Classical Model
Compartments: 2
OFV: 1,247.8
Fractal Model
nfrac: 0.72
OFV: 1,068.5
ΔOFV +179.3
★★★★★
p < 0.0001
Strong anomalous diffusion detected. Classical 2-compartment model significantly underestimates inter-individual variability in propofol distribution kinetics.
Classical Model
Compartments: 1
OFV: baseline
Fractal Model
nfrac: 0.85
OFV: baseline − 13.7
ΔOFV +13.7
★★★★
p = 0.0002
Significant fractional behavior in subcutaneous absorption. Moderate anomalous diffusion detected. The SC absorption depot benefits from Mittag-Leffler kinetics over first-order.
Classical Model
Compartments: 1
OFV: 653.6
Fractal Model
nfrac: ~1.000 (mean)
OFV: 311.5
Range: [0.518 – 2.348]
ΔOFV +342
★★★★★
p < 0.0001
40.2% anomalous
40.2% of children (68/169) show anomalous diffusion. Classical model treats population as homogeneous — FractaLPK reveals critical heterogeneity in pediatric drug transport. Key insight: mean nfrac ≈ 1.0 masks individual anomalous behavior ranging from 0.518 to 2.348.
Classical Model
Compartments: 2
Half-life: 40–55 days
Fractal Model
nfrac: 0.587
k21,f: 0.48 day−α
α = 0.587
★★★★★
Flagship drug
The foundational drug for fractional PK. Very long half-life explained by anomalous tissue redistribution (power-law return from deep compartment). Classical 2-compartment model cannot capture the 40–55 day terminal phase without fractional order.
Classical Model
Compartments: 3
Parameters: 7
Fractal Model
nfrac: 0.54 (SE 0.017)
Parameters: 3
3-CMT → 1-CMT frac
★★★★★
4 fewer params
Fractional 1-compartment model matches classical 3-compartment performance with 4 fewer parameters. First NONMEM-based fractional PopPK implementation (FDE4NONMEM). CV of α estimate = 3.15% — highly precise.
Classical Model
Compartments: 2
Absorption: first-order
Fractal Model
nfrac: 0.60 – 0.93
Per subject: individual
α range 0.60–0.93
★★★★
Subject-specific
75% anomalous
Wide inter-individual variability in fractional order: some subjects (Subject 8, α=1.0) follow classical kinetics while others (Subject 6, α=0.60) show strong anomalous absorption. Bioequivalence assessment benefits from individual α estimation.
Classical Model
Compartments: 2
Fails: non-monotonic C(t)
Fractal Model
nfrac: individual
Captures: local C maxima
Captures rebound
★★★★
Pediatric ALL
High-dose MTX (2–5 g/m²) in pediatric ALL shows non-monotonic concentration profiles (local maxima during elimination). Classical models cannot capture this. Fractional model recognizes all elimination patterns including rebound concentrations critical for toxicity monitoring.
Classical Model
Compartments: 2 + MM
Clearance: Michaelis-Menten
Fractal Model
nfrac: 0.50
Interaction: rifampin effect
α = 0.50
★★★★
Validated on clinical data
Fractional model captures the complex nonlinear PK of lopinavir including drug-drug interaction with rifampin (TB co-treatment). Fixed α=0.5 suggests strong subdiffusion in GI absorption. Critical for HIV/TB co-infected patients where classical models underpredict exposure.
Classical Model
Compartments: 1
OFV: baseline
Fractal Model
nfrac: ~0.95
ΔOFV: not significant
0/12 significant
☆☆☆☆☆
Negative control
Theophylline serves as a negative control: none of 12 subjects show significant fractional behavior. nfrac ≈ 0.95 (close to 1.0 = classical). This validates that FractaLPK does not over-fit — when data is classical, the engine correctly returns α ≈ 1.
Classical Model
Compartments: 2
OFV: wins
Fractal Model
nfrac: not justified
ΔOFV: negative
Classical wins
☆☆☆☆☆
p = n.s.
Negative control. Vancomycin follows classical 2-compartment kinetics. Fractional model does not improve fit. This confirms FractaLPK does not over-fit — when classical diffusion applies, the engine correctly identifies it.
Classical Model
Compartments: 1 + oral abs
OFV: wins
Fractal Model
nfrac: not justified
ΔOFV: +0.3 (n.s.)
ΔOFV +0.3
☆☆☆☆☆
p = 0.58 (n.s.)
Negative control. Tacrolimus high IIV is explained by classical covariates (CYP3A5 genotype, weight). Fractional order adds ΔOFV=0.3 (p=0.58, well below significance threshold of 3.84). Confirms the engine avoids false positives in drugs with high but classically-explained variability.
Classical Model (α=1)
Tumor growth: logistic ODE
Wins: 2/18 (11%)
Fractional Model (RPSM+Cp5)
αopt: 0.491
Wins: 16/18 (89%)
ΔMSE +22.8%
★★★★★
89% fractional advantage
Strongest fractional advantage among 3 treatment arms. Docetaxel-treated NSCLC tumors show α=0.49, indicating strong subdiffusive dynamics. The fractional logistic model (Caputo DαT = rT(1-bT), solved by RPSM + Levin-U acceleration) reduces MSE by 22.8% vs classical. Tumor growth under cytotoxic chemotherapy exhibits memory effects consistent with heterogeneous tissue damage.
Classical Model (α=1)
Tumor growth: logistic ODE
Wins: 7/34 (21%)
Fractional Model (RPSM+Cp5)
αopt: 0.547
Wins: 27/34 (79%)
ΔMSE +18.0%
★★★★★
79% fractional advantage
Key finding: α not significantly different from docetaxel (p=0.46, Mann-Whitney). This suggests α is a tumor-intrinsic property, not treatment-dependent. The fractional order captures the inherent heterogeneity of NSCLC tissue architecture, regardless of whether the patient receives chemotherapy or immunotherapy. Checkpoint inhibitor dynamics are equally subdiffusive (α=0.55).
Classical Model (α=1)
Tumor growth: logistic ODE
Wins: 0/8 (0%)
Fractional Model (RPSM+Cp5)
αopt: 0.507
Wins: 8/8 (100%)
ΔMSE +16.1%
★★★★★
100% fractional advantage
100% fractional advantage in combination chemo-immunotherapy. All 8 patients showed better fit with the fractional model (α=0.51). Combined treatment may induce even more heterogeneous tissue dynamics than monotherapy, though the small sample size warrants caution. This is the first demonstration of RPSM+Levin acceleration applied to clinical tumor dynamics data.
Classical Model
Compartments: 1 + oral abs
OFV: wins
Fractal Model
nfrac: ~0.86 (n.s.)
ΔOFV: negative
Classical wins
☆☆☆☆☆
p = n.s.
Negative control. Lithium renal kinetics are well-described by classical models. Despite narrow therapeutic window, no anomalous diffusion detected. Note: real patient data (not available publicly) could show different results in elderly or renally impaired populations.