Skip to content

RANKL-directed exposure and bone-density turnover

Explore subcutaneous antibody absorption, apparent two-compartment disposition and quasi-steady-state RANKL binding linked to empirical bone-density turnover. Conditional fixed effects do not establish population behavior or biosimilarity.

Population pharmacokinetics/pharmacodynamics analysis confirming biosimilarity of SB16 to reference denosumab ↗
Exploration notes · What are you exploring?

Notes stay on this browser.

Run settings

Run location

Explore this model

Choose a starting point to view its result. Adjust key model inputs when you want to explore a different outcome.

Alternate treatment-coefficient context

What changes when the fitted treatment clearance multiplier is applied to the same dose and covariate context? Fixed-effect exploration; no population or biosimilarity inference.

0–13,140 hour

Study

Alternate treatment-coefficient context

What changes when the fitted treatment clearance multiplier is applied to the same dose and covariate context? Fixed-effect exploration; no population or biosimilarity inference.

Readouts

Total central antibody concentration· nmol/L
Apparent central antibody amount divided by apparent central volume; contains free and algebraically bound antibody.
Unbound central antibody concentration· nmol/L
Latent quasi-steady-state free-antibody estimate; not a separate observed clinical concentration.
Lumbar bone density change· %
Change relative to model baseline from empirical inhibitory turnover. Healthy-volunteer values are unobserved extrapolations.
Cumulative total antibody exposure· nmol*h/L
Integral of total central concentration from simulation start; interval AUC requires differences at defined endpoints.

Study purpose

  • What changes when the fitted treatment clearance multiplier is applied to the same dose and covariate context?

Interpretation limits

  • Deterministic fixed-effect trajectories are distinct from population medians, prediction intervals and formal biosimilarity inference.
  • Dose events contain 408.1632653061224 nmol, representing 60 mg under the retained 147 kDa molecular-weight assumption. Physical amount readouts are in nmol; equivalent events use dimensionless numerical coordinates. No implicit milligram conversion is performed.
  • Population context is categorical and coupled to the initial target baseline; changing the flag requires coordinated initial-state changes.
  • Baseline target and BMD parameters are coupled to explicit initial states and are excluded from independent analysis axes.
  • Disposition volumes and clearances are apparent quantities; target binding is algebraic QSS, not an explicit association/dissociation system.
  • Healthy-volunteer BMD is an unobserved model extrapolation; its scenario exposes PK only.
  • BMD change is relative to model baseline and cumulative exposure starts at simulation time zero; neither is automatically a clinical effect estimate or interval AUCtau.
  • Five retained source conflicts, original individual data, population-modeling environment likelihood/random effects, population predictions, pcVPC and source-figure reproduction remain unresolved.
  • Table 3 weight exponents and retained amount-form equations are explicit conventions, not adjudicated resolutions of the source conflicts.
  • The four non-weight control bounds are exploratory 0.5–1.5× default ranges; no patient distribution or parameter uncertainty is implied.
  • The Hill state derivative is singular at zero; the existing runtime uses numerical Jacobian boundary regularization. No sensitivity or fitting qualification is asserted.
Loading starting example…

Edit inputs

PK disposition

Reference body weight for PMO simulations.

kg
64 → —

Race-specific apparent clearance used by the current scenario.

L/h
0.006 → —
Target interaction

QSS equilibrium constant.

nmol/L
1.56 → —

Denosumab-target complex internalization rate.

1/h
0.022 → —
Bone-density turnover

Lumbar spine BMD elimination rate.

1/h
0.00018 → —
Simulation time
hour
hour
13140 → 168

Time between reported samples.

hour
24 → 1

2 changes · Variation 1

Continue in the background and keep the result.

Biology

Explore subcutaneous antibody absorption, apparent two-compartment disposition and quasi-steady-state RANKL binding linked to empirical bone-density turnover. Conditional fixed effects do not establish population behavior or biosimilarity.

Explore subcutaneous antibody absorption, apparent two-compartment disposition and quasi-steady-state RANKL binding linked to empirical bone-density turnover. Conditional fixed effects do not establish population behavior or biosimilarity.
States & equation dependencies
What are the modeled states and equation-linked processes?Representative technical topology with 7 selected states: A depot coordinate, A central total coordinate, Rankl total, A peripheral free coordinate, Lumbar bmd g CM2, AUC total, Elapsed. Displayed equation-linked dependencies: from A depot coordinate to A central total coordinate; between A peripheral free coordinate and A central total coordinate; between Rankl total and A central total coordinate; from Rankl total to A peripheral free coordinate; from A central total coordinate to Lumbar bmd g CM2; from Rankl total to Lumbar bmd g CM2; from A central total coordinate to AUC total. Displayed model or scenario entry points: Administered input enters A depot coordinate. There are no separately labeled equation controls.TECHNICAL TOPOLOGYWhat are the modeled states and equation-linked processes?Selected equation-linked states · model time unit: hourAdministered inputA depot coordinatedimensionlessA central total coordinatedimensionlessRankl totalnmol/LA peripheral free coordinatedimensionlessLumbar bmd g CM2g/cm**2AUC totalnmol*h/LElapsedh
Teal arrows show relationships between modeled states and do not always represent material transfer. Peach arrows mark administered or scenario-defined entry points.

Assumptions & evidence

Assumptions & limitations

  • Deterministic fixed-effect trajectories are distinct from population medians, prediction intervals and formal biosimilarity inference.
  • Dose events contain 408.1632653061224 nmol, representing 60 mg under the retained 147 kDa molecular-weight assumption. Physical amount readouts are in nmol; equivalent events use dimensionless numerical coordinates. No implicit milligram conversion is performed.
  • Population context is categorical and coupled to the initial target baseline; changing the flag requires coordinated initial-state changes.
  • Baseline target and BMD parameters are coupled to explicit initial states and are excluded from independent analysis axes.
  • Disposition volumes and clearances are apparent quantities; target binding is algebraic QSS, not an explicit association/dissociation system.
  • Healthy-volunteer BMD is an unobserved model extrapolation; its scenario exposes PK only.
  • BMD change is relative to model baseline and cumulative exposure starts at simulation time zero; neither is automatically a clinical effect estimate or interval AUCtau.
  • Five retained source conflicts, original individual data, population-modeling environment likelihood/random effects, population predictions, pcVPC and source-figure reproduction remain unresolved.
  • Table 3 weight exponents and retained amount-form equations are explicit conventions, not adjudicated resolutions of the source conflicts.
  • The four non-weight control bounds are exploratory 0.5–1.5× default ranges; no patient distribution or parameter uncertainty is implied.
  • The Hill state derivative is singular at zero; the existing runtime uses numerical Jacobian boundary regularization. No sensitivity or fitting qualification is asserted.

Parameter origins

  • Discussion gives 2.1 days
  • Discussion gives 3.7 days
  • Derived from Table 3
  • pdfinfo on fetched article PDF
  • Discussion
  • Table 4
  • Section 2.2
  • Table 3 covariate model and Table S1 total mean near 64 kg
  • TheraSAbDab strict citation/year queue row 629
  • Table 3
  • mAb convention for concentration-unit bridge
  • Derived
  • Derived scenario convention
  • Table 1/Figure 9
  • Explicit exact linear nondimensionalization: physical amount = coordinate * 1e-60 nmol.
  • PMC HTML image links
  • Table 4/Eq. 10
  • Eq. 10 derived from Table 4
  • Eq. 9
  • Table 3 and Eq. 7
  • Table 1
  • tables/pmc_tables_summary.json
  • PMC metadata
  • PubMed metadata
  • metadata/europepmc_preprint_title.json
  • Article metadata
  • Eq. 7 derived from Table 3
  • PMC supplementary-material link
  • Table 5
  • Section 3.3
  • Generated validation control
  • Section 2.6

Validation & references

One or more implementation checks are available; this is not a claim of full model reproduction.

Population pharmacokinetics/pharmacodynamics analysis confirming biosimilarity of SB16 to reference denosumab ↗

Available reference curves can be added to the plot when their scenario, readout, time and units match.

Model details

118 parameters · 7 states · 7 equations · 142 derived outputs

Classification & API access
Therapeutic
Denosumab
Modality
Monoclonal antibody
Target
RANKL, TNFSF11, CD254, TRANCE, OPGL, ODF
Disease / scope
Healthy volunteers and postmenopausal women with osteoporosis
ParameterDefaultUnitDescription
Absorption half-life hvabsorption_half_life_hv_day2.0629380373807895dayHV absorption half-life.
Absorption half-life pmoabsorption_half_life_pmo_day3.7027092978629557dayPMO absorption half-life.
Absorption half-life pmoabsorption_half_life_pmo_h88.86502368428528hlog(2)/ka_pmo.
Article pdf pagesarticle_pdf_pages171Frontiers/PMC article PDF page count.
Asian AUC decrease percentasian_auc_decrease_percent19percentAUC decrease in Asian subjects relative to Caucasians.
Black AUC decrease percentblack_auc_decrease_percent11percentAUC decrease in Black subjects relative to Caucasians.
BMD0 g CM2bmd0_g_cm20.76g/cm**2Baseline lumbar spine BMD.
BMD0 iiv percentbmd0_iiv_percent59.85percentInter-individual variability for BMD0.
Bmd measurementsbmd_measurements17161Lumbar spine BMD measurements.
Bmd response 45kg percentbmd_response_45kg_percent7.11percentBMD response for 45 kg subgroup.
Bmd response 64kg percentbmd_response_64kg_percent6.66percentBMD response for 64 kg subgroup.
Bmd response 90kg percentbmd_response_90kg_percent5.54percentBMD response for 90 kg subgroup.
Bmd response asian percentbmd_response_asian_percent5.93percentBMD response for Asian subgroup.
Bmd response black percentbmd_response_black_percent6.15percentBMD response for Black subgroup.
Bmd response caucasian percentbmd_response_caucasian_percent6.45percentBMD response for Caucasian subgroup.
Body weightbody_weight_kg64kgReference body weight for PMO simulations.
Citation rankcitation_rank9451Citation-priority queue rank.
Clearance apparentcl_apparent_L_h0.006L/hRace-specific apparent clearance used by the current scenario.
Clearance asiancl_asian_L_h0.0074L/hClearance in Asian subjects.
Clearance blackcl_black_L_h0.0069L/hClearance in Black subjects.
Clearance caucasiancl_caucasian_L_h0.006L/hClearance in Caucasian subjects.
Clearance iiv percentcl_iiv_percent26.39percentInter-individual variability for CL/F.
Corr peripheral distribution volume clearancecorr_vp_cl0.431Correlation between Vp/F and CL/F IIV.
Denosumab mw gdenosumab_mw_g_mol147000g/molApproximate denosumab molecular weight for mg-to-nmol conversion.
Dose 60mgdose_60mg_nmol408.1632653061224nmol60 mg converted to nmol.
Dosing intervaldosing_interval_h4380hSix months represented as 365/2 days for simulation.
Dosing interval monthsdosing_interval_months6monthsRepeated-dose interval.
Drug-amount coordinate scaledrug_amount_nmol_per_coordinate1e-60nmolFixed physical amount per dimensionless numerical coordinate; not a biological parameter.
Figure image countfigure_image_count9countFetched PMC figure images.
Hill coeffhill_coeff0.17dimensionlessHill coefficient.
IC50 iiv percentic50_iiv_percent9.52percentInter-individual variability for IC50.
Half-maximal inhibitory concentrationic50_nM6.92nmol/LConcentration producing 50 percent of Imax.
Imax fimax_f-1.751Logit-transformed fractional maximum inhibitory effect.
Imax fractionimax_fraction0.14804719803168951exp(ImaxF)/(1+exp(ImaxF)).
Implementation priority scoreimplementation_priority_score141Queue implementation priority score.
Absorption rate hvka_hv_h0.0141/hAbsorption rate constant for healthy subjects.
Absorption rate iiv percentka_iiv_percent56.57percentInter-individual variability for ka.
Absorption rate pmoka_pmo_h0.00781/hAbsorption rate constant for PMO patients.
Kin bmd derived g CM2kin_bmd_derived_g_cm2_h0.0001368g/cm**2/hkout*BMD0 using Table 4 values.
Kin bmd g CM2kin_bmd_g_cm2_h0.00014g/cm**2/hBMD production rate shown in Table 4; derived by kout*BMD0.
Target internalization ratekint_h0.0221/hDenosumab-target complex internalization rate.
Kint iiv percentkint_iiv_percent7.88percentInter-individual variability for kint.
Turnover loss rate bmdkout_bmd_h0.000181/hLumbar spine BMD elimination rate.
Quasi-steady-state binding constant iiv percentkss_iiv_percent58.12percentInter-individual variability for Kss.
Quasi-steady-state binding constantkss_nM1.56nmol/LQSS equilibrium constant.
Ksyn iiv percentksyn_iiv_percent22.46percentInter-individual variability for reported ksyn.
Ksyn reportedksyn_reported_nM_h0.01nmol/L/hReported target synthesis value; table unit is ambiguous, Eq. 7 gives ksyn=R0*kdeg.
Lloqlloq_ng_ml20ng/mLDenosumab assay LLOQ.
Modeled subjectsmodeled_subjects615subjectsSubjects included in PK modeling.
Denosumab amount conversionnmol_per_mg_denosumab6.802721088435374nmol/mg1e6 / molecular weight.
PD additive error g CM2pd_additive_error_g_cm20.02g/cm**2PD additive residual error.
PHASE1 single dosephase1_single_dose_mg60mgPhase I single SC dose.
PHASE1 subjectsphase1_subjects168subjectsPhase I healthy-volunteer subjects.
PHASE3 den then den subjectsphase3_den_then_den_subjects101subjectsPhase III EU-DEN continuation subjects.
PHASE3 den then SB16 subjectsphase3_den_then_sb16_subjects100subjectsPhase III EU-DEN to SB16 transition subjects.
PHASE3 repeated dosephase3_repeated_dose_mg60mgPhase III SC dose at months 0, 6, and 12.
PHASE3 SB16 subjectsphase3_sb16_subjects225subjectsPhase III SB16 arm subjects.
PHASE3 subjectsphase3_subjects456subjectsPhase III PMO patients.
PK additive errorpk_additive_error_nM0.72nmol/LPK additive residual error.
PK proportional errorpk_proportional_error0.071PK proportional residual error.
Pmc html table countpmc_html_table_count20countHTML table-like blocks extracted from PMC.
Pmcid numericpmcid_numeric124030371PMCID numeric component.
Pmid numericpmid_numeric409045581PMID.
Population pmo flagpopulation_pmo_flag11Use PMO ka/Q/R0 when 1; HV values when 0.
Postdose blq samplespostdose_blq_samples11291Post-dose BLQ samples retained as MDV=1.
Postdose quantifiable samplespostdose_quantifiable_samples31331Quantifiable post-dose serum samples.
Postdose samplespostdose_samples42621Post-dose serum samples.
Preprint hit countpreprint_hit_count0countEuropePMC title preprint search hits.
Publicationpublication_year2025yearPublication year.
Q hvq_hv_L_h1.13L/hInter-compartment clearance for healthy subjects.
Q iiv percentq_iiv_percent295.99percentInter-individual variability for Q/F.
Q pmoq_pmo_L_h0.2L/hInter-compartment clearance for PMO patients.
Queue cited by countqueue_cited_by_count0countQueue cited-by count.
R0 hvr0_hv_nM0.98nmol/LBaseline RANKL in healthy volunteers.
R0 iiv percentr0_iiv_percent158.3percentInter-individual variability for R0.
R0 pmor0_pmo_nM15.23nmol/LBaseline RANKL in PMO patients.
Rankl degradation rate from ksyn over R0 pmorankl_kdeg_from_ksyn_over_r0_pmo_h0.00065659881812212731/h0.01 / 15.23 to satisfy Eq. 7 at PMO baseline.
Reference weightreference_weight_kg64kgReference body weight in covariate equations.
Serum concentration recordsserum_concentration_records65831Total serum denosumab concentration records.
Steady state vdsteady_state_vd_L7.64LVc+Vp apparent steady-state volume.
Supplement docx countsupplement_docx_count11Real DOCX supplement count.
Den AUC tau sstable5_den_auc_tau_ss_nM_h53731nmol*h/LDEN median AUCtau,ss.
Den AUC tau ss pi hightable5_den_auc_tau_ss_pi_high_nM_h87790nmol*h/LDEN AUCtau,ss 90 percent PI high.
Den AUC tau ss pi lowtable5_den_auc_tau_ss_pi_low_nM_h33706nmol*h/LDEN AUCtau,ss 90 percent PI low.
Den bmd change percenttable5_den_bmd_change_percent6.59percentDEN BMD change from baseline.
Den bmd change pi high percenttable5_den_bmd_change_pi_high_percent7.58percentDEN BMD change 90 percent PI high.
Den bmd change pi low percenttable5_den_bmd_change_pi_low_percent4.96percentDEN BMD change 90 percent PI low.
Den cmaxtable5_den_cmax_nM40.29nmol/LDEN median Cmax.
Den cmax pi hightable5_den_cmax_pi_high_nM80.45nmol/LDEN Cmax 90 percent PI high.
Den cmax pi lowtable5_den_cmax_pi_low_nM26.04nmol/LDEN Cmax 90 percent PI low.
Den tmaxtable5_den_tmax_h267hDEN median Tmax.
Den tmax pi hightable5_den_tmax_pi_high_h505hDEN Tmax 90 percent PI high.
Den tmax pi lowtable5_den_tmax_pi_low_h59hDEN Tmax 90 percent PI low.
SB16 AUC tau sstable5_sb16_auc_tau_ss_nM_h55040nmol*h/LSB16 median AUCtau,ss.
SB16 AUC tau ss pi hightable5_sb16_auc_tau_ss_pi_high_nM_h85011nmol*h/LSB16 AUCtau,ss 90 percent PI high.
SB16 AUC tau ss pi lowtable5_sb16_auc_tau_ss_pi_low_nM_h33625nmol*h/LSB16 AUCtau,ss 90 percent PI low.
SB16 bmd change percenttable5_sb16_bmd_change_percent6.59percentSB16 BMD change from baseline.
SB16 bmd change pi high percenttable5_sb16_bmd_change_pi_high_percent7.52percentSB16 BMD change 90 percent PI high.
SB16 bmd change pi low percenttable5_sb16_bmd_change_pi_low_percent4.9percentSB16 BMD change 90 percent PI low.
SB16 cmaxtable5_sb16_cmax_nM40.66nmol/LSB16 median Cmax.
SB16 cmax pi hightable5_sb16_cmax_pi_high_nM77.5nmol/LSB16 Cmax 90 percent PI high.
SB16 cmax pi lowtable5_sb16_cmax_pi_low_nM26.9nmol/LSB16 Cmax 90 percent PI low.
SB16 tmaxtable5_sb16_tmax_h259hSB16 median Tmax.
SB16 tmax pi hightable5_sb16_tmax_pi_high_h530hSB16 Tmax 90 percent PI high.
SB16 tmax pi lowtable5_sb16_tmax_pi_low_h52hSB16 Tmax 90 percent PI low.
Typical weight clearancetheta_weight_cl0.93dimensionlessBody-weight exponent on CL/F.
Typical weight central distribution volumetheta_weight_vc1.5dimensionlessBody-weight exponent on Vc/F.
Typical weight peripheral distribution volumetheta_weight_vp0.52dimensionlessBody-weight exponent on Vp/F.
Treatment clearance multipliertreatment_cl_multiplier1ratioTreatment multiplier on clearance; SB16 uses 0.9982.
Treatment clearance ratio SB16 to dentreatment_cl_ratio_sb16_to_den0.9982ratioCL/F ratio for SB16 to DEN when treatment retained as covariate.
Validation run noncevalidation_run_nonce0dimensionlessValidation nonce to avoid stale exact replay jobs.
Central distribution volume fvc_f_L1.58LApparent central volume.
Central distribution volume f iiv percentvc_f_iiv_percent61.69percentInter-individual variability for Vc/F.
Peripheral distribution volume fvp_f_L6.06LApparent peripheral volume.
Peripheral distribution volume f iiv percentvp_f_iiv_percent15.55percentInter-individual variability for Vp/F.
Vpc replicatesvpc_replicates10001VPC simulations generated in population-modeling environment.
Weight 45kg AUC increase percentweight_45kg_auc_increase_percent45percentAUC increase at 45 kg relative to 64 kg.
Weight 90kg AUC decrease percentweight_90kg_auc_decrease_percent39percentAUC decrease at 90 kg relative to 64 kg.

Related models

Feedback: helpdesk@unibiointelligence.com.

Ubi Biologics