Simulations Plus, Inc. · NASDAQ:SLP
Simulations Plus — Technical Presentation (March 2021)
98 slides from Simulations Plus's technical presentation, Mar 9, 2021
Slide 1: Tumor Growth Inhibition Modeling
TUMOR GROWTH INHIBITION MODELING Webinar, 9 March 2021
Slide 2: Agenda
Agenda • Presentation of the models in the TGI library available in Monolix and Simulx • Example 1: Combination therapy in lung cancer xenografts • Example 2: PSA in metastatic Castration-Resistant Prostate Cancer treated with chemotherapy MonolixSuite training 2021 2
Slide 3: TGI library
TGI library MonolixSuite training 2021 3
Slide 4: Common tumor growth models
¥a LIXOFT a Common tumor growth models
Slide 5: Common tumor growth models
Common tumor growth models Tumor growth models without saturation: Tumor growth models with saturation: ▪ Linear ▪ Logistic ▪ Quadratic ▪ Generalized logistic ▪ Exponential ▪ Hybrid Simeoni-logistic ▪ Generalized exponential ▪ Gompertz ▪ Exponential-linear ▪ Gompertz-exponential ▪ Simeoni ▪ Von Bert
Slide 6: Tumor growth models
Tumor growth models Linear model: ▪ constant zero-order growth rate 𝑑𝑇𝑆 = 𝑘𝑔𝑙 𝑑𝑡 𝑇𝑆 = 𝑘𝑔𝑙 ∗ 𝑡 + 𝑇𝑆0 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 𝑘𝑔𝑙 MonolixSuite training 2021 6
Slide 7: Tumor growth models
Tumor growth models Quadratic model: ▪ combines linear and quadratic growth rates 𝑑𝑇𝑆 = 𝑘𝑔𝑙 + 2𝑘𝑔2 ∗ 𝑡 𝑑𝑡 𝑇𝑆 = 𝑘𝑔𝑙 ∗ 𝑡 + 𝑘𝑔2 ∗ 𝑡 2 + 𝑇𝑆0 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 𝑘𝑔2 𝑘𝑔𝑙 MonolixSuite training 2021 7
Slide 8: Tumor growth models
Tumor growth models Exponential model: ▪ assumes that the growth rate of a tumor is proportional to tumor burden (first-order growth) 𝑑𝑇𝑆 = 𝑘𝑔𝑒 ∗ 𝑇𝑆 𝑑𝑡 𝑇𝑆 = 𝑇𝑆0 ∗ 𝑒 𝑘𝑔𝑒∗𝑡 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 Linear scale Log scale MonolixSuite training 2021 8
Slide 9: Tumor growth models
Tumor growth models Generalized exponential model (power law): ▪ assumes that the growth rate of a tumor is proportional to tumor burden (first-order growth) 𝑑𝑇𝑆 = 𝑘𝑔𝑒 ∗ 𝑇𝑆 𝛾 1 𝑑𝑡 𝑇𝑆 = 𝑘𝑔𝑒 1 − 𝛾 𝑡 + 𝑇𝑆01−𝛾 1−𝛾 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 Log scale 𝑘𝑔𝑒 𝛾 MonolixSuite training 2021 9
Slide 10: Tumor growth models
Tumor growth models Exponential-linear model: ▪ assumes that the growth rate of a tumor is proportional to tumor burden (first-order growth) 𝑑𝑇𝑆 𝑘𝑔𝑒 ∗ 𝑇𝑆, 𝑡≤𝜏 𝑇𝑆0 ∗ 𝑒 𝑘𝑔𝑒∗𝑡 , 𝑡≤𝜏 =ቊ 𝑇𝑆 = ൝ 𝑑𝑡 𝑘𝑔𝑙, 𝑡>𝜏 𝑘𝑔𝑙 ∗ 𝑡 − 𝜏 + 𝑇𝑆0 ∗ 𝑒 𝑘𝑔𝑒∗𝜏 , 𝑡>𝜏 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0…
Slide 11: Tumor growth models
Tumor growth models Simeoni model: ▪ approximates the exponential-linear model with a single differential equation Linear scale Log scale 𝑑𝑇𝑆 𝑘𝑔𝑒 ∗ 𝑇𝑆 = 1ൗ 𝑑𝑡 𝜓 𝜓 𝑘𝑔𝑒 1+ ∗ 𝑇𝑆 𝑘𝑔𝑙 𝑘𝑔𝑙 𝑘𝑔𝑒 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 ▪ 𝜓 should be fixed to a high value (20 for example) for a sharp…
Slide 12: Tumor growth models
Tumor growth models Koch model: ▪ assumes a smooth transition between exponential and linear growth phase 1 𝑑𝑇𝑆 2𝑘𝑔𝑒 ∗ 𝑘𝑔𝑙 ∗ 𝑇𝑆 2𝑘𝑔𝑒 𝑡+ 𝑘𝑔𝑙 (𝑇𝑆0−𝑇𝑆൰ = 𝑇𝑆 = 𝑇𝑆0𝑒 𝑑𝑡 𝑘𝑔𝑙 + 2𝑘𝑔𝑒 ∗ 𝑇𝑆 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 Linear scale Log scale 𝑘𝑔𝑙 𝑘𝑔𝑒 MonolixSuite training…
Slide 13: Tumor growth models
Tumor growth models Logistic model: ▪ assumes an exponential growth rate which decelerates linearly with respect to the tumor size. 𝑑𝑇𝑆 𝑇𝑆 𝑇𝑆𝑚𝑎𝑥 ∗ 𝑇𝑆0 = 𝑘𝑔𝑒 ∗ 𝑇𝑆 1 − 𝑇𝑆 = 𝑑𝑡 𝑇𝑆𝑚𝑎𝑥 𝑇𝑆0 + 𝑇𝑆𝑚𝑎𝑥 − 𝑇𝑆0 ∗ 𝑒 −𝑘𝑔𝑒∗𝑡 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 Linear scale Log scale…
Slide 14: Tumor growth models
Tumor growth models Generalized logistic model: ▪ assumes an exponential growth rate kg which decelerates linearly with respect to the tumor size. 𝛾 𝑇𝑆𝑚𝑎𝑥 ∗ 𝑇𝑆0 𝑑𝑇𝑆 𝑇𝑆 𝑇𝑆 = = 𝑘𝑔𝑒 ∗ 𝑇𝑆 1 − 1 𝑑𝑡 𝑇𝑆𝑚𝑎𝑥 𝑇𝑆0𝛾 + 𝑇𝑆𝑚𝑎𝑥 𝛾 − 𝑇𝑆0𝛾 ∗ 𝑒 −𝑘𝑔𝑒∗𝛾∗𝑡 𝛾 Linear scale Log…
Slide 15: Tumor growth models
Tumor growth models Gompertz model: ▪ assumes an exponential decay of the relative growth rate 𝑑𝑇𝑆 𝒂 1−𝑒 −𝛽∗𝑡 = 𝛼𝑒 −𝛽∗𝑡 ∗ 𝑇𝑆 𝑇𝑆 = 𝑇𝑆0 ∗ 𝑒 𝛽 𝑑𝑡 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 Linear scale 𝒂 TS0, 𝛽 𝒂 𝑑𝑇𝑆 𝑇𝑆 TSmax = TS0 ∗ 𝑒 𝛽 = 𝛼 − 𝛽 ln ∗ 𝑇𝑆 𝑑𝑡 𝑇𝑆0 𝛼 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0…
Slide 16: Tumor growth models
Tumor growth models Gompertz model: ▪ assumes an exponential decay of the relative growth rate 𝑑𝑇𝑆 𝑇𝑆𝑚𝑎𝑥 𝑇𝑆0 𝑒 −𝛽∗𝑡 ∗ln(𝑇𝑆 ) = 𝑇𝑆 ∗ 𝛽 ∗ 𝑙𝑛 𝑇𝑆 = 𝑇𝑆𝑚𝑎𝑥 ∗ 𝑒 𝑚𝑎𝑥 𝑑𝑡 𝑇𝑆 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 Linear scale 𝑇𝑆𝑚𝑎𝑥 𝛽 MonolixSuite training 2021 16
Slide 17: Tumor growth models
Tumor growth models Exponential-Gompertz model: ▪ assumes that the tumor follows at first an exponential growth, and is then akin to a Gompertz model once the nutrients start to go scarce 𝑑𝑇𝑆 𝑇𝑆𝑚𝑎𝑥 = min 𝑘𝑔𝑒 ∗ 𝑇𝑆, 𝛽 ∗ 𝑇𝑆 ∗ ln 𝑇𝑆𝑚𝑎𝑥 𝑑𝑡 𝑇𝑆 𝛽 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 𝑘𝑔𝑒…
Slide 18: Tumor growth models
Tumor growth models Hybrid Simeoni-logistic model: ▪ Hybrid model derived from the Simeoni model that combines exponential, linear and logistic growth. 𝑇𝑆 Linear scale 𝑑𝑇𝑆 𝑘𝑔𝑒 ∗ 𝑇𝑆 ∗ 1 − 𝑇𝑆 𝑚𝑎𝑥 = 1ൗ , 𝑑𝑡 𝜓 𝜓 𝑘𝑔𝑒 1+ ∗ 𝑇𝑆 𝑘𝑔𝑙 𝑘𝑔𝑙 𝑇𝑆𝑚𝑎𝑥 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 ▪ 𝜓…
Slide 19: Tumor growth models
Tumor growth models Von Bertalanffy model: ▪ Model based on balance equations of metabolic processes. The growth is proportional to the surface of the tumor and is limited with a loss term. 3 𝑑𝑇𝑆 2 𝑘𝑔 1ൗ 𝑘𝑔 1 − ∗𝑘𝑑∗𝑡 = 𝑘𝑔 ∗ 𝑇𝑆 ൗ3 − 𝑘𝑑 ∗ 𝑇𝑆 𝑇𝑆 = + 𝑇𝑆0 3 − ∗𝑒 3 𝑑𝑡 𝑘𝑑 𝑘𝑑…
Slide 20: Tumor growth models
Tumor growth models Von Bertalanffy model: ▪ Model based on balance equations of metabolic processes. The growth is proportional to the surface of the tumor and is limited with a loss term. 3 𝑑𝑇𝑆 2 𝑘𝑔 1ൗ 𝑘𝑔 1 − ∗𝑘𝑑∗𝑡 = 𝑘𝑔 ∗ 𝑇𝑆 ൗ3 − 𝑘𝑑 ∗ 𝑇𝑆 𝑇𝑆 = + 𝑇𝑆0 3 − ∗𝑒 3 𝑑𝑡 𝑘𝑑 𝑘𝑑…
Slide 21: Tumor growth models
Tumor growth models Generalized Von Bertalanffy model: ▪ Generalization to a power law growth 1 𝑑𝑇𝑆 𝑘𝑝 1−𝛾 𝑘𝑝 1−𝛾 = 𝑘𝑝 ∗ 𝑇𝑆 𝛾 − 𝑘𝑑 ∗ 𝑇𝑆 𝑇𝑆 = + 𝑇𝑆0 − ∗ 𝑒 − 1−𝛾 ∗𝑘𝑑∗𝑡 𝑑𝑡 𝑘𝑑 𝑘𝑑 0≤𝛾≤1 Linear scale Log scale 𝑇𝑆 𝑡 = 0 = 𝑇𝑆0 𝑇𝑆𝑚𝑎𝑥 𝑘𝑔 𝑘𝑑 = 𝑇𝑆𝑚𝑎𝑥 (1−𝛾)…
Slide 22: Common tumor growth models
Common tumor growth models No saturation Linear Quadratic Exponential Power law Simeoni / Exponential-linear Koch Saturation Gompertz Logistic Generalized logistic Simeoni-logistic Von Bertalanffy Generalized Von Bertalanffy MonolixSuite training 2021 22
Slide 23: Additional TG features
Additional TG features MonolixSuite training 2021 23
Slide 24: Different ways to encode the treatment and initial tumor size
Different ways to encode the treatment and initial tumor size
Slide 25: Encoding initial tumor size
Encoding initial tumor size ▪ TS0 as parameter TS0 in input list TS0 not in data ID TIME Y [LONGITUDINAL] input = {kge, kkill, TS0} 1 -45 98 1 -20 150 EQUATION: 1 0 . odeType=stiff 1 12 112 if t<0 dTS = kge*TS else dTS = kge*TS – kkill*TS ▪ TS0 is not TS at time 0 but at the initial end integration
Slide 26: Encoding initial tumor size
Encoding initial tumor size ▪ TS0 as regressor TS0 in input list TS0 in data ID TIME Y TS0 [LONGITUDINAL] input = {kge, kkill, TS0} 1 -45 98 98 TS0 = {use = regressor} 1 -20 150 . EQUATION: 1 0 . . odeType=stiff 1 12 112 . if t<0 dTS = kge*TS else dTS = kge*TS – kkill*TS ▪ TS0 is not TS at time 0 bu
Slide 27: Encoding treatments
Encoding treatments ▪ Joint model for drug concentration and tumor size PK model in structural model Amounts and dosing times in dataset [LONGITUDINAL] ID TIME AMT Y input = {V, k, TS0, kge, kkill} 1 -45 . 98 1 -20 . 150 PK: Cc = pkmodel(V, k) 1 0 0.02 . 1 12 . 112 EQUATION: odeType=stiff TS_0=TS0 ▪
Slide 28: Encoding treatments
Encoding treatments ▪ Exposure read as regressor EXPOSURE regressor in structural EXPOSURE in dataset model ID TIME EXP Y [LONGITUDINAL] 1 -45 0 98 input = {TS0, EXPOSURE, kge, kkill} 1 -20 0 150 EXPOSURE = {use=regressor} 1 0 0.02 . EQUATION: 1 12 0.02 112 odeType=stiff TS_0=TS0 ▪ EXPOSURE can come
Slide 29: Encoding treatments
Encoding treatments ▪ Exposure read as regressor EXPOSURE regressor in structural EXPOSURE in dataset model ID TIME EXP Y [LONGITUDINAL] 1 -45 0 98 input = {TS0, EXPOSURE, kge, kkill} 1 -20 . 150 EXPOSURE = {use=regressor} 1 0 0.02 . EQUATION: 1 12 . 112 odeType=stiff TS_0=TS0 ▪ EXPOSURE can come fr
Slide 30: Encoding treatments
Encoding treatments ▪ Constant treatment at time 0 If/else in model to apply No treatment information in dataset treatment after time 0 ID TIME Y [LONGITUDINAL] 1 -45 98 input = {TS0, kge, kkill} 1 -20 150 EQUATION: 1 0 . odeType=stiff 1 12 112 if t<0 dTS = kge*TS else dTS = kge*TS – kkill*TS ▪ It i
Slide 31: Encoding treatments
Encoding treatments ▪ Constant treatment at time T read as regressor If/else in model to apply T in dataset treatment after time T ID TIME Y T [LONGITUDINAL] 1 -45 98 5 input = {TS0 , kge, kkill, T} T = {use = regressor} 1 -20 150 5 EQUATION: 1 0 . 5 odeType=stiff 1 12 112 5 if t<T dTS = kge*TS else
Slide 32: Encoding treatments
Encoding treatments ▪ Treatment or not as regressor 0/1 If/else in model to apply treatment Treatment arm in dataset or not depending on the arm ID TIME Y TrtArm [LONGITUDINAL] 1 -45 98 1 input = {TS0, kge, kkill, Trt} Trt = {use = regressor} 1 -20 150 1 EQUATION: 1 0 . 1 odeType=stiff 1 12 112 1 if
Slide 33: Encoding treatments
Encoding treatments MonolixSuite training 2021 33
Slide 34: Common tumor growth inhibition models
Common tumor growth inhibition models
Slide 35: Tumor killing hypothesis
Tumor killing hypothesis Skipper-Schabel-Wilcox log-kill hypothesis: Norton-Simon killing hypothesis: 𝑑𝑇𝑆 𝑑𝑇𝑆 = 𝑔𝑟𝑜𝑤𝑡ℎ − 𝐾 ∗ 𝑇𝑆 = 𝑔𝑟𝑜𝑤𝑡ℎ ∗ (1 − 𝐾) 𝑑𝑡 𝑑𝑡 K = killing of tumor cells [R. Simon and R. Norton: The Norton-Simon hypothesis: designing more effective and less toxic…
Slide 36: Tumor killing hypothesis
Tumor killing hypothesis Skipper-Schabel-Wilcox log-kill hypothesis: Norton-Simon killing hypothesis: 𝑑𝑇𝑆 𝑑𝑇𝑆 = 𝑔𝑟𝑜𝑤𝑡ℎ − 𝐾 ∗ 𝑇𝑆 = 𝑔𝑟𝑜𝑤𝑡ℎ ∗ (1 − 𝐾) 𝑑𝑡 𝑑𝑡 With exponential growth and constant K: The inhibition from the Norton-Simon model depends on the growth rate Constant…
Slide 37: Exposure-dependent killing kinetics
Exposure-dependent killing kinetics MonolixSuite training 2021 37
Slide 38: Delay in tumor growth inhibition
Delay in tumor growth inhibition
Slide 39: Delay for treatment effect
Delay for treatment effect Cell distribution: • The treatment effect is visible from the start but attenuated by the delay • The model garantees a minimal delay independently on the strenght of the treatment effect Signal distribution: • The delay depends strongly on the signal intensity MonolixSuit
Slide 40: Delay in Simeoni model
Delay in Simeoni model Shortcut to Simeoni model (TGI) 40 MonolixSuite training 2021 [Simeoni (2004)]
Slide 41: Common resistance models
Va LIXOFT GB A SIMULATIONS PLUS COMPANY Common resistance models
Slide 42: Resistance: Claret model
Resistance: Claret model Claret model 𝑑𝑇𝑆 kge 𝑡 < 0; = 𝑘𝑔𝑒 ∗ 𝑇𝑆 𝑑𝑡 𝑑𝑇𝑆 𝑡 ≥ 0; = 𝑘𝑔𝑒 ∗ 𝑇𝑆 − 𝑘𝑘𝑖𝑙𝑙 ∗ 𝑒 −𝜆𝑡 ∗ 𝑇𝑆 kge 𝑑𝑡 kkill lambda ANALYTICAL SOLUTION: 𝑡 < 0; 𝑇𝑆 = 𝑇𝑆0 ∗ 𝑒 𝑘𝑔𝑒∗𝑡 𝑘𝑘𝑖𝑙𝑙 𝑘𝑔𝑒∗𝑡− (1−𝑒 −𝜆∗𝑡 ) 𝑡 ≥ 0; 𝑇𝑆 = 𝑇𝑆0 ∗ 𝑒 𝜆 With the…
Slide 43: Resistance: Claret model
Resistance: Claret model Shortcut to exponential Claret with Resistance module analytical solution 43 MonolixSuite training 2021 [Claret et al. (2009)]
Slide 44: Resistance: Claret model
Resistance: Claret model 𝐾′ = 𝐾 ∗ 𝑒 −𝜆∗𝑡 kge • accounts for the loss of drug- induced decay over time due to declining efficacy of the drug kge kkill • 𝜆 – resistance parameter lambda 44 MonolixSuite training 2021 [Claret et al. (2009)]
Slide 45: Resistant population of tumor cells
Resistant population of tumor cells • This model assumes that a fraction of the tumor is resistant to the treatment, thus being killed with a smaller rate than the sensitive part of the tumor. • Several possible variants: kkill*Exposure (kkill(r)* Exposure) ksr growth TSs TSr growth(r) krs kd kd • R
Slide 46: Resistant population of tumor cells
Resistant population of tumor cells Model with initial fraction of resistant cells TS_0=(1-f)*TS0 TSr_0=f*TS0 kge ddt_TS = (kge*TSs)-kkill * EXPOSURE*TS ddt_TSr = (kge*TSr)- kkillr * EXPOSURE*TS TotalTS = TS+TSr kkill f kge, kkillr MonolixSuite training 2021 46
Slide 47: Comparing resistance models
Comparing resistance models MonolixSuite training 2021 47
Slide 48: Common models from literature
Common models from literature Evolutionary model (two populations) 𝑑𝑇𝑆𝑠 = −𝐾 ∗ 𝐸𝑋𝑃𝑂𝑆𝑈𝑅𝐸 ∗ 𝑇𝑆𝑠 , 𝑑𝑡 𝑑𝑇𝑆𝑟 = 𝑘ge ∗ 𝑇𝑆𝑟 , 𝑑𝑡 𝑇𝑆𝑠 𝑡 = 0 = 𝑇𝑆0 ∗ 1 − 𝑓 𝑇𝑆𝑟 𝑡 = 0 = 𝑇𝑆0 ∗ 𝑓 𝑇𝑆 = 𝑇𝑆𝑠 + 𝑇𝑆𝑟 ANALYTICAL SOLUTION for constant exposure 𝑇𝑆 = 𝑇𝑆0 ∗ (𝑓 ∗ 𝑒…
Slide 49: Common models from literature
Common models from literature Stein regression-growth model Stein regression-growth Exponential regrowth: 𝑇𝑆0 ∗ 𝑒𝑘ge∗𝑡 𝑡 < 0; 𝑇𝑆 = 𝑇𝑆0 ∗ 𝑒𝑘𝑔𝑒∗𝑡 Exponential decay: 𝑇𝑆0 ∗ 𝑒 −𝑘𝑘𝑖𝑙𝑙 ∗𝑡 𝑡 ≥ 0; 𝑇𝑆 = 𝑇𝑆0 ∗ (𝑒 −𝑘𝑘𝑖𝑙𝑙 ∗𝑡 + 𝑒 𝑘𝑔𝑒∗𝑡 − 1) MonolixSuite training 2021…
Slide 50: Common models from literature
Common models from literature Ribba model 𝑑𝑃 𝑇𝑜𝑡𝑎𝑙𝑇𝑆 = 𝑘𝑝 ∗ 𝑃 1 − + 𝑘𝑄𝑝𝑃 ∗ 𝑄𝑝 − 𝑘𝑃𝑄 ∗ 𝑃 − 𝐾 ∗ 𝑘𝑒 ∗ 𝐸𝑋𝑃𝑂𝑆𝑈𝑅𝐸 ∗ 𝑃 𝑑𝑡 𝑇𝑆𝑚𝑎𝑥 𝑑𝑄 = 𝑡𝑃𝑄 ∗ 𝑃 − 𝑘𝑄 ∗ 𝑘𝑒 ∗ 𝐸𝑋𝑃𝑂𝑆𝑈𝑅𝐸 ∗ 𝑄 𝑑𝑡 𝑑𝑄𝑝 = 𝑘𝑄 ∗ 𝑘𝑒 ∗ 𝐸𝑋𝑃𝑂𝑆𝑈𝑅𝐸 ∗ 𝑄 − 𝑘𝑄𝑝𝑃 ∗ 𝑄𝑝 − 𝑘𝑑 ∗…
Slide 51: Good practices for model definition in Monolix
Good practices for model definition in Monolix
Slide 52: Tumor growth models
Tumor growth models ▪ Model with analytical solution ❑ Example: exponential-linear [LONGITUDINAL] input = {TS0, kge, kgl} EQUATION: TransitionTime = 1/kge*log(kgl/(kge*TS0)) if t<TransitionTime TS = TS0*exp(kge*t) else TS = kgl*(t-TransitionTime)+TS0*exp(kge*TransitionTime) end OUTPUT: output = {TS}
Slide 53: Tumor growth models
Tumor growth models ▪ Model with analytical solution ❑ Example: exponential-linear [LONGITUDINAL] input = {TS0, kge, kgl} EQUATION: TransitionTime = 1/kge*log(kgl/(kge*TS0)) Saturation to avoid if t<TransitionTime infinitely large values TS = min(1e12, TS0*exp(kge*t)) else TS = min(1e12, kgl*(t-Tran
Slide 54: Tumor growth models
Tumor growth models ▪ Model based on ODE system ❑ Example: Simeoni [LONGITUDINAL] input = {TS0, kge, kgl, psi} EQUATION: odeType=stiff ;defining initial conditions of the model: ;t_0=0 TS_0=TS0 ;model description: if TS < 1e12 dTS = (kge*TS/(1+(kge/kgl*max(0,TS))^psi)^(1/psi)) else dTS = 0 end ddt_T
Slide 55: Tumor growth models
Tumor growth models ▪ Model based on ODE system ❑ Example: Simeoni [LONGITUDINAL] input = {TS0, kge, kgl, psi} EQUATION: odeType=stiff ;defining initial conditions of the model: ;t_0=0 TS_0=TS0 ;model description: if TS < 1e12 dTS = (kge*TS/(1+(kge/kgl*max(0,TS))^psi)^(1/psi)) else dTS = 0 end ddt_T
Slide 56: Tumor growth models
Tumor growth models ▪ Model based on ODE system ❑ Example: Simeoni [LONGITUDINAL] input = {TS0, kge, kgl, psi} • Initial integration time • Can be negative EQUATION: odeType=stiff • Default value if not indicated: ;defining initial conditions of the model: time of first dose or observation, ;t_0=0 v
Slide 57: Tumor growth models
Tumor growth models ▪ Model based on ODE system ❑ Example: Simeoni Without t_0 = 0 With t_0 = 0 MonolixSuite training 2021 57
Slide 58: Combination therapy in lung cancer xenografts
Combination therapy in lung cancer xenografts Example 1 58
Slide 59: Introduction
Introduction Case study based on data published and modeled in: • Imbs et al. (2018). Revisiting Bevacizumab + Cytotoxics Scheduling Using Mathematical Modeling: Proof of Concept Study in Experimental Non-Small Cell Lung Carcinoma. CPT: PSP. • Schneider et al. (2019). Optimal Scheduling of Bevacizum
Slide 60: Introduction: lung cancer dataset
Introduction: lung cancer dataset Tumor size Dataset overview: • 77 xenografts of initially 120000 H460 Luc+ dTomato+ cells, tracked with fluorescence Measurements: • OBSID = 1 - tumor size (relative fluorescence unit) • OBSID = 2 - survival Treatments: • 3 drugs, each given 3 times every 2 weeks •
Slide 61: Tumor growth models
Tumor growth models Data for control group in log scale Which tumor growth model? Data for control group in log scale • Not exponential nor linear models • No clear carrying capacity MonolixSuite training 2021 61
Slide 62: Tumor growth inhibition data
Tumor growth inhibition data Data for Chemo group: treatment Data for all groups except Control: bevacizumab seems to make a difference with effect is small, and seems delayed concomitant administration and 3-days gap, but not with 8-days gap MonolixSuite training 2021 62
Slide 63: Survival data
Survival data Survival data split by Group MonolixSuite training 2021 63
Slide 64: Modeling workflow
Modeling workflow The modeling workflow can be done in 4 steps: 1. Tumor growth model estimated on Control group Use last estimates 2. Tumor growth inhibition model for chemotherapy estimated on Chemo group Use last estimates 3. Tumor growth inhibition model for chemotherapy combined with bevacizuma
Slide 65: Step 1: Tumor growth models
Step 1: Tumor growth models MonolixSuite training 2021 65
Slide 66: Step 1: Tumor growth models
Step 1: Tumor growth models Exponential-linear Koch Logistic The exponential-linear (or Simeoni) model with a sharp switch between exponential and linear phases gives the best results MonolixSuite training 2021 66
Slide 67: Step 2: TGI
Step 2: TGI Possible inhibition model for the effect of chemotherapy: Killing hypothesis: • Log-kill • Norton-Simon Dynamics: • First-order • Michaelis-Menten • Hill • Exponential Delay: • Cell distribution • Signal distribution ➔ 16 combinations ➔ The library allows to easily test different hypothe
Slide 68: Step 2: TGI
Step 2: TGI [LONGITUDINAL] input = {TS0, kge, kgl, psi, kkill, tau, V, k} EQUATION: Best model from the library: odeType=stiff PK: Simeoni tumor growth with ;initial conditions of the model: Norton-Simon linear killing and EXPOSURE = pkmodel(V, k) signal distribution t_0=0 TS_0=TS0 K1_0=0 K2_0=0 K3_
Slide 69: Step 2: TGI
Step 2: TGI [LONGITUDINAL] input = {TS0, kge, kgl, psi, kkill, tau} EQUATION: Model from the library: odeType=stiff PK: Simeoni tumor growth with ;initial conditions of the model: Norton-Simon linear killing and signal distribution t_0=0 TS_0=TS0 K1_0=0 K2_0=0 Extension of the model: K3_0=0 ;=======
Slide 70: Step 3: Combination therapy
Step 3: Combination therapy [LONGITUDINAL] input = {TS0, kge, kgl, psi, kkill, tau, delta, Tlag} EQUATION: Model from the library: odeType=stiff PK: Simeoni tumor growth with ;=======bevacizumab ;initial conditions of the model: Norton-Simon linear killing and ka_b = 2.6875 k_b = 0.1143 signal distr
Slide 71: Step 3: Combination therapy
Step 3: Combination therapy ▪ The final project is given in: starting_material/2_TGI/r01_trtcomb.mlxtran ▪ Inter-individual variability was removed on several parameters ▪ Correlation group with eta_kge, eta_kgl, eta_TS0 ▪ Good RSEs MonolixSuite training 2021 71
Slide 72: Step 4: joint TGI-TTE model
Step 4: joint TGI-TTE model Survival model: delayed Weibull after TS reaches a threshold TSth … ; computing time when TS>TSth TimeTSth_0 = 0 if TS < TSth xTime = 1 else xTime = 0 end ddt_TimeTSth = xTime ; hazard if TS < TSth h=0 else h = p/Te * max(1e-6,(t-TimeTSth)/Te)^(p-1) Definition of hazard f
Slide 73: Step 4: joint TGI-TTE model
Step 4: joint TGI-TTE model TTE VPC split by group MonolixSuite training 2021 73
Slide 74: PSA in metastatic Castration-Resistant Prostate Cancer treated with chemotherapy
PSA in metastatic Castration-Resistant Prostate Cancer treated with chemotherapy Example 2 74
Slide 75: Introduction: PSA + survival dataset
Introduction: PSA + survival dataset ▪ Published in: ❑ Desmée, S. et al. (2017). Using the SAEM algorithm for mechanistic joint models characterizing the relationship between nonlinear PSA kinetics and survival in prostate cancer patients. Biometrics, 73(1), 305–312. ❑ Data from the control arm of p
Slide 76: Data set
Data set Treatment period Regressors LOQ Covariates for Dummy doses 1 = PSA concentration stratification to visualize → marker of tumor size start and end 2 = death of treatment MonolixSuite training 2021 76
Slide 77: Introduction: PSA + survival dataset
Introduction: PSA + survival dataset Treatment period TGI data shows emergence of resistance Time=0: Start of treatment MonolixSuite training 2021 77
Slide 78: TGI model with Claret resistance
TGI model with Claret resistance [LONGITUDINAL] input = {TS0, kge, kkill, lambda} TS0 = {use=regressor} Model from library: EQUATION: • Exponential growth and log-kill treatment effect odeType=stiff • No fixed initial time • TS0 read as regressor TS_0=TS0 • Treatment effect applied after time 0 K =
Slide 79: TGI model with Claret resistance
TGI model with Claret resistance [LONGITUDINAL] input = {TS0, TimeEndTrt, kge, kkill, lambda} TS0 = {use=regressor} Model from library: TimeEndTrt = {use=regressor} EQUATION: • Exponential growth and log-kill treatment effect odeType=stiff • No fixed initial time • TS0 read as regressor TS_0=TS0 • T
Slide 80: TGI model with Claret resistance
TGI model with Claret resistance Result for exponential tumor growth and log-kill ➔ Need for a maximal tumor size ➔ After comparing several options, the Simeoni-logistic function gives the best result MonolixSuite training 2021 80
Slide 81: TGI model with Claret resistance
TGI model with Claret resistance Comparing Norton-Simon and log-kill treatment effects → LK gives the best results Log-kill Norton-Simon MonolixSuite training 2021 81
Slide 82: Comparing different hypotheses
Comparing different hypotheses Comparing resistance models: Comparing delays: → two population model than Claret resistance → Cell distribution gives better results than signal distribution Claret 2 pop Signal distribution Cell distribution MonolixSuite training 2021 82
Slide 83: Final model
Final model MonolixSuite training 2021 83
Slide 84: VPC bias
VPC bias VPC split by maximal time of observation Under-prediction for small maxTime and over-prediction for large maxTime might be a VPC dias due to non-random dropout MonolixSuite training 2021 84
Slide 85: Dropout and VPC
Dropout and VPC Tumor progression Simulations for VPC VPC without dropout Empirical percentiles Prediction intervals MonolixSuite training 2021
Slide 86: Dropout and VPC
Dropout and VPC Tumor progression Simulations for VPC VPC with dropout Empirical percentiles Prediction intervals MonolixSuite training 2021
Slide 87: Va LIXOFT
Va LIXOFT
Slide 88: Additional tumor growth features
Additional tumor growth features
Slide 89: Additional TG features
Additional TG features MonolixSuite training 2021 89
Slide 90: Additional TG features
Additional TG features Logistic growth with dynamic TSmax due to angiogenesis Stimulatory capacity of the tumor upon the vasculature Intrinsic loss rate via angiogenic factors Endogenous inhibition of previously generated vasculature by inhibition of endothelial cell proliferation, via inhibitors re
Slide 91: Additional TG features
Additional TG features Exponential growth with immune dynamics model Killing of tumor cells by effector immune cells Constant source rate and death Effector cells are inactivated proportional to the population through contact with tumor of effector cells cells according to a mass- action dynamic Eff
Slide 92: Additional TG features
Additional TG features 92 MonolixSuite training 2021 [de Pillis et al. (2006)]
Slide 93: Tumor growth models
Tumor growth models ▪ Model based on ODE system ❑ Example: Simeoni [LONGITUDINAL] input = {TS0, kge, kgl, psi} Statement to use the stiff ODE solver. EQUATION: Default ODE solver: non-stiff odeType=stiff ;defining initial conditions of the model: t_0=0 TS_0=TS0 ;model description: ddt_TS = (kge*TS/(
Slide 94: Tumor killing hypothesis
Tumor killing hypothesis Skipper-Schabel-Wilcox log-kill hypothesis: Norton-Simon killing hypothesis: 𝑑𝑇𝑆 𝑑𝑇𝑆 = 𝑔𝑟𝑜𝑤𝑡ℎ − 𝐾 ∗ 𝑇𝑆 = 𝑔𝑟𝑜𝑤𝑡ℎ ∗ (1 − 𝐾) 𝑑𝑡 𝑑𝑡 With exponential-linear growth: With a Gompertz growth and multiple doses: Constant treatment “the chance of eradicating…
Slide 95: Dropout and VPC
Dropout and VPC Tumor progression Simulations for VPC VPC with dropout and censored observations Empirical percentiles Prediction intervals MonolixSuite training 2021
Slide 96: Dropout and VPC
Dropout and VPC Tumor progression Simulations for VPC VPC with dropout and censored observations Empirical percentiles Prediction intervals Simulated censored observations are sampled from the conditional distribution: 𝜃) 𝑝 𝑦𝐵𝐿𝑄 𝑦𝑛𝑜𝑛𝐵𝐿𝑄 , 𝜓, መ MonolixSuite training 2021
Slide 97: VPC correction for censored observations
VPC correction for censored observations Adding censored observations until time 1500 for all ids: Dropout Censored observations added after dropout MonolixSuite training 2021 97
Slide 98: VPC correction for censored observations
VPC correction for censored observations Empirical percentiles take into account missing times via simulated observations (based on the model) MonolixSuite training 2021 98
Simulations Plus — Technical Presentation (March 2021) on 6ix