# Model-driven optimization of the scheduling of a novel anti-cancer prodrug administered subcutaneously

Anne Rodallec

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## To cite this version:

Anne Rodallec. Model-driven optimization of the scheduling of a novel anti-cancer prodrug administered subcutaneously. Pharmacometrics in France, Sep 2024, Paris, France. hal-04726595

HAL Id: hal-04726595

https://hal.science/hal-04726595v1

Submitted on 20 Nov 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Inria

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Inserm

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COMPO

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COMPUTATIONAL ONCOLOGY

# Model-driven optimization of the scheduling of a novel anti-cancer prodrug administered subcutaneously

Dr Anne Rodallec

COMPO - COMputational Pharmacology in Oncology

CRCM

Conseil de Ressources en Canalogie de Marseille

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Faculté de Pharmacie

Aix-Marseille Université
<figure><img src="image_8.png" /><figcaption>Dr S Benzekry & Pr J Ciccolini</figcaption></figure>

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* Taxanes: poor solubility and toxicities (Cremophor EL)

* Development of new hydrophilic polymers (Applied to Paclitaxel)

* Subcutaneous administration

* Cheaper

* Less toxic, safe

* More comfortable

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<figure><img src="image_11.png" /><figcaption>Dr Julien Nicolas</figcaption></figure>

université
PARIS-SACLAY

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<figure><img src="image_17.png" /><figcaption>Dr Julien Nicolas</figcaption></figure>

université
PARIS-SACLAY

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erc

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cnrs

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### Thermonano working plan

- Polymer synthesis

- Screening

- PK studies

- PD studies

- Data analysis

- Optimization
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Data PK n=4

→ Longer exposure

→ Higher MTD

→ Higher efficacy

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Data PD n=9

Time after tumor inoculation (days)

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1. Experimental data from Julien Nicolas' team

2. Pop PK Modeling

3. PK results

4. PD Modeling

5. Implementation of Pop_PK results in PD Model

6. Final results

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Non longitudinal data
Proportionnal error model set at 10%

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<footnote>* Defined by the model; parameters without RE</footnote>
IV PTX

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SC PTX-PAAm

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<table><thead><tr><th>PARAMETER</th><th>ESTIMATE</th><th>RSE %</th></tr></thead><tbody><tr><td colspan="3">FIXED EFFECT</td></tr><tr><td>V1 (ml)</td><td>10.73</td><td>5.82</td></tr><tr><td>K<sub>12</sub></td><td>0.65</td><td>12.8</td></tr><tr><td>K<sub>21</sub></td><td>0.51</td><td>0.0852</td></tr><tr><td>K<sub>8</sub></td><td>2.76</td><td>0.134</td></tr><tr><td>K<sub>h</sub></td><td>0.047</td><td>13.5</td></tr><tr><td colspan="3">STANDARD DEVIATION OF THE RANDOM EFFECT</td></tr><tr><td>ΩV1</td><td>0.26</td><td>19.4</td></tr><tr><td>ΩK<sub>12</sub></td><td>0.21</td><td>37</td></tr><tr><td>ΩK<sub>8</sub></td><td>0.57</td><td>19.9</td></tr></tbody></table>

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Pop-PK (fixed)

Untreated tumor growth

Drug Effect

Drug Resistance

$$ \text{Exponential} \qquad \frac{dTV}{dt} = \lambda \cdot TV $$

$$ \text{Power Law} \qquad \frac{dTV}{dt} = \alpha \cdot TV^{\gamma} $$

$$ \text{Logistic} \qquad \frac{dTV}{dt} = \lambda \cdot TV \cdot \left(1 - \frac{TV}{TV_{max}}\right) $$

$$ \text{Gompertz} \qquad \frac{dTV}{dt} = \alpha \cdot \exp((-\beta \cdot t)) \cdot TV $$

$$ \text{Reduced Gompertz} \qquad \frac{dTV}{dt} = (\beta \cdot \gamma) - \beta \cdot \log\left(\frac{TV}{TV_0}\right) \cdot TV $$

TV = tumor volume (mm³), TV₀ = initial tumor volume (i.e., 10, because 10 millions of cells were first inoculated), t = time (hours)
## Model PD: Untreated Tumor Growth

<table><thead><tr><th>Model</th><th>-2LL</th><th>AIC</th><th>Nber of para (F + R)</th></tr></thead><tbody><tr><td>Logistic</td><td>1388</td><td>1394</td><td>4 (2+2)</td></tr><tr><td>Gompertz</td><td>1394</td><td>1408</td><td>4 (2+2)</td></tr><tr><td>Reduced Gompertz</td><td>1415</td><td>1425</td><td>3 (2+1)</td></tr><tr><td>Power Law</td><td>1421</td><td>1433</td><td>3 (2+1)</td></tr><tr><td>Exponential</td><td>1549</td><td>1557</td><td>3 (1+1)</td></tr></tbody></table>

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Logistic

Reduced Gompertz
saturation

Vaghi C, Rodallec A, Fanciullino R, Ciccolini J, Mochel JP, Mastri M, Poignard C, Ebos JML, Benzekry S. Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS Comput Biol. 2020 Feb 25;16(2):e1007178.

COMPO

COMPUTATIONAL ONCOLOGY

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Inserm

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Pop-PK (fixed)

Reduced Gompertz

Drug Effect

Drug Resistance

**Log Kill**

$$ \frac{dTV}{dt} = G - e \cdot C \cdot TV $$

**Norton Simon**

$$ \frac{dTV}{dt} = G - e \cdot C \cdot G $$

**Iliadis Barbolosi**

$$ \frac{dTV}{dt} = G - e \cdot (C - C_{min})^+ \cdot TV $$

**Simeoni**

$$ \frac{dTV_1}{dt} = G - k_{tran} \cdot C \cdot TV_1 $$

$$ \frac{dTV_2}{dt} = k_{tran} \cdot C \cdot TV_1 - k_{tran} \cdot TV_2 $$

$$ \frac{dTV_3}{dt} = k_{tran} \cdot (TV_2 - TV_3) $$

$$ \frac{dTV_4}{dt} = k_{tran} \cdot (TV_3 - TV_4) $$

G = the tumor growth term, C = PTX free concentration (µg/ml)

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Model PD: drug effect

<table><thead><tr><th>Model</th><th>-2LL</th><th>AIC</th><th>Nber of para (F + R)</th></tr></thead><tbody><tr><td>Simeoni</td><td>5624</td><td>5632</td><td>2 (1+1)</td></tr><tr><td>Iliadis Barbolosi</td><td>5636</td><td>5646</td><td>4 (2+2)</td></tr><tr><td>Log Kill</td><td>5637</td><td>5646</td><td>2 (1+1)</td></tr><tr><td>Norton Simon</td><td>5684</td><td>5692</td><td>2 (1+1)</td></tr></tbody></table>

Simeoni

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misspecification

Iliadis Barbolosi

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Time (hours)

Log Kill

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Pop-PK (fixed)

Tumor growth

Drug effect

Drug Resistance

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* Defined by the model; parameters without RE, ** Resistance acquired after second administration

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VPC

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Prediction
distribution

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Individual fit

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<table><thead><tr><th>PARAMETER</th><th>ESTIMATE</th><th>RSE %</th></tr><tr><th colspan="3">FIXED EFFECT</th></tr></thead><tbody><tr><td>V1 (ml)</td><td>10.73</td><td>5.82</td></tr><tr><td>K<sub>12</sub></td><td>0.65</td><td>12.8</td></tr><tr><td>K<sub>21</sub></td><td>0.51</td><td>0.0852</td></tr><tr><td>K<sub>e</sub></td><td>2.76</td><td>0.134</td></tr><tr><td>K<sub>b</sub></td><td>0.047</td><td>13.5</td></tr><tr><td>γ</td><td>7.17</td><td>5.25</td></tr><tr><td>β</td><td>0.0013</td><td>10.3</td></tr><tr><td>ktran</td><td>0.05</td><td>0.402</td></tr><tr><td>Emax1</td><td>15.48</td><td>40.1</td></tr><tr><td>Emax2</td><td>13.8</td><td>3.51</td></tr><tr><td>EC50</td><td>462.7</td><td>1.16</td></tr></tbody></table>

<table><thead><tr><th colspan="2">SD OF THE RANDOM EFFECT</th></tr></thead><tbody><tr><td>ΩV1</td><td>0.26</td><td>19.4</td></tr><tr><td>ΩK<sub>12</sub></td><td>0.21</td><td>37</td></tr><tr><td>ΩK<sub>b</sub></td><td>0.57</td><td>19.9</td></tr><tr><td>ΩK<sub>β</sub></td><td>0.15</td><td>24.5</td></tr><tr><td>ΩEmax1</td><td>1.23</td><td>25.4</td></tr></tbody></table>

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Prediction of SC PTX-PAAm 60 mg/kg group using our final PK/PD model on Simulx®

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MTD: 60mg/kg

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> 180mg/kg

MRT: 0.9H

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22.2H

<table><thead><tr><td>Treatment groups</td><td>Total dose (µg)</td><td>Loading dose (µg - mg/kg)</td><td>Treatment dose (µg - mg/kg)</td><td>Consolidation treatment (µg - mg/kg)</td><td>Number of administrations</td></tr></thead><tbody><tr><td>Group 1</td><td>3960</td><td>-</td><td>1320 - 60</td><td>-</td><td>3</td></tr><tr><td>Group 2</td><td>3960</td><td>-</td><td>3960 - 180</td><td>-</td><td>1</td></tr><tr><td>Group 3</td><td>3969</td><td>-</td><td>189 - 8.6</td><td>-</td><td>21</td></tr><tr><td>Group 4</td><td>3961</td><td>1320 - 60</td><td>-</td><td>139 - 6.3</td><td>19</td></tr><tr><td>Group 5</td><td>6601</td><td>3960 - 180</td><td>-</td><td>139 - 6.3</td><td>19</td></tr><tr><td>Group 6</td><td>6594</td><td>-</td><td>314 - 14.3</td><td>-</td><td>21</td></tr><tr><td>Group 7</td><td>11883</td><td>3960 - 180</td><td>-</td><td>417 - 19</td><td>19</td></tr></tbody></table>

MTD: Maximal tolerated dose; MRT: Mean residence time

Unpublished data

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* Predictive PK/PD Model

→ interest of Loading dose (180 mg/kg)

→ + daily adm. (14.3-19 mg/kg)

* Limits:

→ Different doses for PK and PD data -> No data on PK linearity

→ Lack of safety studies (no toxicity observed)

* Perspectives:

→ Model optimization using the new data

→ Applications to new polymers and other linked chemotherapies (i.e., vinblastine)

→ Further mechanistic modeling of the resistance

→ Testing new device for daily administration
Needle

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Mice actuator

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<figure><img src="image_79.png" /><figcaption>Dr Patricia Piris</figcaption></figure>

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# Thank you!

Inria

Offre n°2024-08121

Post-Doctoral Research Visit F/M Optimization of therapeutic strategies for pediatric cancers using mathematical modeling of intra-tumor heterogeneity

**Contract type** : Fixed-term contract

**Level of qualifications required** : PhD or equivalent

**Fonction** : Post-Doctoral Research Visit

**Level of experience** : Recently graduated

Contact:
sebastien.benzekry@inria.fr

**ZEUS** project: ARTIFICIAL INTELLIGENCE TO OPTIMIZE CYTARABINE IN LEUKEMIA PATIENTS

☑ Position: Post-Doctoral Fellowship

☑ Duration: 24 months, full-time

☑ Starting: ASAP

☑ Location: COMPO Team, School of Pharmacy, Timone Health Campus, Marseille France

☑ Employer: Aix Marseille Uni

☑ Required skills: Pharmacometrics, Pop-PK, Machine Learning & Coding, Data Analysis, Oncology

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Contact:
raphaelle.fanciullino@univ-amu.fr

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COMPO
COMPUTATIONAL ONCOLOGY

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Institut
Laennec,
sciences numériques
et IA pour la santé
Aix-Marseille Université

COMPO
COMPUTATIONAL ONCOLOGY

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Inserm

Inria
Overview of the tested efficacy models to fit the PD data
(Randy. Lee)

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Overview of the tested efficacy models that were extended with resistance
(Randy. Lee)

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Biological reasoning behind the observed resistance model

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"MDR1 transcript expression was elevated by the fourth week in the 10-MET group, but a single treatment of 10 nM was insufficient to promote MDR1 expression at week 1. In contrast, a single treatment of 25 nM PTX was sufficient to increase expression at week 1"

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Comparaison experiment June 2019 and 2024

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Subcutaneous injection and bioavailability

<caption>TABLE 1
Overview of marketed IgGs and IgG Fc-fusion proteins administered via the subcutaneous route</caption>

Data on time to maximum serum concentration and bioavailability collected from the European Medicines Agency (EMA) Summary of Product Characteristics (http://www.ema.europa.eu/ema/index.jsp?uri=pages/home/Home_Page.jsp&mid=), EMA assessment reports, or the Food and Drug Administration homepage (http://www.accessdata.fda.gov/scripts/center/drugsatfa).

<table><thead><tr><th>INN Name</th><th>Trade Name</th><th>Antibody Type</th><th>Target</th><th>T<sub>max</sub> in Humans</th><th>Bioavailability in Humans and Animals</th></tr><tr><th></th><th></th><th></th><th></th><th>days</th><th>%</th></tr></thead><tbody><tr><td>Adalimumab</td><td>Humira</td><td>IgG1</td><td>TNF</td><td>5.5</td><td>Humans: 64<br>Cynomolgus monkey: 96</td></tr><tr><td>Canakinumab</td><td>Ilaris</td><td>IgG1</td><td>IL-1β</td><td>7</td><td>Humans: 70<br>Marmoset: 60</td></tr><tr><td>Denosumab</td><td>Prolia</td><td>IgG2</td><td>RANK-L</td><td>10</td><td>Humans: 78<br>Mice: 86<br>Cynomolgus monkey: 28–100<sup>a</sup></td></tr><tr><td>Golimumab</td><td>Simponi</td><td>IgG1</td><td>TNF</td><td>2–6</td><td>Humans: 53<br>Cynomolgus monkey: 77</td></tr><tr><td>Omalizumab</td><td>Xolair</td><td>IgG1</td><td>IgE</td><td>7–8</td><td>Humans: 62<br>Mice: 90<br>Cynomolgus monkey: 64–104</td></tr><tr><td>Rituximab</td><td>Mabthera</td><td>IgG1</td><td>CD20</td><td>3</td><td>Humans: 71<br>Mice: 63<br>Minipig: 71</td></tr><tr><td>Tocilizumab</td><td>Actemra / RoActemra</td><td>IgG1</td><td>IL-6R</td><td>—</td><td>Humans: 80<br>Minipig: 84<br>Cynomolgus monkey: 72</td></tr><tr><td>Trastuzumab</td><td>Herceptin</td><td>IgG1</td><td>HER2</td><td>3</td><td>Humans: 82<br>Mice: 83<br>Minipig: 82<br>Cynomolgus monkey: ca. 100</td></tr><tr><td>Ustekinumab</td><td>Stelara</td><td>IgG1</td><td>IL-12/23p40</td><td>8.5</td><td>Humans: 57 (24–95)<br>Cynomolgus monkey: 97</td></tr><tr><td>Abatacept</td><td>Orencia</td><td>Fc-fusion protein</td><td>CD80/86</td><td>3–5</td><td>Humans: 79<br>Mice: 78–110<br>Rat: 41–63</td></tr><tr><td>Etanercept</td><td>Enbrel</td><td>Fc-fusion protein</td><td>TNF</td><td>3</td><td>Humans: 76<br>Mice: 58<br>Cynomolgus monkey: 73</td></tr><tr><td>Rilonacept</td><td>Arcalyst</td><td>Fc-fusion protein</td><td>IL-1α, IL-1β, IL-1ra</td><td>—</td><td>Humans: 43<br>Mice: 78<br>Rats: 54<br>Cynomolgus monkey: 70</td></tr><tr><td>Romiplostim</td><td>Nplate</td><td>Fc-fusion protein</td><td>Thrombopoietin receptor</td><td>0.6</td><td>Humans: —<br>Rats: 21–28<br>Cynomolgus monkey: 19<br>Rhesus monkey: 45–74</td></tr></tbody></table>

If > 20 KDa:

first-pass catabolism at the subcutaneous administration site or in the draining lymphatics

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Non compartmental PK

<table><caption>Table 2. Main Pharmacokinetic Parameters of Free Ptx Determined by LC-MS/MS after IV Injection of Taxol (Taxol<sup>IV</sup>) at 7 mg kg<sup>-1</sup> and after SC Injection of P3d<sup>SC</sup>, P3e<sup>SC</sup>, and P3c<sup>SC</sup> at 7 mg kg<sup>-1</sup> (Ptx equiv)</caption><thead><tr><td>parameter</td><td>Taxol<sup>IV</sup></td><td>P3d<sup>SC</sup></td><td>P3e<sup>SC</sup></td><td>P3c<sup>SC</sup></td></tr></thead><tbody><tr><td>t<sub>1/2</sub> (h)</td><td>1.7</td><td>1.5</td><td>13.9</td><td>1.6</td></tr><tr><td>t<sub>max</sub> (h)</td><td>0.25</td><td>1</td><td>1</td><td>2</td></tr><tr><td>C<sub>max</sub> (ng mL<sup>-1</sup>)</td><td>4657</td><td>310</td><td>105</td><td>41</td></tr><tr><td>AUC<sub>0-&infin;</sub> (ng mL<sup>-1</sup> h)</td><td>4631</td><td>986</td><td>1299</td><td>186</td></tr><tr><td>MRT (h)</td><td>0.9</td><td>2.5</td><td>22.2</td><td>3.3</td></tr><tr><td>apparent bioavailability<sup>a</sup> (%)</td><td>100</td><td>21</td><td>28</td><td>4</td></tr></tbody></table>

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