Model Modifications

Extending the NTIUNHDM with immunotherapy and nutritional interventions

Enhanced Therapeutic Model

We extended the original NTIUNHDM to incorporate two clinically relevant interventions:

  • Immunotherapy: Checkpoint inhibitors and CAR-T cells that enhance immune response against tumor cells
  • Nutritional Support: Targeted dietary intervention that enhances normal cell growth while inhibiting tumor proliferation

Treatment Protocols

  • Immunotherapy: Applied during days 30-60
  • Nutritional Support: Begins at day 70 and continues
Normal Cells
Tumor Cells
Immune Cells
Immunotherapy
Nutrition

Modified Model Equations

Normal Cell Dynamics with Nutritional Support
\[\frac{dN}{dt} = r N(1 - \beta_1 N)(1 + f F) - \eta NI - \gamma NT\]

Parameters:

$$r$$
$$\beta_1$$
$$f$$
$$F$$

Treatment Dynamics

Checkpoint Inhibitor Dynamics
\[\frac{dC_1}{dt} = k_1 u_{immuno}(t) - \gamma_1 C_1\]

Parameters:

$$k_1$$
$$\gamma_1$$
$$u_{immuno}(t)$$
CAR-T Cell Dynamics
\[\frac{dC_2}{dt} = k_2 u_{immuno}(t) - \gamma_2 C_2\]

Parameters:

$$k_2$$
$$\gamma_2$$
$$u_{immuno}(t)$$
Nutritional Intervention Dynamics
\[\frac{dF}{dt} = \epsilon u_{nutrition}(t) - \phi F\]

Parameters:

$$\epsilon$$
$$\phi$$
$$u_{nutrition}(t)$$

Biological Justification

Immunotherapy Rationale

Modern cancer immunotherapies enhance the body's natural immune response against cancer cells. Checkpoint inhibitors prevent tumor cells from evading immune detection, while CAR-T cell therapy provides engineered T cells that specifically target tumor antigens. Our model captures both the immediate boost to immune function and the gradual clearance of these agents.

Key Parameters

  • τ₁ = 0.5: Checkpoint inhibitor efficacy
  • τ₂ = 0.3: CAR-T cell efficacy
  • γ₁ = 0.1, γ₂ = 0.2: Clearance rates
  • k₁ = 0.4, k₂ = 0.3: Absorption rates
Nutritional Intervention Rationale

Emerging clinical evidence suggests that targeted nutritional interventions can both support normal cell function and create unfavorable conditions for tumor growth. Specific nutrients enhance immune surveillance, reduce inflammation, and improve metabolic conditions that disadvantage cancer cells. Our model incorporates these effects through direct modulation of both normal and tumor cell growth rates.

Key Parameters

  • f = 0.4: Nutritional impact coefficient
  • ε = 0.5: Intervention uptake rate
  • φ = 0.1: Natural decay rate
Study ResultsModified Model Results