scholarly journals Long time dynamics of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tania Biswas ◽  
Elisabetta Rocca
Keyword(s):  
Prostate Cancer ◽  
Phase Field ◽  
Field Model ◽  
Antiangiogenic Therapy ◽  
Phase Field Model ◽  
Cancer Growth ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics

scholarly journals Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects

2020 ◽  
Vol 30 (07) ◽  
pp. 1253-1295 ◽  
Author(s):  
Pierluigi Colli ◽  
Hector Gomez ◽  
Guillermo Lorenzo ◽  
Gabriela Marinoschi ◽  
Alessandro Reali ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Cell Death ◽  
Tumor Growth ◽  
Phase Field ◽  
Clinical Studies ◽  
Advanced Prostate Cancer ◽  
Antiangiogenic Therapy ◽  
Specific Antigen ◽  
Cytotoxic Chemotherapy ◽  
Cancer Growth

Chemotherapy is a common treatment for advanced prostate cancer. The standard approach relies on cytotoxic drugs, which aim at inhibiting proliferation and promoting cell death. Advanced prostatic tumors are known to rely on angiogenesis, i.e. the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or in combination with standard cytotoxic protocols. However, the complex genetic alterations that originate and sustain prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient’s tumor. Here, we present a mathematical model of prostate cancer growth and chemotherapy that may enable physicians to test and design personalized chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction–diffusion dynamics. Tumor proliferation and apoptosis (i.e. programmed cell death) can be parameterized with experimentally-determined values. Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples the tumor phase field with the production of prostate-specific antigen, which is a prostate cancer biomarker that is extensively used in the clinical management of the disease. We prove the well posedness of our model and we run a series of representative simulations leveraging an isogeometric method to explore untreated tumor growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well as common outcomes of cytotoxic and antiangiogenic mono therapy and combined therapy. Additionally, our model also reproduces the usual temporal trends in tumor volume and prostate-specific antigen evolution observed in experimental and clinical studies.

scholarly journals Sharp-interface formation during lithium intercalation into silicon

2017 ◽  
Vol 29 (1) ◽  
pp. 118-145 ◽  
Author(s):  
E. MECA ◽  
A. MÜNCH ◽  
B. WAGNER
Keyword(s):  
Free Boundary ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Lithium Ion ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Time Dynamics

In this study, we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as amorphous silicon (a-Si). The governing equations couple a viscous Cahn–Hilliard-Reaction model with elasticity in the framework of the Cahn–Larché system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in lithium ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface intersects the free boundary of the Si layer. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.

Long-time stabilization of solutions to a phase-field model with memory

2001 ◽  
Vol 1 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Eduard Feireisl
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Long Time ◽  
With Memory

scholarly journals Long-time behaviour and convergence towards equilibria for a conserved phase field model

2003 ◽  
Vol 10 (1-2) ◽  
pp. 239-252
Author(s):  
Hana Petzeltová ◽  
Françoise Issard-Roch ◽  
Eduard Feireisl
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

scholarly journals Mathematical analysis of a phase-field model of brain cancers with chemotherapy and antiangiogenic therapy effects

2021 ◽  
Vol 7 (1) ◽  
pp. 1536-1561
Author(s):  
Monica Conti ◽  
◽  
Stefania Gatti ◽  
Alain Miranville ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Phase Field ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Field Model ◽  
Antiangiogenic Therapy ◽  
Phase Field Model ◽  
Optimal Treatment ◽  
Biologically Relevant ◽  
Nonnegative Solutions

<abstract><p>Our aim in this paper is to study a mathematical model for brain cancers with chemotherapy and antiangiogenic therapy effects. We prove the existence and uniqueness of biologically relevant (nonnegative) solutions. We then address the important question of optimal treatment. More precisely, we study the problem of finding the controls that provide the optimal cytotoxic and antiangiogenic effects to treat the cancer.</p></abstract>

MARMOT Phase-Field Model for the U-Si System

2016 ◽  
Author(s):  
Larry Kenneth Aagesen ◽  
Daniel Schwen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model
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