Dumitru Trucu

University of Dundee · Division of Mathematics

The COVID-19 pandemic has placed a particular burden on hospitals: from intra-hospital transmission of the infections to reduced admissions of non-COVID-19 patients. There are also high costs associated with the treatment of hospitalised COVID-19 patients, as well as reductions in revenues due to delayed and cancelled treatments. In this study we i...

Cutaneous melanoma is a highly invasive tumor and, despite the development of recent therapies, most patients with advanced metastatic melanoma have a poor clinical outcome. The most frequent mutations in melanoma affect the BRAF oncogene, a protein kinase of the MAPK signaling pathway. Therapies targeting both BRAF and MEK are effective for only 5...

In this study we investigate computationally tumour-oncolytic virus (OV) interactions that take place within a heterogeneous extracellular matrix (ECM). The ECM is viewed as a mixture of two constitutive phases, namely a fibre phase and a non-fibre phase. The multiscale mathematical model presented here focuses on the nonlocal cell-cell and cell-EC...

Cancer invasion of the surrounding tissue is a multiscale process of collective cell movement that involves not only tumour cells but also other immune cells in the environment, such as the tumour-associated macrophages (TAMs). The heterogeneity of these immune cells, with the two extremes being the pro-inflammatory and anti-tumour M1 cells, and th...

Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to...

Cutaneous melanoma is a highly invasive tumor and, despite the development of recent therapies, most patients with advanced metastatic melanoma have a poor clinical outcome. The most frequent mutations in melanoma affect the BRAF oncogene, a protein kinase of the MAPK signaling pathway. Therapies targeting both BRAF and MEK are effective for only 5...

In this study we investigate computationally tumour-oncolytic virus(OV) interactions that take place within a heterogeneous ExtraCellular Matrix (ECM). The ECM is viewed as a mixture of two constitutive phases, namely a fibre phase and a non-fibre phase. The multiscale mathematical model presented here focuses on the nonlocal cell-cell and cell-ECM...

Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to...

Brain-related experiments are limited by nature, and so biological insights are often limited or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new biological hypotheses, researchers have started using mathematical models that can simulate tumour evolution. However...

The process of local cancer cell invasion of the surrounding tissue is key for the overall tumour growth and spread within the human body, the past 3 decades witnessing intense mathematical modelling efforts in these regards. However, for a deep understanding of the cancer invasion process these modelling studies require robust data assimilation ap...

Brain-related experiments are limited by nature, and so biological insights are often restricted or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new biological hypotheses, researchers started using mathematical models that can simulate tumour evolution. However,...

We propose and study computationally a novel non-local multiscale moving boundary mathematical model for tumour and oncolytic virus (OV) interactions when we consider the go or grow hypothesis for cancer dynamics. This spatio-temporal model focuses on two cancer cell phenotypes that can be infected with the OV or remain uninfected, and which can ei...

The specific structure of the extracellular matrix (ECM), and in particular the density and orientation of collagen fibres, plays an important role in the evolution of solid cancers. While many experimental studies discussed the role of ECM in individual and collective cell migration, there are still unanswered questions about the impact of nonloca...

Cancer invasion of the surrounding tissue is a multiscale process that involves not only tumour cells but also other immune cells in the environment, such as the tumour-associated macrophages (TAMs). The heterogeneity of these immune cells, with the two extremes being the pro-inflammatory and anti-tumour M1 cells, and the anti-inflammatory and pro-...

The success of oncolytic virotherapies depends on the tumour microenvironment, which contains a large number of infiltrating immune cells. In this theoretical study, we derive an ODE model to investigate the interactions between breast cancer tumour cells, an oncolytic virus (Vesicular Stomatitis Virus), and tumour-infiltrating macrophages with dif...

Invasion of the surrounding tissue is one of the recognised hallmarks of cancer [32], which is accomplished through a complex heterotypic multiscale dynamics involving tissue-scale random and directed movement of the population of both cancer cells and other accompanying cells (including here, the family of tumour-associated macrophages) as well as...

Oncolytic virus (OV) therapy is a promising treatment for cancer due to the OVs selective ability to infect and replicate inside cancer cells, thus killing them, without harming healthy cells. In this work, we present a new non-local multiscale moving boundary model for the spatio-temporal cancer-OV interactions. This model explores an important do...

Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. During the complex interaction between cancer cell population and the extracellular matrix (ECM), of key importance is the role played by both bulk two-scale dynamics of ECM fibres within collective movement of the tumour cells and...

Oncolytic viral therapies is one of the new promising strategies against cancer, due to the ability of oncolytic viruses to specifically replicate inside cancer cells and kill them. There is increasing evidence that a sub-class of viruses that contain fusion proteins (triggering the formation of syncytia) can lead to better oncolytic results. Since...

Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. As a tumour increases in malignancy, the cancer cells adopt the ability to mutate into secondary cell subpopulations giving rise to a heterogeneous tumour. T...

Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. Occurring over many different temporal and spatial scales, the first stage of invasion is the secretion of matrix degrading enzymes (MDEs) by the cancer cells that consequently degrade the surrounding extracellular matrix (ECM). Thi...

Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. Occurring over many different temporal and spatial scales, the first stage of local invasion is the secretion of matrix-degrading enzymes (MDEs) and the resu...

Recognised as one of the hallmarks of cancer, local cancer cell invasion is a complex multiscale process that combines the secretion of matrix-degrading enzymes with a series of altered key cell processes (such as abnormal cell proliferation and changes in cell–cell and cell–matrix adhesion leading to enhanced migration) to degrade important compon...

Oncolytic viruses (OV) are viruses that can replicate selectively within cancer cells and destroy them. While the past few decades have seen significant progress related to the use of these viruses in clinical contexts, the success of oncolytic therapies is dampened by the complex spatial tumour-OV interactions. In this work, we present a novel mul...

Although novel targeted therapies have significantly improved the overall survival of patients with advanced melanoma, understanding and combatting drug resistance remains a major clinical challenge. Using partial differential equations, we describe the evolution of a cellular population through time, space, and phenotype dimensions, in the presenc...

Although novel targeted therapies have significantly improved the overall survival of patients with advanced melanoma, understanding and combatting drug resistance remains a major clinical challenge. Using partial differential equations, we describe the evolution of a cellular population through time, space, and phenotype dimensions, in the presenc...

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates do...

miR-451-AMPK-mTOR system. Development, parameter estimation, analysis, sensitivity analysis, and theoretical implications of the miR-451-AMPK-mTOR core control system. (PDF)

Cancer cell invasion is recognised as one of the hallmarks of cancer and involves several inner-related multiscale processes that ultimately contribute to its spread into the surrounding tissue. In order to gain a deeper understanding of the tumour invasion process, we pay special attention to the interacting dynamics between the cancer cell popula...

Central to the quest for a deeper understanding of the cancer growth and spread process, the naturally multiscale character of cancer invasion demands appropriate multiscale modelling and analysis approach. The cross-talk between the tissue scale (macro-scale) cancer cell population dynamics and the cell-scale (micro-scale) proteolytic molecular pr...

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the...

Sensing and reciprocating cellular systems (SARs) are important for the operation of many biological systems. Production in interferon (IFN) SARs is achieved through activation of the Jak-Stat pathway, and downstream upregulation of IFN regulatory factor (IRF)-3 and IFN transcription, but the role that high and low affinity IFNs play in this proces...

Cancer cell invasion, recognised as one of the hallmarks of cancer, is a complex process involving the secretion of matrix-degrading enzymes that have the ability to degrade the surrounding extracellular matrix (ECM). Combined with cell proliferation and migration, and changes in cell-cell and cell-matrix adhesion, the tumour is able to spread into...

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these pro...

Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell in...

Recognised as a key stage in cancer growth and spread in the human body, the cancer cell invasion process is crucial for metastatic spread and the subsequent development of secondary cancers. Tissue scale proliferation and migration in conjunction with a pallet of arising cell-scale dynamics including altered adhesion and secretion of matrix degrad...

Known as one of the hallmarks of cancer [30], cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extr...

The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating...

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a...

Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many inter-related genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade extracellular matrix. Combined with abnormal excessive p...

In this chapter we present a novel framework that enables a rigorous analysis of processes occurring on three (or more) independent scales (e.g. intracellular, cellular, tissue). We give details of the establishment of this new multiscale concept and discuss a number of important fundamental properties that follow. This framework also offers a new...

Cancer invasion of tissue is a key aspect of the growth and spread of cancer and is crucial in the process of metastatic spread, i.e., the growth of secondary cancers. Invasion consists in cancer cells secreting various matrix degrading enzymes (MDEs) which destroy the surrounding tissue or extracellular matrix (ECM). Through a combination of proli...

Background: Understanding the mechanisms of the growth and spread of cancer cells in the human breast and providing effective treatment continues to remain a significant challenge. Cancer cell invasion of breast tissue plays a pivotal role in the metastatic cascade through complex, coupled dynamics of the constituent processes occurring over a rang...

In this article, we propose a new notion of multiscale convergence, called ‘three-scale’, which aims to give a topological framework in which to assess complex processes occurring at three different scales or levels within a heterogeneous medium. This generalizes and extends the notion of two-scale convergence, a well-established concept that is no...

The identification of the space- and time-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. While boundary and initial conditions are prescribed, additional temperature measurements are considered inside the solution domain. The problem is approached both from a global and a local perspec...

The identification of the space-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. While Dirichlet boundary conditions are assumed, the additional measurement necessary to render a unique solution is either a heat-flux measurement or a time-average temperature measurement inside the space...

The identification of the temperature-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. If Neumann boundary conditions are prescribed, then the additional measurement sufficient to render a unique solution is a temperature measurement on a part of the boundary. A numerical approach based...

In this article, we investigate both analytical and numerical techniques for the identification of the constant perfusion coefficient in the transient bio-heat conduction equation. In this inverse coefficient identification problem, the additional measurement necessary to render a unique solution may be a heat flux, an interior temperature or an av...

The identification of the space-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. In this inverse coefficient identification problem, the additional measurement necessary to render a unique solution is a boundary temperature measurement. A numerical approach based on a Crank-Nicolson fini...

The identification of the time-dependent perfusion coefficient in the transient bio-heat conduction equation is investigated. In this inverse coefficient identification problem, the additional measurement necessary to render a unique solution may be a heat flux, interior temperature or mass measurement which is taken permanently along the time inte...