# Mechanistic Modeling of Joint Circulating Cell-free DNA Concentration-Tumor Size Kinetics under Immune-Checkpoint Inhibitors in Advanced Cancer

Linh Nguyen Phuong, Frederic Fina, Romain Zakrajsek, Lucie Della-Negra, Pascale Tomasini, Jean-Laurent Deville, Laurent Greillier, Caroline Gaudy-Marqueste, Audrey Boutonnet, Frédéric Ginot, et al.

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## ► To cite this version:

Linh Nguyen Phuong, Frederic Fina, Romain Zakrajsek, Lucie Della-Negra, Pascale Tomasini, et al. Mechanistic Modeling of Joint Circulating Cell-free DNA Concentration-Tumor Size Kinetics under Immune-Checkpoint Inhibitors in Advanced Cancer. PAGE 2025 - 33th Annual meeting of the Population Approach Group of Europe, Jun 2025, Thessalokini, Greece. hal-05241536

HAL Id: hal-05241536

https://inria.hal.science/hal-05241536v1

Submitted on 5 Sep 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Mechanistic Modeling of Joint Circulating Cell-free DNA Concentration—Tumor Size Kinetics under Immune-Checkpoint Inhibitors in Advanced Cancer

L. Nguyen Phuong, F. Fina, R. Zakrajsek, L. Della Negra, P. Tomasini, J.-L. Deville, L. Greillier, C.

Gaudy-Marqueste, A. Boutonnet, F. Ginot, J.-C. Garcia, S. Salas, S. Benzekry

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Size

Cell-free DNA

Immunotherapy

Signature

Monitoring
# Immunotherapy in oncology: how to predict progression?

* 2011+ : FDA approval of immune-checkpoint inhibitors (ICI) targeting PD-1)

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* 20-40 % long-term response<fnref n="1" />

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## PREDICTING PROGRESSION?

**Gold standard biomarkers:** PD-L1 expression (+ TMB)

**New biomarker:** liquid biopsy<fnref n="2" /> → Circulating cell-free DNA (cfDNA)

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Half-life: 15min-2h

Non-invasive

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Systemic

Cost-effective

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<footnote n="1">¹Gilberto De Castro et al., J Clin Oncol, 2022; Sharma et al., Cell, 2017</footnote>

<footnote n="2">²Siravegna et al., Nat Rev Clin Oncol, 2017</footnote>

<footnote n="3">³Ribba et al., Front Pharmacol, 2023</footnote>
# CfDNA size profile as a promising biological marker

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adelis
ADVANCED
SEPARATIVE
TECHNOLOGIES

## µLAS technology:

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* Independent of genome position

* No need of prior DNA extraction

* Only needs 1 µL of plasma

* Cost-effective ~ 15€/sample

* 2 bp - accuracy on fragments sizes

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<figure><img src="image_15.png" /></figure>

* Apoptosis

* Necrosis

* Active secretion

<figure><img src="image_16.png" /></figure>
<figure><img src="image_17.png" /></figure>

Develop a **mechanistic model** of the **joint cfDNA – tumor kinetics (TK)** in advanced cancer patients undergoing ICI

Assess pre-treatment **cfDNA size profiles** and **early, on-treatment, model-based parameters** as predictors of immunotherapy resistance
# SChISM: Size CfDNA Immunotherapy Signature Response

126 patients

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Head and
neck
(HNSCC)

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Lung
(NSCLC)

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Kidney
(ccRCC)

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Bladder
(UC)

ICI

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Cycle 1

Cycle 2

Cycle 3

~ 3 months:
progression ?

<figure><img src="image_25.png" /></figure>

## Outcomes:

* Early progression (EP)

* Progression-free survival (PFS)
# SChISM: Size CfDNA Immunotherapy Signature Response

## Clinical variables

Age, tumor type, sex, Eastern Cooperative Oncology Group (ECOG)

## Biological variables

Neutrophil to lymphocyte ratio (NLR)

Lactate dehydrogenase level (LDH)

## CfDNA variables

Total concentration (pg/µl) $C_{TOT}$

Location of the peaks (bp) $P_1, P_2$

Height of the peaks (pg/µl) $HP_1, HP_2$

Half-width of first peak $HW_1$

Absolute concentrations (pg/µl): $C_{a→b}$

Relative concentrations $R_{a→b}$ (over $C_{TOT}$)

<figure><img src="image_26.png" /></figure>

16 cfDNA-derived variables
High proportion of long fragments at baseline is associated with response

<figure><img src="image_27.png" /></figure>
Patients cluster according to their fragment size distribution

Short
fragments

Long
fragments

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Short and long fragments showed different kinetics

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Lesion type - Non-target - Target
Short and long fragments showed different kinetics

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# Joint modeling of tumor and size-dependent cfDNA kinetics

1. Tumor cells (Sum of Largest Diameters, SLD, T) comprise two sub-populations: treatment-**resistant** cells $T_R$ and treatment-**sensitive** $T_S$ ones.

2. Short fragments $D_S$ 540-75) bp) are **proportionally released through**:

* **T growth**, through **active secretion** during **proliferation**

* **T_S death** through **apoptosis**

3. Long fragments $D_L$ 1650-540) bp) are **proportionally released through**:

* **T growth**, through **active secretion** and/or **necrosis** of the tumor microenvironment

* **T_S death** through **necrosis**

4. CfDNA is **cleared** from the circulation by liver and kidneys, **depending on fragment size** $f_s(D_s)$, $f_l(D_l)$.

$$ 
\left\{ 
\begin{aligned}
\frac{dT_R}{dt} &= \alpha \cdot T_R \\
\frac{dT_S}{dt} &= \begin{cases} \alpha \cdot T_S & \text{if } t < 0 \\ (\alpha - \beta) \cdot T_S & \text{if } t \ge 0 \end{cases} \\
T &= T_R + T_S \\
\frac{dD_S}{dt} &= \lambda_S \cdot (\alpha \cdot T + \beta \cdot T_S) - f_S(D_S) \\
\frac{dD_L}{dt} &= \lambda_L \cdot (\alpha \cdot T + \beta \cdot T_S) - f_L(D_L)
\end{aligned}
\right. 
$$

Initial conditions:

$$ 
\left\{ 
\begin{aligned}
\mathbf{T}_S(\mathbf{t} = \mathbf{0}) &= \mathbf{T}_{S0} \\
\mathbf{T}_R(\mathbf{t} = \mathbf{0}) &= \mathbf{T}_{R0} \\
\mathbf{D}_S(\mathbf{t} = \mathbf{0}) &= \mathbf{D}_{S0} \\
\mathbf{D}_L(\mathbf{t} = \mathbf{0}) &= \mathbf{D}_{L0}
\end{aligned}
\right. 
$$

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# Population approach

## Non-linear mixed-effects

$$ 
\theta = \{T_{R_0}, T_{S_0}, \alpha, \beta, D_{S_0}, \lambda_s, k_{D_s}, D_{l_0}, \lambda_l, k_{D_l}\} \\ 
\forall \theta_k \in \theta, \log(\theta_k) \sim \mathcal{N}(\log(\theta_{k \text{pop}}), \omega_{\theta_k}^2)
$$

1) Tumor size parameter identification **independently** of the cfDNA data

Tumor error model: constant

2) Joint tumor—cfDNA parameters identification with tumor population parameters fixed

cfDNA error models: proportional

n = 109

## Number of samples per patient

<table><thead><tr><th></th><th>median (min-max)</th></tr></thead><tbody><tr><td>Tumor imaging</td><td>2 (1–10)</td></tr><tr><td>cfDNA samples</td><td>7 (1–20)</td></tr></tbody></table>

Best clearance function: **linear**

<figure><img src="image_37.png" /></figure>

Clearance - constant - linear - saturated

$$ 
\left\{ 
\begin{aligned}
\frac{dD_s}{dt} &= \lambda_s \cdot (\alpha \cdot T + \beta \cdot T_s) - kD_s \cdot D_s \\
\frac{dD_l}{dt} &= \lambda_l \cdot (\alpha \cdot T + \beta \cdot T_s) - kD_l \cdot D_l
\end{aligned}
\right. 
$$
# Model diagnostics

## TK model

STOCHASTIC APPROXIMATION
C.V. S.E. R.S.E.(%)

### FIXED EFFECTS

<table><tr><td>α<sub>pop</sub></td><td>0.065</td><td>0.015</td><td>23</td></tr><tr><td>β<sub>pop</sub></td><td>0.36</td><td>0.045</td><td>12</td></tr><tr><td>T<sub>R0pop</sub></td><td>7.9</td><td>1.7</td><td>22</td></tr><tr><td>T<sub>S0pop</sub></td><td>43</td><td>4.1</td><td>9.7</td></tr></table>

### STANDARD DEVIATION OF THE RANDOM EFFECTS

<table><tr><td>ω<sub>αpop</sub></td><td>0.9</td><td>110</td><td>0.13</td><td>14</td></tr><tr><td>ω<sub>βpop</sub></td><td>0.83</td><td>99</td><td>0.12</td><td>14</td></tr><tr><td>ω<sub>T<sub>R0pop</sub></sub></td><td>0.88</td><td>110</td><td>0.15</td><td>17</td></tr><tr><td>ω<sub>T<sub>S0pop</sub></sub></td><td>0.86</td><td>100</td><td>0.073</td><td>8.5</td></tr></table>

### ERROR MODEL PARAMETERS

<table><tr><td>a</td><td>8.7</td><td>0.74</td><td>8.5</td></tr></table>

Correlation of the estimates
∈ [-0.12, 0.44]

Condition number = 4.74

## Joint model

STOCHASTIC APPROXIMATION
C.V. S.E. R.S.E.(%)

### FIXED EFFECTS

<table><tr><td>D<sub>s0pop</sub></td><td>11</td><td>0.94</td><td>8.9</td></tr><tr><td>D<sub>l0pop</sub></td><td>1.4</td><td>0.1</td><td>7.4</td></tr><tr><td>λ<sub>spop</sub></td><td>0.38</td><td>0.047</td><td>12</td></tr><tr><td>λ<sub>lpop</sub></td><td>0.086</td><td>0.013</td><td>15</td></tr><tr><td>k<sub>D<sub>spop</sub></sub></td><td>0.29</td><td>0.038</td><td>13</td></tr><tr><td>k<sub>D<sub>lpop</sub></sub></td><td>0.53</td><td>0.089</td><td>17</td></tr></table>

### STANDARD DEVIATION OF THE RANDOM EFFECTS

<table><tr><td>ω<sub>D<sub>s0pop</sub></sub></td><td>0.71</td><td>82</td><td>0.07</td><td>9.9</td></tr><tr><td>ω<sub>D<sub>l0pop</sub></sub></td><td>0.51</td><td>54</td><td>0.062</td><td>12</td></tr><tr><td>ω<sub>λ<sub>spop</sub></sub></td><td>0.94</td><td>120</td><td>0.095</td><td>10</td></tr><tr><td>ω<sub>λ<sub>lpop</sub></sub></td><td>0.96</td><td>120</td><td>0.094</td><td>9.8</td></tr><tr><td>ω<sub>k<sub>D<sub>spop</sub></sub></sub></td><td>0.95</td><td>120</td><td>0.11</td><td>11</td></tr><tr><td>ω<sub>k<sub>D<sub>lpop</sub></sub></sub></td><td>1.2</td><td>170</td><td>0.12</td><td>11</td></tr></table>

### ERROR MODEL PARAMETERS

<table><tr><td>b<sub>SHORT</sub></td><td>0.43</td><td>0.013</td><td>3</td></tr><tr><td>a<sub>TK</sub></td><td>8.7</td><td></td><td></td></tr><tr><td>b<sub>LONG</sub></td><td>0.55</td><td>0.018</td><td>3.2</td></tr></table>

## Tumor kinetics

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## Short fragments

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## Long fragments

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<figure><img src="image_41.png" /></figure>

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## Individual predictions

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## IWRES
# Parameters of the dynamic modeling are predictive of the PFS

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Full kinetics
(n = 109)

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<figure><img src="image_49.png" /></figure>

Early-on treatment
(6 weeks, n = 90)

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# The model describes different size-dependent cfDNA kinetics

## PFS

### Censored Progression

* Observed data

<figure><img src="image_51.png" /></figure>
<figure><img src="image_52.png" /></figure>

# Conclusions and perspectives

* ICI-treated patients with lower fragmentation of cfDNA before treatment tend to respond better and to have longer PFS.

* Mechanistic modeling offers biological insights to explain the interplay between cfDNA and tumor kinetics.

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# Acknowledgement

## Inria

Sébastien Benzekry

Lucie Della-Negra

Romain Zakrajsek

Marc Lavielle

## AP-HM

Sébastien Salas

Laurent Greillier

Pascale Tomasini

Jean-Laurent Deville

Caroline Gaudy-Marqueste

Safae Chouati

Marie-Annick Pelletier

## ID-solutions oncology

Frédéric Fina

Paul Dufossé

## Adelis

Frédéric Ginot

Jean-Charles Garcia

Audrey Boutonnet

## COMPO team

Anastasiia Bakhmach

Anne Rodallec

Salih Benamara

Florence Gattaccecca

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team.inria.fr/compo/

## Funding

amU

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

amU

Institut cancer et immunologie
Aix Marseille Université

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Thanks for your attention!