assignments on constant parameters: a covariate changed before the simulation (a change of an experiment) changes every organ, a change during the simulation does not, unless the definition names it in PBPKDefinition.dynamic. The kidney mass carries the CKD factor of the kidney volume (fimp_Mki, 1 until its source is read, see Impairment).

Populations¶

A population is the reference individual of each sex, which becomes the default individual of the model (BW, HEIGHT, AGE), and the distributions of the covariates, data for a later sampler of virtual individuals. The reference anatomy stays ICRP 89 for every population: the organs of another population's reference individual follow from the scaling at its body weight and height. The population is chosen when the model is built, PBPKDefinition(population="white_american_nhanes", sex=Sex.FEMALE, ...), the European reference individuals of ICRP 89 are the default.

Generated from data/populations/*.toml by scripts/pbpk_tables.py; the notes of every number are in the data file.

The NHANES populations are the adults of 20 to 49 years of the examinations 2013-2018 as preprocessed by httk (HTTK-Pop, Ring 2017), survey-weighted means and standard deviations; the East Asian population is the Asian Reference Man of Tanaka 1996 with the distributions of the Japanese of the same tables. PK-Sim also offers a Japanese population of national statistics of 2015; its primary data were not read, so the library has none. ICRP 89 gives reference values, not distributions: the European population has no covariate distributions.

The covariate distributions are data of the library and never SBML distrib uncertainties: run_simulation --uncertainty draws every parameter with a distrib uncertainty and must draw only the uncertainty of the fits.