tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter Class Reference

Finite difference solver for reaction-diffusion tumour growth simulation over regular grids. More...

#include <tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter.h>

Inheritance diagram for tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter:

Public Member Functions
	tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter ()
	~tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter ()
bool	check ()
void	execute ()
vtkSmartPointer< vtkImageData >	getFinalCellDensityImage ()
vtkSmartPointer< vtkImageData >	getFinalCellDensityGradientImage ()
void	setBrainMapImage (vtkImageData *image)
void	setDiffusionTensorImage (vtkSmartPointer< vtkImageData > image)
void	setInitialCellDensityImage (vtkSmartPointer< vtkImageData > image)
void	setProliferationRateImage (vtkSmartPointer< vtkImageData > image)
void	setSimulatedTime (double time)
void	setTimeStep (double step)
Public Member Functions inherited from tgstkImageProcessorBase
virtual	~tgstkImageProcessorBase ()
Public Member Functions inherited from tgstkAlgorithmBase
virtual	~tgstkAlgorithmBase ()
bool	update ()
Public Member Functions inherited from tgstkObjectBase
virtual	~tgstkObjectBase ()
std::string	getObjectName ()

Private Attributes
double	simulatedTime
double	timeStep
vtkSmartPointer< vtkImageData >	brainMapImage
vtkSmartPointer< vtkImageData >	finalCellDensityImage
vtkSmartPointer< vtkImageData >	finalCellDensityGradientImage
vtkSmartPointer< vtkImageData >	initialCellDensityImage
vtkSmartPointer< vtkImageData >	proliferationRateImage
vtkSmartPointer< vtkImageData >	diffusionTensorImage

Additional Inherited Members
Protected Member Functions inherited from tgstkImageProcessorBase
	tgstkImageProcessorBase ()
bool	_assertImageNumberOfScalarComponents (vtkSmartPointer< vtkImageData > image, std::vector< int > numberOfScalarComponents, std::string name)
bool	_assertImageScalarType (vtkSmartPointer< vtkImageData > image, std::vector< int > scalarTypes, std::string name)
bool	assertEqualImageDimensions (std::vector< vtkSmartPointer< vtkImageData >> images)
bool	assertEqualImageSpacings (std::vector< vtkSmartPointer< vtkImageData >> images)
Protected Member Functions inherited from tgstkAlgorithmBase
	tgstkAlgorithmBase ()
template<typename Type >
bool	_assertNotNullPtr (Type var, std::string name)
template<typename Type >
bool	_assertValueInRange (Type var, Type min, Type max, std::string name)
template<typename Type1 , typename Type2 >
bool	_assertValueIsEqual (Type1 var1, Type2 var2, std::string name1, std::string name2)
Protected Member Functions inherited from tgstkObjectBase
	tgstkObjectBase ()
Static Protected Member Functions inherited from tgstkImageProcessorBase
template<typename Type >
static void	fillImage (vtkSmartPointer< vtkImageData > image, Type value)
static vtkSmartPointer< vtkImageData >	getNewImageFromReferenceImage (vtkSmartPointer< vtkImageData > reference, int type, int numberOfComponents=1)
Protected Attributes inherited from tgstkObjectBase
std::string	objectName

Detailed Description

Finite difference solver for reaction-diffusion tumour growth simulation over regular grids.

tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter solves the reaction-diffusion tumour growth problem introduced in [4] [2] [7] [6] [8] :

\begin{cases} &\frac{\partial c(\bar{r}, t)}{\partial t} = \bar{\nabla} \cdot \left( \bar{\bar{D}}(\bar{r}) \, \bar{\nabla} c(\bar{r}, t) \right) + \rho(\bar{r}) \, c(\bar{r}, t) \left( 1-c(\bar{r}, t) \right) & \forall \bar{r} \in \Omega, \; \forall t > 0 \\ &c(\bar{r}, 0) = c_0(\bar{r}) & \forall \bar{r} \in \Omega \\ &\left( \bar{\bar{D}}(\bar{r}) \, \bar{\nabla} c(\bar{r}, t) \right) \cdot \bar{n}_{\partial \Omega}(\bar{r}) = 0 & \forall \bar{r} \in \partial \Omega \end{cases}

where \(c(\bar{r}, t)\) is the nomarlised tumour cell density at location \(\bar{r}\) and time \(t\) with \(c(\bar{r}, t) \in [0, 1], \; \forall \bar{r}, t\); \(\bar{\bar{D}}(\bar{r})\) is the tumour diffusion tensor field; \(\rho(\bar{r})\) is the tumour proliferation rate field; \(\Omega\) is the solving domain; \(c_0(\bar{r})\) is the initial normalised cell density field at time \(t=0\); and \(\bar{n}_{\partial \Omega}(\bar{r})\) is the unit normal vector pointing outwards the domain boundary \(\partial \Omega\) at location \(\bar{r} \in \partial \Omega\).

The problem is solved using a forward Euler finite difference scheme implemented in CUDA:

\[ c_{i,j,k}^{n+1} = c_{i,j,k}^n + \Delta t \left(\text{div}_{i,j,k}^n + \rho_{i,j,k} \, c_{i,j,k}^n \, (1-c_{i,j,k}^n) \right) \]

where subscript \(i, j, k\) refers to voxel \((i,j,k)\); superscript \(n\) refers to simulation step \(n\); \(\Delta t\) is the time step; and \(\text{div}_{i,j,k}^n\) is the divergence of the tumour cell flux given by \(\bar{\nabla} \cdot \left(\bar{\bar{D}}(\bar{r}) \, \bar{\nabla} c(\bar{r}, t) \right)\). The divergence term \(\text{div}_{i,j,k}^n\) is computed using a 3D extension of the standard stencil presented in [5].

The initial tumour cell density \(c_0(\bar{r})\), diffusion tensor \(\bar{\bar{D}}(\bar{r})\), and proliferation rate \(\rho(\bar{r})\) fields as well as the brain map defining the domain \(\Omega\) can be specified by the user as vtkImageData objects. The simulated time \(T\) and time step \(\Delta t\) can also be specified.

Warning

As the CUDA implementation performs in single precision floating point, a loss of precision may occur.

Constructor & Destructor Documentation

tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter()

tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter

(

)

~tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter()

tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::~tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter

(

)

Member Function Documentation

check()

bool tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::check ( )

virtual

Reimplemented from tgstkAlgorithmBase.

execute()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::execute ( )

virtual

Implements tgstkAlgorithmBase.

getFinalCellDensityGradientImage()

vtkSmartPointer< vtkImageData > tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::getFinalCellDensityGradientImage

(

)

Gets the final normalised tumour cell density gradient image \(\bar{\nabla}c(\bar{r}, T)\) in \(\text{mm}^{-1}\).

The image scalar type is VTK_DOUBLE. The image has 3 scalar components ( \(\!\partial_x c, \partial_y c, \partial_z c\)).

getFinalCellDensityImage()

vtkSmartPointer< vtkImageData > tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::getFinalCellDensityImage

(

)

Gets the final normalised tumour cell density image \(c(\bar{r}, T)\).

The image scalar type is VTK_DOUBLE.

setBrainMapImage()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::setBrainMapImage

(

vtkImageData *

image

)

Sets the bain map image defining the solving domain \(\Omega\).

The image scalar type must be VTK_UNSIGNED_SHORT. The different brain tissues must be referenced as specified by the tgstkBrainTissueType enum type.

setDiffusionTensorImage()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::setDiffusionTensorImage

(

vtkSmartPointer< vtkImageData >

image

)

Sets the tumour diffusion tensor image \(\bar{\bar{D}} (\bar{r})\) in \(\text{mm}^2\text{ d}^{-1}\).

The image scalar type must be VTK_DOUBLE. The image must have 6 scalar components ( \(\!D_{xx}, D_{xy}, D_{xz}, D_{yy}, D_{yz}, D_{zz}\) – implicitly symmetric).

setInitialCellDensityImage()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::setInitialCellDensityImage

(

vtkSmartPointer< vtkImageData >

image

)

Sets the initial normalised tumour cell density image \(c_0(\bar{r})\).

The image scalar type must be VTK_DOUBLE. The image values must be in range \([0; 1]\).

setProliferationRateImage()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::setProliferationRateImage

(

vtkSmartPointer< vtkImageData >

image

)

Sets the tumour proliferation rate image \(\rho(\bar{r})\) in \(\text{d}^{-1}\).

The image scalar type must be VTK_DOUBLE. The image values must be \(\geq 0\).

setSimulatedTime()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::setSimulatedTime

(

double

time

)

Sets the time duration to simulate \(T\) in \(\text{d}\).

The value must be \(\geq 0\).

setTimeStep()

void tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::setTimeStep

(

double

step

)

Sets the smilation time step \(\Delta t\) in \(\text{d}\).

The value must be \(> 0\).

Warning

For numerical stability, the time step value should verify:

\[ \Delta t \leq \min_{\bar{r}} \frac{1}{2} \left(\frac{D_{xx} (\bar{r})}{\Delta x^2} + \frac{D_{yy}(\bar{r})}{\Delta y^2} + \frac{D_{zz}(\bar{r})}{\Delta z^2}\right)^{-1} \]

where \(\Delta x\), \(\Delta y\), and \(\Delta z\) are respectively the voxel size in \(x\), \(y\), and \(z\) in \(\text{mm}\).

Member Data Documentation

brainMapImage

vtkSmartPointer<vtkImageData> tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::brainMapImage

private

diffusionTensorImage

vtkSmartPointer<vtkImageData> tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::diffusionTensorImage

private

finalCellDensityGradientImage

vtkSmartPointer<vtkImageData> tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::finalCellDensityGradientImage

private

finalCellDensityImage

vtkSmartPointer<vtkImageData> tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::finalCellDensityImage

private

initialCellDensityImage

vtkSmartPointer<vtkImageData> tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::initialCellDensityImage

private

proliferationRateImage

vtkSmartPointer<vtkImageData> tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::proliferationRateImage

private

simulatedTime

double tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::simulatedTime

private

timeStep

double tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter::timeStep

private

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The documentation for this class was generated from the following files:

• tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter.h
• tgstkFiniteDifferenceReactionDiffusionTumourGrowthFilter.cpp