Pharmacokinetics and dosing models, epidemic models, diagnostic test statistics, survival analysis, biomechanics, neuron models and medical-imaging physics (quantitative only, no clinical advice).
Biomedical Science (biomedical-science-ai999x) is an offline Python package for biomedical science. It covers pharmacokinetics and dosing models, epidemic models, diagnostic test statistics, survival analysis, biomechanics, neuron models and medical-imaging physics (quantitative only, no clinical advice).
It has 86 capabilities — 86 computational procedures — in 9 topics, the largest being Pharmacokinetic models, Medical-imaging physics, Biomechanics, Neuron models, Epidemic models and Survival analysis. Ask a question in words with ask(), or call a capability by name with typed inputs with solve(). Every answer carries its value and unit, the steps that produced it and the formula in LaTeX.
When a question is not determined — a value is missing, an input is out of range, or the request is outside the package — it says so and names what it needs, instead of guessing. It runs on an ordinary CPU without a network connection (Python >=3.10), and the same question always gets the same answer.
pip install biomedical-science-ai999x hf download AI999X/biomedical-science-ai999x --local-dir biomedical-science-ai999x
Each question below was put to biomedical-science-ai999x and the answer shown is the one it returned, with the steps it took.
IV bolus concentration: D = 500 mg, V = 40 L, k = 0.1 1/h, t = 6 h
D = 500 mg, V = 40 L, k = 0.1 1/h, t = 6 hC = 0.006860145451 kg/m^3, fraction_remaining = 0.5488116361 kg/m^3SIR final size: R0 = 2.5, s0 = 0.99, i0 = 0.01
R0 = 2.5, s0 = 0.99, i0 = 0.01s_inf = 0.1058941943, attack = 0.8841058057Kaplan-Meier survival: times = [2, 3, 3, 5, 8, 9, 12, 15], events = [1, 0, 1, 1, 0, 1, 1, 0], t = 6
times = [2, 3, 3, 5, 8, 9, 12, 15], events = [1, 0, 1, 1, 0, 1, 1, 0], t = 6S_t = 0.6, median = 9GHK voltage: T = 310 K, PK = 1, PNa = 0.04, PCl = 0.45, K_o = 4 mmol/L, K_i = 140 mmol/L, Na_o = 145 mmol/L, Na_i = 12 mmol/L, Cl_o = 116 mmol/L, Cl_i = 4 mmol/L
T = 310 K, PK = 1, PNa = 0.04, PCl = 0.45, K_o = 4 mmol/L, K_i = 140 mmol/L, Na_o = 145 mmol/L, Na_i = 12 mmol/L, Cl_o = 116 mmol/L, Cl_i = 4 mmol/LV_m = -0.07506627615 Vm.solve("bmed_odds_ratio_ci", a=20, b=80, c=10, d=90, level=0.95) a = 20, b = 80, c = 10, d = 90, level = 0.95OR = 2.25, lower = 0.9942948923, upper = 5.091547829Body mass index: m = 70 kg, h = 1.75 m
m = 70 kg, h = 1.75 mBMI = 22.85714286, BMI_prime = 0.9142857143Cohen's kappa: counts = [[40, 10], [5, 45]]
counts = [40 10; 5 45]kappa = 0.7, p_observed = 0.85Gaussian PSF MTF: fwhm = 0.5 mm, f = 1 1/mm
fwhm = 0.5 mm, f = 1 1/mmMTF = 0.4106858004, f50 = 882.5424006 1/mEvery snippet was run as shown; the output under it is what it printed.
import biomedical_science_ai999x as m
a = m.ask("IV bolus concentration: D = 500 mg, V = 40 L, k = 0.1 1/h, t = 6 h")
print(a.outcome)
print(a.values)
for step in a.steps:
print(step["name"])SOLVED
{'C': 0.00686014545118, 'fraction_remaining': 0.548811636094}
One-compartment IV bolus: concentration at a time (a model calculation, not medical advice)
import biomedical_science_ai999x as m
a = m.solve("bmed_odds_ratio_ci", a=20, b=80, c=10, d=90, level=0.95)
print(a.outcome)
print(a.values)SOLVED
{'OR': 2.25, 'lower': 0.994294892282, 'upper': 5.09154782882}
import biomedical_science_ai999x as m
# an input is missing: the answer says what it needs instead of guessing
a = m.solve("bmed_odds_ratio_ci")
print(a.outcome)
print(a.message)NEEDS_INPUT
bmed_odds_ratio_ci needs a, b, c, d, level (exposed with the outcome; exposed without the outcome; unexposed with the outcome; unexposed without the outcome; confidence level (95% or 0.95)). Example: solve('bmed_odds_ratio_ci', a=20, b=80, c=10, d=90, level=0.95).
biomedical-science-ai999x "IV bolus concentration: D = 500 mg, V = 40 L, k = 0.1 1/h, t = 6 h"
C = 0.00686015 kg/m^3, fraction_remaining = 0.548812 1. One-compartment IV bolus: concentration at a time (a model calculation, not medical advice): C(t) = (D/V) exp(-k t) with D = 500 mg, V = 40 L, k = 0.1 1/h, t = 6 h -> C = 0.00686015 kg/m^3, fraction_remaining = 0.548812 Assumptions: one compartment, instantaneous mixing; first-order elimination; t >= 0 …
Every value in these figures was computed by the package, each point a run of solve(); in a notebook, plot() and plot_relation() draw a capability's curves the same way.
12 of its 86 formulas; every one is in the capability browser below.
Search by name, formula, input or topic. Each capability opens to show what it takes, what it returns, when it applies, and a question it answered.
bmed_bmrThe basal metabolic rate estimated by the Mifflin-St Jeor (1990) or the revised Harris-Benedict (Roza and Shizgal 1984) regression from mass, height, age and sex, in kcal/day, W and MJ/day; a model calculation, not dietary or medical advice.
m body mass [kg]h height [m]age age in years (adults)sex sex (the equations have a male and a female form) choiceequation regression: mifflin_st_jeor or harris_benedict_revised choiceBMR_kcal_day basal metabolic rate in kcal/dayBMR_W basal metabolic rate (W) [W]BMR_MJ_day basal metabolic rate in MJ/daybmed_bmiThe body mass index BMI = m/h^2 (kg/m^2) and BMI prime (BMI/25) as a calculation from mass and height; no category or health advice is given.
m body mass [kg]h height [m]BMI body mass index in kg/m^2BMI_prime BMI/25bmed_indicator_dilution_cardiac_outputThe cardiac output (volume flow) from the mass of an injected indicator and its sampled first-pass concentration curve, by the Stewart-Hamilton principle with a trapezoidal area.
m mass of indicator injected [kg]t sampling times in s, strictly increasing vectorC indicator concentrations in mg/L (first pass, recirculation excluded) vectorAUC area under the concentration curve, mg*s/LCO cardiac output m / AUC [m^3/s]bmed_kelvin_voigt_creepThe strain of a Kelvin-Voigt (spring parallel to dashpot) tissue model a time t after a constant stress is applied.
sigma applied constant stress [Pa]E spring modulus [Pa]eta dashpot viscosity (Pa*s) [Pa*s]t time since loading [s]strain strain at time tbmed_poiseuille_vessel_flowLaminar (Hagen-Poiseuille) flow of a Newtonian fluid through a rigid vessel: volume flow rate, mean velocity, wall shear stress and hydraulic resistance from the pressure drop, radius, length and viscosity.
dP pressure drop along the vessel [Pa]r vessel radius [m]L vessel length [m]mu viscosity of the blood (Newtonian) [Pa*s]Q volume flow rate [m^3/s]v_mean mean velocity [m/s]tau_wall wall shear stress [Pa]R_hyd hydraulic resistance [Pa*s/m^3]bmed_respiratory_mechanics_fitAirway resistance, respiratory compliance and the end-expiratory pressure of the single-compartment equation of motion P = R Q + V/C + P0, fitted by least squares to sampled pressure, flow and volume.
P airway pressures in cmH2O vectorQ flows in L/s at the same instants vectorV volumes above end-expiration in L at the same instants vectorR resistance, cmH2O*s/LC compliance, L/cmH2OP0 pressure at zero flow and volume, cmH2Obmed_sls_creepThe creep strain of a standard linear solid (a spring E_inf parallel to a Maxwell arm E1-eta) a time t after a constant stress is applied, and the final strain.
sigma applied constant stress [Pa]E_inf equilibrium (parallel) spring modulus [Pa]E1 spring modulus of the Maxwell arm [Pa]eta dashpot viscosity of the Maxwell arm [Pa*s]t time since loading [s]strain strain at time tstrain_inf final strain sigma/E_infbmed_sls_stress_relaxationThe stress of a standard linear solid a time t after a step strain eps0 is imposed, and the relaxed (equilibrium) stress.
eps0 imposed step strain (a pure number, e.g. 0.05)E_inf equilibrium spring modulus [Pa]E1 spring modulus of the Maxwell arm [Pa]eta dashpot viscosity of the Maxwell arm [Pa*s]t time since the strain step [s]stress stress at time t [Pa]stress_inf relaxed stress E_inf eps0 [Pa]bmed_elbow_lever_muscle_forceFor a horizontal forearm held in static equilibrium, the elbow-flexor muscle force and the joint reaction force from the hand load, the forearm weight, their distances from the elbow and the muscle's insertion distance and angle.
W load held in the hand (weight) [N]d_load distance of the load from the elbow [m]W_arm weight of the forearm and hand [N]d_arm distance of the forearm's centre of mass from the elbow [m]d_muscle distance of the muscle insertion from the elbow [m]theta angle between the muscle and the forearm [rad]F_muscle muscle force [N]R_x joint reaction along the forearm (towards the hand positive) [N]R_y joint reaction, upward positive [N]R magnitude of the joint reaction [N]bmed_windkessel_diastolic_decayThe arterial pressure of a two-element Windkessel model during diastole (no inflow), decaying from P0 towards the venous pressure with time constant RC.
P0 pressure at the start of diastole [Pa]Pv venous (outflow) pressure [Pa]R peripheral resistance [Pa*s/m^3]C arterial compliance [m^3/Pa]t time into diastole [s]P arterial pressure at time t [Pa]bmed_windkessel_input_impedanceThe modulus and phase of the input impedance of a two-element (R, C) or three-element (Zc, R, C) Windkessel model of the arterial tree at a stated frequency.
model Windkessel model choiceR peripheral resistance [Pa*s/m^3]C arterial compliance [m^3/Pa]f frequency [Hz]Zc characteristic impedance of the aorta (three-element model only) [Pa*s/m^3] optionalZ_mod impedance modulus [Pa*s/m^3]phase_deg impedance phase in degreesbmed_cohens_kappaCohen's kappa (chance-corrected agreement) and the observed agreement of two raters or two diagnostic tests classifying the same subjects, from their k x k agreement table.
counts agreement table: rows = categories given by rater A, columns = categories given by rater B matrixkappa Cohen's kappap_observed observed proportion of agreementbmed_dx_youden_cutoffThe score threshold that maximises the Youden index J = sensitivity + specificity - 1 over all observed cut-offs, with the sensitivity and specificity there.
scores_pos scores of the diseased subjects vectorscores_neg scores of the non-diseased subjects vectorthreshold optimal cut-off (score >= threshold is test-positive)sensitivity sensitivity at the cut-offspecificity specificity at the cut-offJ Youden index at the cut-offbmed_dx_roc_aucThe area under the ROC curve of a continuous diagnostic score from the scores of diseased and non-diseased subjects: the probability that a diseased subject scores higher (ties count one half), with the Mann-Whitney U.
scores_pos scores of the diseased (condition-positive) subjects vectorscores_neg scores of the non-diseased subjects vectorAUC area under the ROC curveU Mann-Whitney U of the diseased groupbmed_dx_threshold_sensitivity_specificityThe confusion-matrix counts, sensitivity and specificity of a continuous diagnostic score when scores at or above a threshold are called positive.
scores_pos scores of the diseased subjects vectorscores_neg scores of the non-diseased subjects vectorthreshold cut-off: a score >= threshold is test-positivesensitivity TP/(TP + FN)specificity TN/(TN + FP)TP true positivesFN false negativesTN true negativesFP false positivesbmed_dx_sensitivity_specificity_ciSensitivity and specificity of a diagnostic test from its 2x2 counts, each with a Wilson score confidence interval at the stated level.
TP true positives integerFN false negatives integerTN true negatives integerFP false positives integerlevel confidence level (95% or 0.95)sensitivity TP/(TP + FN)sens_lower lower Wilson limitsens_upper upper Wilson limitspecificity TN/(TN + FP)spec_lower lower Wilson limitspec_upper upper Wilson limitbmed_epi_reed_frost_final_sizeThe probability distribution of the number of susceptibles eventually infected in a Reed-Frost chain-binomial epidemic in a small closed group, its mean and the chance of no spread.
n initial number of susceptibles (1 to 30) integerm initial number of infectives (1 to 30) integerp probability that one infective infects one given susceptible in a generation (0 < p < 1)mean_final expected number of susceptibles infectedP_no_spread probability that no susceptible is infecteddistribution probabilities of 0, 1, ..., n susceptibles infectedbmed_epi_r_from_growth_rateThe reproduction number implied by an observed exponential growth rate when the generation interval follows a gamma distribution of stated mean and standard deviation (Wallinga-Lipsitch).
r exponential growth rate (negative for a decline) [1/s]Tg_mean mean generation interval [s]Tg_sd standard deviation of the generation interval [s]R reproduction numberbmed_epi_seir_final_sizeThe final susceptible fraction and the attack fraction of an SEIR epidemic (the latent stage does not change the final size) from R0 and the initial susceptible, exposed and infectious fractions.
R0 basic reproduction number beta/gammas0 initial susceptible fractione0 initial exposed (latent) fractioni0 initial infectious fractions_inf susceptible fraction at the endattack fraction infected during the epidemic, s0 - s_infbmed_epi_seir_growth_rateThe early exponential growth (or decline) rate of an SEIR epidemic in a fully susceptible population, from R0, the rate of leaving the latent stage and the recovery rate.
R0 basic reproduction number beta/gammasigma rate of leaving the latent stage (1/latent period) [1/s]gamma recovery rate (1/infectious period) [1/s]r initial growth rate (negative when R0 < 1) [1/s]bmed_epi_seir_peakThe largest infectious fraction of an SEIR epidemic and the time at which it occurs, from the transmission, incubation and recovery rates and the initial fractions.
beta transmission rate [1/s]sigma rate of leaving the latent stage (1/latent period) [1/s]gamma recovery rate [1/s]s0 initial susceptible fractione0 initial exposed (latent) fractioni0 initial infectious fractiont_peak time of the peak of the infectious fraction [s]i_max peak infectious fractions_at_peak susceptible fraction at the peake_at_peak exposed fraction at the peakbmed_epi_sir_final_sizeThe fraction still susceptible when an SIR epidemic ends and the fraction infected during it, from R0 and the initial susceptible and infected fractions (the final-size relation).
R0 basic reproduction number beta/gammas0 initial susceptible fractioni0 initial infected fraction (> 0)s_inf susceptible fraction at the endattack fraction infected during the epidemic, s0 - s_infbmed_epi_sir_peakThe largest infected fraction of an SIR epidemic and the time at which it occurs, from the transmission and recovery rates and the initial fractions.
beta transmission rate [1/s]gamma recovery rate [1/s]s0 initial susceptible fractioni0 initial infected fraction (> 0)i_max peak infected fractiont_peak time of the peak [s]bmed_epi_sis_prevalenceThe infected fraction of an SIS model (no immunity after recovery) at time t and the endemic equilibrium it approaches.
beta transmission rate [1/s]gamma recovery rate [1/s]i0 initial infected fractiont time [s]i infected fraction at time ti_star endemic infected fraction (0 when beta <= gamma)bmed_nnt_ciThe absolute risk reduction (control risk minus treated risk) of a two-arm trial with its Wald confidence interval, and the number needed to treat with the interval obtained by inverting it.
events_t events in the treated group integern_t size of the treated group integerevents_c events in the control group integern_c size of the control group integerlevel confidence level (95% or 0.95)ARR absolute risk reductionARR_lower lower limitARR_upper upper limitNNT number needed to treat 1/ARRNNT_lower 1/ARR_upperNNT_upper 1/ARR_lowerbmed_incidence_rate_ratio_ciThe ratio of the incidence rates (events per person-time) of two groups with the log-scale Wald confidence interval at the stated level.
events1 events in group 1 integertime1 person-time of group 1 (the same unit for both groups)events2 events in group 2 (reference) integertime2 person-time of group 2level confidence level (95% or 0.95)IRR incidence rate ratio group 1 / group 2lower lower limitupper upper limitbmed_mantel_haenszel_odds_ratioThe Mantel-Haenszel odds ratio pooled over strata of 2x2 tables (adjusting for a confounder), with the Robins-Breslow-Greenland confidence interval at the stated level.
tables one row [a, b, c, d] per stratum: exposed cases, exposed non-cases, unexposed cases, unexposed non-cases matrixlevel confidence level (95% or 0.95)OR_MH Mantel-Haenszel pooled odds ratiolower lower limitupper upper limitbmed_odds_ratio_ciThe odds ratio of an exposure-outcome 2x2 table (case-control or cohort) with the Woolf logit confidence interval at the stated level.
a exposed with the outcome integerb exposed without the outcome integerc unexposed with the outcome integerd unexposed without the outcome integerlevel confidence level (95% or 0.95)OR odds ratio ad/(bc)lower lower confidence limitupper upper confidence limitbmed_relative_risk_ciThe risk ratio of exposed to unexposed in a cohort 2x2 table with the log-scale (Katz) confidence interval at the stated level.
a exposed with the outcome integerb exposed without the outcome integerc unexposed with the outcome integerd unexposed without the outcome integerlevel confidence level (95% or 0.95)RR risk ratio [a/(a + b)]/[c/(c + d)]lower lower confidence limitupper upper confidence limitbmed_smr_exact_ciThe standardized mortality or incidence ratio observed/expected with the exact (Garwood) Poisson confidence interval at the stated level.
observed observed number of deaths or cases (0 to 1000) integerexpected expected number from reference rateslevel confidence level (95% or 0.95)SMR observed / expectedlower lower exact limitupper upper exact limitbmed_hounsfield_unitsThe CT number HU = 1000 (mu - mu_water)/(mu_water - mu_air) of a material from its linear attenuation coefficient and those of water and air (air 0 by default, then 1000 (mu - mu_water)/mu_water).
mu linear attenuation coefficient of the material [1/m]mu_water linear attenuation coefficient of water [1/m]mu_air linear attenuation coefficient of air (default 0) [1/m] optionalHU CT number in Hounsfield unitsmu_rel mu/mu_waterbmed_mri_adc_fitThe apparent diffusion coefficient and the b = 0 signal from diffusion-weighted signals at two or more b-values, by a least-squares fit of ln S against b (mono-exponential decay).
b b-values in s/mm^2 vectorS signals at those b-values (any one unit) vectorADC apparent diffusion coefficient, mm^2/sS0 fitted signal at b = 0 (unit of S)bmed_gaussian_psf_mtfThe modulation transfer function at a spatial frequency of an imaging system with a Gaussian point-spread function of stated FWHM, and the frequency at which the MTF falls to 50 %.
fwhm full width at half maximum of the point-spread function [m]f spatial frequency (cycles per length) [1/m]MTF modulation transfer at ff50 spatial frequency where the MTF is 0.5 [1/m]bmed_larmor_frequencyThe Larmor frequency f = (gamma/2 pi) B of nuclear spins in a field B: protons by default (42.577478461 MHz/T, CODATA 2022), or another nucleus with its stated gamma/2 pi in MHz/T.
B magnetic flux density (T) [T]gamma_bar reduced gyromagnetic ratio gamma/2 pi in MHz/T (default: the proton) optionalf Larmor frequency [Hz]f_MHz Larmor frequency in MHzomega angular Larmor frequency [rad/s]bmed_mri_ernst_angleThe Ernst angle alpha_E = arccos(exp(-TR/T1)) that maximises the steady-state signal of a spoiled gradient-echo sequence, and that largest signal as a fraction of M0 (T2* decay excluded).
TR repetition time [s]T1 longitudinal relaxation time [s]alpha Ernst angle [rad]alpha_deg Ernst angle in degreesS_rel signal at the Ernst angle, fraction of M0 (no T2* decay)bmed_mri_inversion_recoveryThe longitudinal magnetisation (fraction of M0, signed) at inversion time TI in a repeated inversion-recovery sequence with repetition time TR, and the inversion time that nulls the tissue.
T1 longitudinal relaxation time [s]TR repetition time [s]TI inversion time [s]Mz_ratio Mz/M0 at TI (negative before the null)TI_null inversion time of zero signal [s]bmed_mri_t2_fitThe transverse relaxation time T2 and the extrapolated signal at TE = 0 from signals at several echo times, by a least-squares fit of ln S against TE.
TE echo times in ms vectorS signals at those echo times (any one unit) vectorT2 transverse relaxation time, msS0 fitted signal at TE = 0 (unit of S)bmed_mri_spin_echo_signalThe steady-state spin-echo signal S = M0 (1 - exp(-TR/T1)) exp(-TE/T2) of a tissue with relaxation times T1 and T2, for repetition time TR and echo time TE.
M0 equilibrium magnetisation (relative proton density)TR repetition time [s]TE echo time [s]T1 longitudinal relaxation time [s]T2 transverse relaxation time [s]S signal in the units of M0bmed_mri_spoiled_gradient_echoThe steady-state signal of a spoiled gradient-echo sequence with flip angle alpha, repetition time TR and echo time TE for a tissue with T1 and T2*.
M0 equilibrium magnetisation (relative proton density)TR repetition time [s]TE echo time [s]T1 longitudinal relaxation time [s]T2star effective transverse relaxation time T2* [s]alpha flip angle [rad]S signal in the units of M0bmed_snr_averagingThe signal-to-noise ratio after averaging N acquisitions with independent noise, SNR_N = SNR_1 sqrt(N), or the smallest number of averages that reaches a target SNR.
SNR1 signal-to-noise ratio of one acquisitionN number of averages (give N or SNR_target) integer optionalSNR_target target SNR (give N or SNR_target) optionalSNR SNR after averaginggain SNR gain sqrt(N)N number of averagesbmed_ultrasound_interfaceThe intensity reflection and transmission coefficients and the pressure amplitude coefficients of an ultrasound wave meeting a flat interface between two media at normal incidence.
Z1 acoustic impedance of the first medium [kg/(m^2*s)]Z2 acoustic impedance of the second medium [kg/(m^2*s)]R intensity reflection coefficientT intensity transmission coefficientr_p pressure reflection coefficientt_p pressure transmission coefficientbmed_ultrasound_matching_layerThe intensity transmission coefficient from a transducer (impedance Z1) through a matching layer (impedance Zm, thickness d, sound speed c_m) into tissue (Z2) at frequency f, and the layer's phase thickness.
Z1 impedance of the source medium (transducer) [kg/(m^2*s)]Zm impedance of the matching layer [kg/(m^2*s)]Z2 impedance of the load medium (tissue) [kg/(m^2*s)]d layer thickness [m]c_m sound speed in the layer [m/s]f frequency [Hz]T intensity transmission coefficientkd phase thickness of the layer (rad)bmed_ultrasound_wavelengthThe wavelength lambda = c/f of ultrasound of frequency f in a medium with speed of sound c (1540 m/s, the soft-tissue convention, by default), with the period and wavenumber.
f ultrasound frequency [Hz]c speed of sound (default 1540 m/s) [m/s] optionalwavelength wavelength [m]wavelength_mm wavelength in mmperiod period 1/f [s]k wavenumber 2 pi/lambda [1/m]bmed_xray_attenuation_layersThe transmitted fraction and intensity of a narrow monoenergetic X-ray beam crossing successive tissue layers, from each layer's mass attenuation coefficient, density and thickness.
I0 incident intensity [W/m^2]mu_rho mass attenuation coefficient of each layer, cm^2/g vectorrho density of each layer, g/cm^3 vectorx thickness of each layer, cm vectorT transmitted fractionI transmitted intensity [W/m^2]bmed_fitzhugh_nagumo_fixed_pointThe resting (fixed) point of the FitzHugh-Nagumo model v' = v - v^3/3 - w + I, w' = eps (v + a - b w), the trace and determinant of its Jacobian and whether it is stable (resting) or unstable (repetitive firing).
a parameter ab parameter b (0 < b < 1)eps time-scale ratio eps (> 0)I applied current (dimensionless)v_star fixed-point vw_star fixed-point wtrace trace of the Jacobiandeterminant determinant of the Jacobianstable true when the fixed point is stablebmed_ghk_current_densityThe current density carried by one ion species through a membrane of given permeability at a stated membrane potential, from the GHK current (constant-field) equation; outward current positive.
P membrane permeability to the ion [m/s]z valence of the ion (+1, +2, -1, ...) integerC_in inside concentration [mol/m^3]C_out outside concentration [mol/m^3]V membrane potential, inside relative to outside [V]T absolute temperature (or degC) [K]I current density, outward positive [A/m^2]bmed_ghk_voltageThe resting membrane potential of the Goldman-Hodgkin-Katz voltage equation from the relative permeabilities and the inside and outside concentrations of K+, Na+ and Cl-.
T absolute temperature (or degC) [K]PK relative permeability to K+ (> 0)PNa relative permeability to Na+PCl relative permeability to Cl-K_o outside K+ [mol/m^3]K_i inside K+ [mol/m^3]Na_o outside Na+ [mol/m^3]Na_i inside Na+ [mol/m^3]Cl_o outside Cl- [mol/m^3]Cl_i inside Cl- [mol/m^3]V_m membrane potential, inside relative to outside [V]bmed_hh_potassium_conductance_clampThe potassium conductance gK = gK_max n^4 and the gate n a time t after the membrane is stepped from a holding potential (at steady state) to a new clamped potential, in the Hodgkin-Huxley model.
gK_max maximal K conductance [S/m^2]V_hold holding potential before the step [V]V_step clamped potential after the step [V]t time after the step [s]g_K K conductance at time t [S/m^2]n K gate n at time tbmed_hh_gating_steady_stateThe steady-state values of the Hodgkin-Huxley gating variables m, h and n at a clamped membrane potential, from the 1952 squid-axon rate functions.
V clamped membrane potential [V]m_inf Na activation at steady stateh_inf Na inactivation at steady staten_inf K activation at steady statebmed_hh_resting_potentialThe membrane potential at which the steady-state Na, K and leak currents of the Hodgkin-Huxley model sum to zero (the resting potential), from the maximal conductances and reversal potentials.
gNa maximal Na conductance [S/m^2]gK maximal K conductance [S/m^2]gL leak conductance [S/m^2]ENa Na reversal potential [V]EK K reversal potential [V]EL leak reversal potential [V]V_rest zero-current steady-state potential [V]bmed_lif_firing_rateThe interspike interval and firing rate of a leaky integrate-and-fire neuron driven by a constant current, with reset and an absolute refractory period.
tau_m membrane time constant [s]R_m membrane resistance [ohm]I constant input current [A]V_rest resting potential [V]V_th spike threshold [V]V_reset reset potential [V]t_ref absolute refractory period [s]rate firing rate [Hz]ISI interspike interval [s]bmed_cable_steady_stateThe steady-state voltage at distance x along a passive cylindrical cable held at V0 at x = 0, and the input resistance there, for a sealed end, a killed (short-circuited) end or a semi-infinite cable.
Rm specific membrane resistance [ohm*m^2]Ri axial (cytoplasmic) resistivity [ohm*m]d cable diameter [m]x distance from the stimulated end [m]V0 steady voltage at x = 0 (relative to rest) [V]end far-end condition choiceL cable length (sealed or killed end only) [m] optionalV_x voltage at x (relative to rest) [V]R_in input resistance at x = 0 [ohm]bmed_lif_subthreshold_voltageThe membrane potential of a passive RC membrane (the subthreshold leaky integrate-and-fire neuron) a time t after a constant current starts, from its initial potential.
tau_m membrane time constant [s]R_m membrane resistance [ohm]I constant input current [A]V_rest resting potential [V]V0 potential at t = 0 [V]t time [s]V membrane potential at time t [V]bmed_postsynaptic_potentialThe postsynaptic potential of a passive RC membrane receiving a synaptic current I0 exp(-t/tau_s) at t = 0: its value at time t, the time of its peak and the peak value.
tau_m membrane time constant [s]tau_s synaptic current decay time constant [s]R_m membrane resistance [ohm]I0 peak synaptic current (negative for inward) [A]t time after the synaptic event [s]V_t potential change at time t [V]t_peak time of the peak [s]V_peak peak potential change [V]bmed_pk_bioavailability_from_profilesThe absolute bioavailability F from the dose-normalised areas under an oral and an IV concentration-time profile (linear trapezoids from the first to the last sample).
D_iv IV dose [kg]t_iv IV sampling times (one time unit for both profiles) vectorC_iv IV concentrations (one concentration unit for both profiles) vectorD_oral oral dose [kg]t_oral oral sampling times vectorC_oral oral concentrations vectorAUC_iv IV area (units of the lists)AUC_oral oral area (units of the lists)F absolute bioavailability (AUC_oral/D_oral)/(AUC_iv/D_iv)bmed_pk_auc_trapezoidThe area under a sampled concentration-time curve from the first to the last sample, by the linear trapezoidal rule or the linear-up/log-down rule (stated).
t sampling times, strictly increasing, in one time unit vectorC concentrations at those times, in one concentration unit vectormethod linear trapezoids, or linear while rising and logarithmic while falling choiceAUC area from the first to the last sample, in (unit of C) x (unit of t)bmed_pk_terminal_half_life_fitThe first-order elimination rate constant, half-life and back-extrapolated concentration from a straight-line least-squares fit of ln C against time (mono-exponential decline).
t sampling times, in one time unit (results are per that unit) vectorC concentrations at those times, in one concentration unit (C0 is in that unit) vectork elimination rate constant, per time unit of tt_half half-life, in the time unit of tC0 back-extrapolated concentration at t = 0, in the unit of Cbmed_pk_nca_iv_bolusNon-compartmental parameters from a concentration-time profile after an IV bolus: AUC to the last sample (linear trapezoids), terminal rate constant from the last n points, half-life, AUC to infinity, clearance and terminal volume.
D IV bolus dose [kg]t sampling times in h, the first at 0 (measured or back-extrapolated C0) vectorC concentrations in mg/L at those times vectorn_terminal number of last points used for the terminal slope (3 to n - 1) integerAUC_last AUC from 0 to the last sample, mg*h/Llambda_z terminal rate constant, 1/ht_half terminal half-life, hAUC_inf AUC from 0 to infinity (observed C_last / lambda_z added), mg*h/LCL clearance D / AUC_inf, L/hVz terminal volume CL / lambda_z, Lbmed_pk_auc_iv_bolusThe area under the plasma concentration-time curve from 0 to infinity and from 0 to t after an IV bolus in a one-compartment model.
D bolus dose [kg]CL clearance [m^3/s]V volume of distribution [m^3]t end of the partial area [s]AUC_inf area from 0 to infinity [kg*s/m^3]AUC_0_t area from 0 to t [kg*s/m^3]bmed_pk_time_to_steady_state_fractionThe time after the start of a constant-rate infusion at which a one-compartment model reaches a stated fraction of its steady-state concentration.
CL clearance [m^3/s]V volume of distribution [m^3]f fraction of steady state (90% or 0.9)t time to reach f of steady state [s]bmed_pk_infusion_concentrationThe plasma concentration of a one-compartment model during a constant-rate intravenous infusion started at t = 0, and the steady-state concentration it approaches.
R0 infusion rate [kg/s]CL clearance [m^3/s]V volume of distribution [m^3]t time since the start of the infusion [s]C concentration at time t [kg/m^3]C_ss steady-state concentration R0/CL [kg/m^3]bmed_pk_effect_site_concentrationThe effect-site concentration of a one-compartment model linked to an effect compartment (rate ke0) after an IV bolus, the time of its peak and the peak value.
D bolus dose [kg]V volume of distribution [m^3]k elimination rate constant [1/s]ke0 effect-site equilibration rate constant [1/s]t time after the dose [s]Ce effect-site concentration at time t [kg/m^3]t_peak time of the effect-site peak [s]Ce_peak peak effect-site concentration [kg/m^3]bmed_pk_hepatic_clearance_parallel_tubeThe hepatic clearance and extraction ratio of the parallel-tube liver model, in which the concentration falls along the sinusoids, from blood flow, unbound fraction and intrinsic clearance.
Q hepatic blood flow [m^3/s]fu unbound fraction in blood (0 < fu <= 1)CL_int intrinsic clearance of unbound drug [m^3/s]CL_H hepatic clearance [m^3/s]E extraction ratiobmed_pk_hepatic_clearance_well_stirredThe hepatic clearance and extraction ratio of the well-stirred (venous equilibrium) liver model from hepatic blood flow, unbound fraction and intrinsic clearance.
Q hepatic blood flow [m^3/s]fu unbound fraction in blood (0 < fu <= 1)CL_int intrinsic clearance of unbound drug [m^3/s]CL_H hepatic clearance [m^3/s]E extraction ratiobmed_pk_short_infusionThe plasma concentration of a one-compartment model at time t after the start of a constant-rate infusion lasting T_inf (during or after the infusion), and the concentration at the end of the infusion.
R0 infusion rate [kg/s]T_inf duration of the infusion [s]CL clearance [m^3/s]V volume of distribution [m^3]t time since the start of the infusion [s]C concentration at time t [kg/m^3]C_end concentration at the end of the infusion [kg/m^3]bmed_pk_loading_maintenanceFor a one-compartment model, the bolus and the constant infusion rate that together hold the model concentration at a target value from the start (model calculation only, not a dosing recommendation).
C_target target model concentration [kg/m^3]V volume of distribution [m^3]CL clearance [m^3/s]LD loading bolus of the model [kg]R0 maintenance infusion rate of the model [kg/s]bmed_pk_michaelis_menten_concentrationThe concentration a time t after an IV bolus in a one-compartment model with saturable Michaelis-Menten elimination, from the closed form with the Lambert W function.
C0 initial concentration [kg/m^3]Vmax maximum elimination rate (amount per time) [kg/s]Km Michaelis constant [kg/m^3]V volume of distribution [m^3]t time after the dose [s]C concentration at time t [kg/m^3]bmed_pk_michaelis_menten_steady_stateThe steady-state concentration of a one-compartment model with Michaelis-Menten elimination given a constant dosing rate below Vmax.
R0 constant dosing rate (amount per time) [kg/s]Vmax maximum elimination rate [kg/s]Km Michaelis constant [kg/m^3]C_ss steady-state concentration [kg/m^3]bmed_pk_michaelis_menten_timeThe time for the concentration of a one-compartment model with Michaelis-Menten elimination to fall from C0 to C.
C0 initial concentration [kg/m^3]C target concentration (< C0) [kg/m^3]Vmax maximum elimination rate [kg/s]Km Michaelis constant [kg/m^3]V volume of distribution [m^3]t time to fall from C0 to C [s]bmed_pk_iv_bolus_concentrationThe plasma concentration of a one-compartment model a time t after an intravenous bolus dose, with first-order elimination; also the fraction of the dose remaining.
D bolus dose [kg]V volume of distribution [m^3]k elimination rate constant [1/s]t time after the dose [s]C concentration at time t [kg/m^3]fraction_remaining fraction of the dose still in the bodybmed_pk_oral_concentrationThe plasma concentration and partial AUC of a one-compartment model with first-order absorption (rate ka) and elimination (rate k) after a single oral dose with bioavailability F.
F bioavailable fraction (0 < F <= 1; 80% or 0.8)D oral dose [kg]V volume of distribution [m^3]ka absorption rate constant [1/s]k elimination rate constant [1/s]t time after the dose [s]C concentration at time t [kg/m^3]AUC_0_t area under the curve from 0 to t [kg*s/m^3]bmed_pk_oral_peakThe time of the peak plasma concentration and the peak concentration of a one-compartment model with first-order absorption after a single oral dose.
F bioavailable fraction (0 < F <= 1)D oral dose [kg]V volume of distribution [m^3]ka absorption rate constant [1/s]k elimination rate constant [1/s]t_max time of the peak [s]C_max peak concentration [kg/m^3]bmed_pk_nth_dose_ivThe peak concentration just after the nth of equal IV bolus doses given every tau, and the concentration a time t later, in a one-compartment model (superposition).
D each bolus dose [kg]V volume of distribution [m^3]k elimination rate constant [1/s]tau dosing interval [s]n number of the dose (1 = first) integert time after the nth dose (0 to tau) [s]C_max_n concentration just after the nth dose [kg/m^3]C concentration a time t after the nth dose [kg/m^3]bmed_pk_steady_state_ivThe steady-state peak, trough and average concentrations and the accumulation factor of a one-compartment model given equal IV bolus doses every tau.
D each bolus dose [kg]V volume of distribution [m^3]k elimination rate constant [1/s]tau dosing interval [s]C_max_ss steady-state peak (just after a dose) [kg/m^3]C_min_ss steady-state trough (just before a dose) [kg/m^3]C_avg_ss average concentration over an interval at steady state [kg/m^3]R_ac accumulation factor: steady-state peak over first-dose peakbmed_pk_steady_state_oralThe steady-state peak concentration, the time of the peak after a dose and the trough of a one-compartment model with first-order absorption given equal oral doses every tau.
F bioavailable fraction (0 < F <= 1)D each oral dose [kg]V volume of distribution [m^3]ka absorption rate constant [1/s]k elimination rate constant [1/s]tau dosing interval [s]C_max_ss steady-state peak [kg/m^3]t_max_ss time of the peak after a dose [s]C_min_ss steady-state trough (at the dosing times) [kg/m^3]bmed_pk_intermittent_infusion_steady_stateThe steady-state peak (end of infusion) and trough (end of interval) of a one-compartment model given infusions of duration T_inf at rate R0 every tau.
R0 infusion rate [kg/s]T_inf duration of each infusion [s]tau dosing interval [s]CL clearance [m^3/s]V volume of distribution [m^3]C_max_ss steady-state concentration at the end of an infusion [kg/m^3]C_min_ss steady-state concentration at the end of an interval [kg/m^3]bmed_pk_two_compartment_bolusThe hybrid rate constants alpha and beta, the coefficients A and B and the central concentration at time t of a two-compartment model after an IV bolus, from the volume V1 and the micro-constants k10, k12, k21.
D bolus dose [kg]V1 central volume [m^3]k10 elimination rate constant from the central compartment [1/s]k12 transfer rate constant central to peripheral [1/s]k21 transfer rate constant peripheral to central [1/s]t time after the dose [s]alpha fast (distribution) rate constant [1/s]beta slow (terminal) rate constant [1/s]A coefficient of exp(-alpha t) [kg/m^3]B coefficient of exp(-beta t) [kg/m^3]C central concentration at time t [kg/m^3]bmed_pk_two_compartment_micro_constantsThe central volume, the micro rate constants k10, k12, k21, the clearance and the steady-state volume of a two-compartment model from the biexponential fit C = A exp(-alpha t) + B exp(-beta t) of an IV bolus.
D bolus dose [kg]A coefficient of the fast exponential [kg/m^3]alpha fast rate constant [1/s]B coefficient of the slow exponential [kg/m^3]beta slow rate constant [1/s]V1 central volume [m^3]k10 elimination rate constant [1/s]k12 central to peripheral [1/s]k21 peripheral to central [1/s]CL clearance [m^3/s]Vss volume of distribution at steady state [m^3]bmed_cox_hazard_ratioThe log hazard ratio, hazard ratio, its standard error and Wald confidence interval of a Cox proportional-hazards model with a single covariate, by maximum partial likelihood with Efron's handling of ties.
times follow-up times vectorevents 1 = event, 0 = censored vectorx covariate value of each subject (e.g. 1 = treated, 0 = control) vectorlevel confidence level (95% or 0.95)beta log hazard ratio per unit of xHR hazard ratio exp(beta)se standard error of betaHR_lower lower Wald limit of the hazard ratioHR_upper upper Wald limit of the hazard ratiobmed_exponential_survival_fitThe maximum-likelihood constant hazard of an exponential survival model from censored follow-up data, with the implied mean and median survival times.
times follow-up times, all positive (one time unit) vectorevents 1 = event, 0 = censored vectorhazard events per unit timemean mean survival 1/hazardmedian median survival ln 2 / hazardbmed_exponential_hazard_ratioThe ratio of the maximum-likelihood constant hazards of two groups (group 1 relative to group 2) with the log-scale Wald confidence interval.
times1 follow-up times, group 1 (positive) vectorevents1 1 = event, 0 = censored, group 1 vectortimes2 follow-up times, group 2 (reference) vectorevents2 1 = event, 0 = censored, group 2 vectorlevel confidence level (95% or 0.95)HR hazard ratio group 1 / group 2lower lower limitupper upper limitbmed_km_survival_medianThe Kaplan-Meier (product-limit) estimate of the survival probability at time t and the median survival time from follow-up times with event or censoring indicators.
times follow-up times (one time unit; results in that unit) vectorevents 1 = event observed, 0 = censored, one per time vectort time at which S(t) is reportedS_t Kaplan-Meier survival probability at tmedian median survival: first time with S <= 0.5 (none when not reached)bmed_km_confidence_intervalThe Kaplan-Meier survival estimate at time t with its confidence interval on the log(-log) scale (Greenwood variance; the exponential Greenwood interval) at the stated level.
times follow-up times (one time unit) vectorevents 1 = event, 0 = censored vectort time at which S(t) is reportedlevel confidence level (95% or 0.95)S_t Kaplan-Meier estimate at tlower lower confidence limitupper upper confidence limitbmed_logrank_testThe log-rank (Mantel-Cox) chi-square statistic and p-value for equal survival in two groups from follow-up times and event indicators.
times1 follow-up times, group 1 vectorevents1 1 = event, 0 = censored, group 1 vectortimes2 follow-up times, group 2 vectorevents2 1 = event, 0 = censored, group 2 vectorchi_square log-rank chi-square (1 degree of freedom)p_value two-sided p-valuebmed_nelson_aalen_hazardThe Nelson-Aalen estimate of the cumulative hazard at time t from follow-up times with event or censoring indicators.
times follow-up times (one time unit) vectorevents 1 = event, 0 = censored vectort time at which H(t) is reportedH_t cumulative hazard at tbmed_restricted_mean_survival_timeThe restricted mean survival time up to tau: the area under the Kaplan-Meier survival curve from 0 to tau.
times follow-up times (one time unit) vectorevents 1 = event, 0 = censored vectortau restriction time (in the unit of the times)RMST restricted mean survival time, in the time unit15 files, 43.4 MB in total. The largest:
| File | Size |
|---|---|
| model.safetensors | 18.9 MB |
| dist/biomedical_science_ai999x-1.0.1-py3-none-any.whl | 14.9 MB |
| onnx/search/encoder.int8.onnx | 4.9 MB |
| docs/biomedical_science_ai999x_capabilities.pdf | 3.5 MB |
| onnx/search/index.json | 403.3 KB |
| docs/biomedical_science_ai999x_capabilities.html | 312 KB |
| docs/biomedical_science_ai999x_capabilities.md | 244.7 KB |
| onnx/search/tokenizer.json | 176.4 KB |
| README.md | 26.3 KB |
| LICENSE | 11.4 KB |
| evaluation/release_gate.md | 2.3 KB |
| evaluation/KNOWLEDGE_CARD.md | 1.4 KB |
Biomedical Science answers questions in biomedical science: pharmacokinetics and dosing models, epidemic models, diagnostic test statistics, survival analysis, biomechanics, neuron models and medical-imaging physics (quantitative only, no clinical advice). Each answer gives the value with its unit, the steps and the formula in LaTeX.
With pip: pip install biomedical-science-ai999x. The same files are on Hugging Face (hf download AI999X/biomedical-science-ai999x --local-dir biomedical-science-ai999x) and GitHub.
Yes. It is a Python package that runs on an ordinary CPU without a network connection (Python >=3.10); no GPU and no API key are needed.
86 capabilities in 9 topics, including Pharmacokinetic models, Medical-imaging physics, Biomechanics, Neuron models, Epidemic models.
Field: Life Sciences. Tasks: Question Answering, Token Classification, Text Classification, Sentence Similarity, Feature Extraction.
Asked "IV bolus concentration: D = 500 mg, V = 40 L, k = 0.1 1/h, t = 6 h", it answers: C = 0.00686015 kg/m^3, fraction_remaining = 0.548812.
It says so and names what is missing or out of range, instead of guessing a number.