Reaction-Diffusion model

ReactionDiffusion3D

Bases: TumorGrowthModel3D

A 3D reaction-diffusion model for simulating tumor growth.

This class extends the TumorGrowthModel3D base class to implement a reaction-diffusion framework with support for radiotherapy and chemotherapy. The model incorporates spatial diffusion, proliferation dynamics, and treatment effects.

Attributes:

Name	Type	Description
k	Tensor	Tumor growth rate parameter (proliferation rate).
d	Tensor	Tumor diffusion coefficient (spatial spread rate).
theta	Tensor	Carrying capacity of the tumor cells (maximum density).
bcs	Tensor	Boundary conditions derived from the patient brain mask.
brain_mask	Tensor	Binary mask indicating the brain region.
radiotherapy_specification	Optional[RadiotherapySpecification]	Specification of radiotherapy protocol.
radiotherapy_days	Optional[dict]	Dictionary mapping days (since initial time) to radiotherapy doses.
chemotherapy_specifications	Optional[List[ChemotherapySpecification]]	List of chemotherapy protocols.
t_initial	datetime	Initial time of the simulation.
fd_stencil_backward_coeff	List[Tensor]	Backward finite-difference coefficients for each axis.
fd_stencil_central_coeff	List[Tensor]	Central finite-difference coefficients for each axis.
fd_stencil_forward_coeff	List[Tensor]	Forward finite-difference coefficients for each axis.
device	device	The device on which to perform computations (e.g., CPU or GPU).

Methods:

Name	Description
__init__	Initializes the model with parameters and treatment specifications.
forward	Computes the rate of change of tumor density at a given time step.
callback_step	Applies treatment effects (e.g., radiotherapy) and ensures constraints on the tumor density.
_compute_laplacian	Computes the spatial Laplacian of the tumor density field.
_backward_slice	Extracts the backward slice along a given axis.
_central_slice	Extracts the central slice along a given axis.
_forward_slice	Extracts the forward slice along a given axis.

__init__(k, d, theta, patient_data, initial_time, *, radiotherapy_specification=None, chemotherapy_specifications=None, radiotherapy_days=None, require_grad=True, device=torch.device('cpu'))

Initializes the ReactionDiffusion3D model with patient-specific data and parameters.

Parameters:

Name	Type	Description	Default
k	Tensor	Tumor proliferation rate tensor.	required
d	Tensor	Tumor diffusion coefficient tensor.	required
theta	Tensor	Tumor carrying capacity tensor.	required
patient_data	HGGPatientData	Patient-specific data including brain mask and imaging.	required
initial_time	datetime	Initial simulation time.	required
radiotherapy_specification	Optional[RadiotherapySpecification]	Radiotherapy protocol.	None
chemotherapy_specifications	Optional[List[ChemotherapySpecification]]	Chemotherapy protocols.	None
radiotherapy_days	Optional[dict]	Mapping of radiotherapy days to doses.	None
require_grad	bool	Whether the parameters k and d require gradients.	True

callback_step(t, u, dt)

Handles per-step updates during the simulation, including applying treatment effects.

This method updates the tumor density field by applying radiotherapy effects (if specified) and ensures the tumor density is clamped within valid bounds.

Parameters:

Name	Type	Description	Default
t	Tensor	Current simulation time.	required
u	Tensor	Tumor density field.	required
dt	Tensor	Time step duration.	required

Returns:

Name	Type	Description
u	Tensor	Updated tumor density field.

callback_step_adjoint(t, u, dt)

Handles per-step updates during the backward pass of the adjoint method.

This method updates the adjoint variables by applying radiotherapy effects (if specified).

Parameters:

Name	Type	Description	Default
t	Tensor	Current simulation time.	required
u	Tensor	Adjoint variables.	required
dt	Tensor	Time step duration.	required

Returns:

Name	Type	Description
u	Tensor	Updated adjoint variables.

forward(t, u)

Computes the rate of change of tumor density at a given time step.

Parameters:

Name	Type	Description	Default
t	Tensor	Current simulation time (in days).	required
u	Tensor	Tumor density field.	required

Returns:

Type	Description
Tensor	torch.Tensor: Rate of change of tumor density.