Simulation and patient-specific scale tissue modelling of the growth of prostate cancer
In an embodiment, a simulation of the evolution of a tumor in a prostate gland of a subject is based at least on a coupled system of reaction-diffusion equations and a patient-specific geometric model of the prostate gland of the subject. The use of reaction-diffusion equations and a patient-specific geometric model provides a tumor model that predicts the expected progression of prostate cancer in the subject. The tumor model may be used to devise a customized treatment for the subject.
1. A method of modeling progression of prostate cancer in a subject, comprising:
performing operations on a computer system to generate a tumor growth model for a prostate gland of the subject, wherein the operations include:
simulating evolution of a tumor in the prostate gland of the subject, wherein said simulating of the evolution of the tumor is based at least on a coupled system of reaction-diffusion equations and a patient-specific geometric model of the prostate gland of the subject, wherein at least one of the reaction-diffusion equations is an equation representing the dynamics of tissue prostate-specific anitgen (PSA) p(x,t), and wherein a value p(x,t) of the tissue PSA field p represents a tissue PSA concentration at position x and time, and wherein the equation representing the dynamics of tissue PSA p(x,t) includes one or more of the following:
a term that represents a rate at which healthy cells produce PSA;
a term that represents a rate at which cancerous cells produce PSA; and
a decay term that represents a natural decay of the tissue PSA.
2. The method of claim 1 , wherein the patient-specific geometric model is designed based on one or more medical images of the prostate gland of the subject.
3. The method of claim 1 , wherein the patient-specific geometric model comprises a three-dimensional tensor-product spline.
4. The method of claim 1 , wherein said simulating of the evolution of the tumor is performed according to a finite element method, or isogeometric analysis, or a finite difference method, or a finite volume method, or a mesh-free method, or an immersed method.
5. The method of claim 1 , wherein the patient-specific geometric model is constructed based on a discretization method used for constructing geometric models and/or solving partial differential equation mathematical models on geometric models.
6. The method of claim 1 , wherein one or more of the reaction-diffusion equations include: an equation representing dynamics of an evolution of a tumor phase field ϕ or an equation representing dynamics of a nutrient field σ, wherein a value ϕ(x,t) of the tumor phase field ϕ represents an extent to which cells at position x and time t are cancerous, and wherein a value σ(x,t) of the nutrient field σ represents a nutrient concentration at position x and time t.
7. The method of claim 6 , wherein the operations further include one or more of the following:
analyzing an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time to estimate a real-world time at which the tumor will:
penetrate a capsule of the prostate gland of the subject;
invade a tissue outside (or near) the prostate gland of the subject;
reach a specified part of the prostate gland of the subject;
transition from ellipsoidal growth to fingered growth; or
make contact with the urethra of the subject; and
outputting the real-world time or an indication of the real-world time via an output device.
8. The method of claim 6 , wherein the operations further include one or more of the following:
generating a video based on at least a portion of an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time, wherein the video illustrates evolution of a boundary of the tumor over time; and
displaying the video via a display device.
9. The method of claim 6 , wherein the operations further include one or more of the following:
generating an image based on an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time, wherein said image illustrates a cross section through the geometric model, wherein image includes one or more curves corresponding a boundary of the tumor; and
displaying the image via display device.
10. The method of claim 6 , wherein the operations further include one or more of the following:
generating a 3D rendering of the prostate gland and the tumor based at least on an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time and the geometric model; and
displaying the 3D rendering via a display device.
11. The method of claim 6 , wherein the operations further include one or more of the following:
estimating a stage of prostate cancer development in the subject based on an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time and multiparametric magnetic resonance imaging (MRI) image data of the prostate gland of the subject; and
displaying an indication of the estimated stage.
12. The method of claim 6 , wherein the operations further include:
computing a boundary of the tumor based on a level set of the phase field; and
displaying the boundary of the tumor via a display device.
13. The method of claim 6 , wherein the operations further include:
computing a boundary of the tumor based on a level set of the phase field;
computing a volume of the tumor based on the computed boundary; and
displaying an indication of the computed volume.
14. The method of claim 6 , wherein the operations further include projecting a three-dimensional field onto a model space corresponding to the geometric model, to approximate the initial tumor with the phase field.
15. The method of claim 6 , wherein the operations further include:
controlling a robotic surgical tool based on an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time in order to remove at least a portion of the tumor.
16. The method of claim 6 , wherein the operations further include:
determining an insertion path of a biopsy needle based on an output dataset representing the evolution of the tumor phase field ϕ, the nutrient field σ, and the tissue PSA field p on the geometric model over an interval in simulated time, in order to increase a likelihood of obtaining samples of tumor tissue; and
displaying an image or video indicating the insertion path.
17. The method of claim 1 , wherein the equation representing the dynamics of tissue PSA p(x,t) includes one or more of the following:
a term that is proportional to 1−ϕ, wherein a value ϕ(x,t) of a tumor phase field ϕ represents an extent to which cells at position x and time t are cancerous;
a term that is proportional to the phase field ϕ;
a term that is proportional to a negative of the tissue PSA field.
18. A non-transitory memory medium storing program instructions, wherein the program instructions, when executed by a computer system, cause the computer system to perform the method comprising:
generating a tumor growth model for a prostate gland of a subject, wherein generating the tumor growth model includes:
simulating evolution of a tumor in the prostate gland of the subject, wherein said simulating of the evolution of the tumor is based at least on a coupled system of reaction-diffusion equations and a patient-specific geometric model of the prostate gland of the subject, wherein at least one of the reaction-diffusion equations is an equation representing the dynamics of tissue prostate-specific antigen (PSA) p(x,t), and wherein a value p(x,t) of the tissue PSA field p represents a tissue PSA concentration at position x and time t, and wherein the equation representing the dynamics of tissue PSA p(x,t) includes one or more of the following:
a term that is proportional to 1−ϕ, wherein a value ϕ(x,t) of a tumor phase field ϕ represents an extent to which cells at position x and time t are cancerous;
a term that is proportional to the phase field ϕ; and
a term that is proportional to a negative of the tissue PSA field.
19. A computer system comprising:
a processor; and
memory storing program instructions, wherein the program instructions, when executed by a processor, cause the processor to generate a tumor growth model for a prostate gland of the subject by:
simulating evolution of a tumor in the prostate gland of the subject, wherein said simulating of the evolution of the tumor is based at least on a coupled system of reaction-diffusion equations and a patient-specific geometric model of the prostate gland of the subject, wherein at least one of the reaction-diffusion equations is an equation representing the dynamics of tissue prostate-specific antigen (PSA) p(x,t), and wherein a value p(x,t) of the tissue PSA field p represents a tissue PSA concentration at position x and time t, and wherein the equation representing the dynamics of tissue PSA p(x,t) includes one or more of the following:
a term that is proportional to 1−ϕ, wherein a value ϕ(x,t) of a tumor phase field ϕ represents an extent to which cells at position x and time t are cancerous;
a term that is proportional to the phase field ϕ; and
a term that is proportional to a negative of the tissue PSA field.