Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top

2021 | Book

Constitutive Modelling of Soft Biological Tissue from Ex Vivo to in Vivo: Myocardium as an Example Read chapter Read first chapter

Methods of Mathematical Oncology

Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020

Editors: Prof. Takashi Suzuki, Prof. Clair Poignard, Prof. Mark Chaplain, Prof. Vito Quaranta

Publisher: Springer Singapore

Book Series : Springer Proceedings in Mathematics & Statistics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access
insite
SEARCH

About this book

This book presents original papers reflecting topics featured at the international symposium entitled “Fusion of Mathematics and Biology” and organized by the editor of the book. The symposium, held in October 2020 at Osaka University in Japan, was the core event for the final year of the research project entitled “Establishing International Research Networks of Mathematical Oncology.” The project had been carried out since April 2015 as part of the Core-to-Core Program of Japan Society for the Promotion of Science (JSPS). In this book, the editor presents collaborative research from prestigious organizations in France, the UK, and the USA. By utilizing their individual strengths and realizing the fusion of life science and mathematical science, the project achieved a combination of mathematical analysis, verification by biomedical experiments, and statistical analysis of chemical databases.
Mathematics is sometimes regarded as a universal language. It is a valuable property that everyone can understand beyond the boundaries of culture, religion, and language. This unifying force of mathematics also applies to the various fields of science. Mathematical oncology has two aspects, i.e., data science and mathematical modeling, and definitely helps in the prediction and control of biological phenomena observed in cancer evolution.
The topics addressed in this book represent several methods of applying mathematical modeling to scientific problems in the natural sciences. Furthermore, novel reviews are included that may motivate many mathematicians to become interested in biological research.

Table of Contents

Frontmatter

Mathematical Modeling

Frontmatter
Constitutive Modelling of Soft Biological Tissue from Ex Vivo to in Vivo: Myocardium as an Example
Abstract
Imbalance of stress/strain microenvironment can lead to adverse remodelling and pathogenesis in various soft tissues, tumour included. Therefore, there is a critical need for accurate quantification of the biomechanical homeostasis in soft tissue through mathematical modelling, which is critically dependent on constitutive models, the mathematical descriptions that approximate the mechanical behaviours of material under specific conditions by considering information from subcellular, cellular and tissue levels. In most soft biological tissue, collagen is the major component of the extracellular matrix, its architecture largely determines the material property (stiffness). In this work, we will use myocardium as an example to show how we can develop a constitutive law from various ex vivo experiments within the continuum mechanics framework, and demonstrate the applications to real patient data. We will further focus on parameter calibrations from ex/in vivo measurements. We believe this approach of constitutive modelling and calibration can be applied to various soft biological tissues and shed light on physiological and pathological mechanobiology.
Debao Guan, Xiaoyu Luo, Hao Gao
Mathematical Modeling of Gastro-Intestinal Metastasis Resistance to Tyrosine Kinase Inhibitors
Abstract
In this paper, we study a continuum mechanics model of gastrointestinal stroma tumor (GIST) evolution under the action of two specific treatments. The first-line treatment is a specific tyrosine kinase inhibitor (TKI), with a cytotoxic effect, that induces direct cell death. The second-line treatment is a multi-targeted TKI, with both cytotoxic and anti-angiogenic effect. The model is a coupled hyperbolic/elliptic system based on mass balance equations on cell densities coupled with a diffusion equation on the nutrients and oxygen concentrations. The tumor model involves 3 proliferating cell densities and a necrotic phase. Each proliferating cell density responds differently to the treatments: \(P_1\)-cells are killed by both treatments, \(P_2\)-cells are affected by the second-line treatment only, and \(P_3\) cells are resistant to both therapies. The necrotic cells are eliminated at a rate \(1/\tau \). We first prove the well-posedness of the model for any non-negative \(\tau \). Then we study the asymptotic behavior of the solution as \(\tau \) goes to zero. In particular, we proved that the limit problem correspond to a tumor growth model without necrosis. This is of great interest regarding the modeling, since it proves the continuity with respect to \(\tau \) of the family of \(\tau \)-dependent, ensuring the consistency of the modeling.
Thierry Colin, Thomas Michel, Clair Poignard
Mathematical Modeling and Experimental Verification of the Proneural Wave
Abstract
Spatio-temporal pattern formation during development is regulated by interactions of multiple signaling pathways. To understand complex signaling networks, we used the Drosophila visual system as a model because neural differentiation progresses in a spatiotemporally ordered manner. During the development of the visual system, a wave of differentiation, called the proneural wave, sweeps across the brain surface and determines the timing of differentiation of neuroepithelial cells into neuroblasts, which are neural stem cells in Drosophila. Propagation of the proneural wave is regulated through a combination of signaling pathways, including the Notch, EGF, and JAK/STAT. We combined mathematical modeling with in vivo experiments, the results of which revealed that Notch-mediated lateral inhibition and EGF-mediated reaction diffusion determine the speed of progression of the proneural wave. We reported that JAK/STAT signaling has a noise-canceling function to assure robust neuroblast differentiation. Furthermore, we introduced a continuation method from spatially discretized models while conserving the cell size and lattice. This mathematical method enables us to introduce information from spatially discrete to spatially continuous models, rendering it suitable for applications in both experimental and mathematical analyses. Our interdisciplinary studies have revealed new functions of signaling pathways that have previously been difficult to address by conventional biological experiments.
Yoshitaro Tanaka, Tetsuo Yasugi
Exploring Similarity Between Embedding Dimension of Time-Series Data and Flows of an Ecological Population Model
Abstract
Cancer cells interact with tissue cells in a complex manner. Immune cells had that initially participated in eliminating cancer cells are often educated to become assisting cancer growth. Identifying causal relationship of cellular interactions that mediate cancer progression is crucial to understand how cancer cells grow, evolve, and persist. A mathematical model that describes dynamics of cancer cell population is constructed based on a given causal relationship among model ingredients. Mathematical modeling has been employed to explain cancer progression patterns in terms of dynamical system.
Daiki Kumakura, Shinji Nakaoka
Mathematical Modeling for Angiogenesis
Abstract
Angiogenesis is the morphogenetic phenomenon in which new blood vessels emerge from an existing vascular network and configure a new network. To understand complex movements of endothelial cells and molecular processes that drive angiogenic morphogenesis, time-lapse live imaging of dynamic collective cell migration and mathematical modeling have proven highly informative. This paper focuses on recent mathematical models for the dynamics of endothelial cells during angiogenesis and presents the importance of both repulsive and attractive two-body interactions by showing results of simulation.
Tatsuya Hayashi
Floating Potential Boundary Condition in Smooth Domains in an Electroporation Context
Abstract
In electromagnetism, a conductor that is not connected to the ground is an equipotential whose value is implicitly determined by the constraint of the problem. It leads to a nonlocal constraints on the flux along the conductor interface, so-called floating potential problems. Unlike previous numerical study that tackle the floating potential problems with the help of advanced and complex numerical methods, we show how an appropriate use of Steklov-Poincaré operators enables to obtain the solution to these partial differential equations with a non local constraint as a linear (and well-designed) combination of \(N+1\) Dirichlet problems, N being the number of conductors not connected to a ground potential. In the case of thin highly conductive inclusions, we perform an asymptotic analysis to approach the electroquasistatic potential at any order of accuracy. In particular, we show t hat the so-called floating potential approaches the electroquasistatic potential with a first order accuracy. This enables us to characterize the configurations for which floating potential approximation has to be used to accurately solve the electroquasistatic problem.
A. Collin, S. Corridore, C. Poignard
Free Boundary Problem of Cell Deformation and Invasion
Abstract
A novel approach of free boundary problem of invadopodia formation and invasion is proposed in this paper. The modeling of invadopodia formation and invasion of cell involving the interaction across plasma membrane is considered. The formation is formulated by Stefan problem approach which is known as free boundary problem where the boundary membrane is priori unknown. Changes in cell membrane will lead to protrusions of cell membrane. A normal growing cell in tissue on an organ will be altered into cancerous cells after some processes of mutation in genes. We proposed level set method to indicate the moving plasma membrane and to represent the behavior of the cell interface. An efficient and a straightforward enthalpy method (phase change problem) is then used to provide the description of the cell membrane diffusion. We successfully show the formation of invadopodia and migration of a single cell modeling.
Nuha Loling Othman, Takashi Suzuki
Multi-level Mathematical Models for Cell Migration in Confined Environments
Abstract
The aim of this contribution is to put together in a systematic way several approaches operating at different scales that were recently developed to describe the phenomenon of physical limit of migration, that occurs when the environment surrounding cells results restrictive, and to apply it to tumour growth and invasion. In particular, we will present: (i) a mechanical model of the behaviour of a cell within a microchannel that gives a blockage criterium for its penetration; (ii) a cellular Potts model to describe the dependence of the speed of a malignant cell from the mechanical characteristics both of its compartments (i.e., nucleus and cytosol) and of its environment; (iii) a multiphase model embodying such effects; (iv) the proper interface conditions to implement to deal with tumour invasion across matrix membranes and cell linings.
Luigi Preziosi, Marco Scianna
Mathematical Modeling of Cancer Signaling Addressing Tumor Heterogeneity
Abstract
One of the obstacles for cancer therapies is the heterogeneity of cancers. Heterogeneity in signal transduction within the same cell population contributes to drug resistance and stemness, and the diversity of cancer subtypes contributes to different therapeutic efficacy between individuals. However, the whole mechanisms associated with heterogeneity in signal transduction are poorly understood. In this review, I introduce several mathematical modeling studies to deal with cell-to-cell variability and diversity of cancer subtypes. Mathematical modeling studies to analyze the heterogeneity of signal transduction should provide new insights that will promote the next generation of cancer therapies, such as overcoming drug resistance and personalized medicine.
Shigeyuki Magi
Mathematical Modelling of Cancer Invasion: A Review
Abstract
A defining feature of cancer is the capability to spread locally into the surrounding tissue, with cancer cells spreading beyond any normal boundaries. Cancer invasion is a complex phenomenon involving many inter-connected processes at different spatial and temporal scales. A key component of invasion is the ability of cancer cells to alter and degrade the extracellular matrix through the secretion of matrix-degrading enzymes. Combined with excessive cell proliferation and cell migration (individual and collective), this facilitates the spread of cancer cells into the local tissue. Along with tumour-induced angiogenesis, invasion is a critical component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we present an overview of the various mathematical models and different modelling techniques and approaches that have been developed over the past 25 years or so and which focus on various aspects of the invasive process.
Nikolaos Sfakianakis, Mark A. J. Chaplain
The First Step Towards the Mathematical Understanding of the Role of Matrix Metalloproteinase-8 in Cancer Invasion
Abstract
The role of matrix metalloproteinases-8 (MMP-8) in the cancer progression is quite complex, with contradictory indications as to whether it suppresses or assists the local growth of cancer. In addition, while other types of MMPs appear in either soluble or (cancer cell) membrane-bound form MMP-8 seems to appear in both. We take the first step in unravelling this dual nature of MMP-8 by shedding some mathematical light into its properties. To this end, we develop a mathematical model to investigate the impact of both soluble and membrane-bound MMPs in the early stages of local invasion of cancer cells. We propose an extension to a previously developed three-dimensional, hybrid atomistic-collective, cancer invasion model that allows the description of individual cancer cells along side with macroscopic tissue representations, and for the natural transition between these phases. We further assume that the soluble MMPs are produced by polymorphonuclear neutrophils, that pre-exist in the environment, and that they get activated by the cancer cells. The membrane-bound MMPs are expressed on the membrane of the cancer cells and along with the soluble MMPs, participate in the degradation of the extracellular matrix and, in effect, directly influence the migration of the cancer cells in what is understood to be a self-generated haptotaxis invasion strategy. With a series of numerical experiments and simulations we investigate the potential of the model in producing various invasion patterns, some resembling, qualitatively, to experimental invasion assays.
Anna Wilson, Thomas Williams, Nikolaos Sfakianakis

Biological Prediction

Frontmatter
Mathematical Modeling of the Dimerization of EGFR and ErbB3 in Lung Adenocarcinoma
Abstract
The most common driver mutations in lung adenocarcinoma occur in the EGFR gene. Gefitinib, an EGFR tyrosine kinase inhibitor, is an effective therapy for lung adenocarcinoma with EGFR mutations. However, resistant tumors inevitably arise. One of the mechanisms conferring gefitinib resistance is the amplification of the MET gene, which is observed in 5–22% of all cases. A previous study suggested that MET overexpression may cause gefitinib resistance through ErbB3, and most likely through the formation of EGFR-ErbB3 heterodimers. In this study, we focused on the dimer formation of EGFR and ErbB3 in lung adenocarcinoma cells and built a mathematical model using ordinary differential equations. To simulate the dimerization process of EGFR and ErbB3, we determined the molecular concentrations of each on the cell surface by flow cytometry and estimated unknown reaction constants by dimensional analysis. Our mathematical model would provide a quantitative understanding of dimer formation, one which cannot be obtained by a molecular biology methods.
Takeshi Ito, Takashi Suzuki, Yoshinori Murakami
Selective Regulation of the Insulin-Akt Pathway by Simultaneous Processing of Blood Insulin Pattern in the Liver
Abstract
Insulin exhibits several temporal patterns, such as the 10- to 15-min pulsatile (minutes), additional (hours), and basal (days) secretions, leading to selective insulin responses in vivo; however, the mechanisms by which different temporal patterns of insulin selectively regulate downstream molecules remain unknown. Revealing the mechanisms of selective regulation by temporal patterns of insulin is pivotal for understanding insulin actions in vivo.
We examined selective regulation of the insulin-Akt pathway and its mechanisms in the liver under hyperinsulinemic-euglycemic clamp conditions. We obtained time series data of the insulin-Akt pathway molecules using different stimulation patterns and developed a mathematical model that could reproduce these data. We found that all temporal patterns of the blood insulin levels are encoded into the insulin receptor (IR), and downstream molecules selectively and simultaneously decode them via protein kinase B (Akt or PKB). Mathematical modeling revealed the mechanisms via differences in network structures, sensitivity, and time constants. Moreover, we simulated the type II diabetes mellitus (T2DM) condition using the model and found that abnormal blood insulin patterns might contribute to the pathogenesis and/or progression of T2DM. Given that almost all hormones exhibit distinct temporal patterns, temporal coding may be a general principle of system homeostasis by hormones.
Hiroyuki Kubota
Mathematical Simulation of Linear Ubiquitination in T Cell Receptor-Mediated NF-κB Activation Pathway
Abstract
The linear ubiquitin chain assembly complex (LUBAC), composed of the HOIP, HOIL-1L, and SHARPIN subunits, activates the canonical nuclear factor-κB (NF-κB) pathway through the Met1 (M1)-linked linear ubiquitination activity. On the course of the T cell receptor (TCR)-mediated NF-κB activation pathway, LUBAC transiently associates with and linearly ubiquitinates the CARMA1-BCL10-MALT1 (CBM) complex. In contrast, the linear ubiquitination of NEMO, a substrate of the TNF-α-induced NF-κB activation pathway, was limited in the TCR pathway. A linear ubiquitin-specific deubiquitinase (DUB), OTULIN, plays a major role in downregulating LUBAC-mediated TCR signaling. Mathematical modeling indicated that linear ubiquitination of the CBM complex accelerates the activation of IκB kinase (IKK), as compared with the activity induced by linear ubiquitination of NEMO alone. Moreover, simulations of the sequential linear ubiquitination of the CBM complex suggested that the allosteric regulation of linear (de)ubiquitination of CBM subunits is controlled by the ubiquitin-linkage lengths. Thus, unlike the TNF-α-induced NF-κB activation pathway, the TCR-mediated NF-κB activation in T cells has a characteristic mechanism to induce LUBAC-mediated NF-κB activation.
Daisuke Oikawa, Naoya Hatanaka, Takashi Suzuki, Fuminori Tokunaga
Time Changes in the VEGF-A Concentration Gradient Lead Neovasculature to Engage in Stair-Like Growth
Abstract
Arteriovenous malformations consist of tangles of arteries and veins that are often connected by a fistula. The causes of and mechanisms underlying the development of these clinical entities are not fully understood. We previously reported a novel in vivo angiogenesis model as a useful disease model of arteriovenous malformation. With this model, the arterial graft was collected from the left carotid artery and sutured to the left jugular vein as a patchwork. The neovasculature extended from the branch of the subclavian artery toward the arterial graft. We measured the neovasculature, which had sprouted from arterioles, in the tissue samples. In the present study, we collected the arterial patch graft and adipose tissue surrounding the arterial graft and examined the distribution of the VEGF concentration by an enzyme-linked immunosorbent assay. At the area most distant from the arterial graft, the VEGF-A concentration changed over time in a sine wave pattern that gradually attenuated. A mathematical model was then constructed using the results, and a mathematical simulation of the neovasculature growth was performed. The new vessels grew in a stair-like pattern in this simulation, a result that matched those obtained through histological measurements.
Yukinobu Ito, Dhisa Minerva, Sohei Tasaki, Makoto Yoshida, Takashi Suzuki, Akiteru Goto
Mathematical Modeling of Tumor Malignancy in Bone Microenvironment
Abstract
We construct a multi-scaled mathematical model of tumor malignancy in bone microenvironment including tumor cells, osteoblasts, and ostoclasts underlined by NF-\(\kappa \)B family, RANKL, RNK, and OPG molecules. Pathways causing change of the amounts of osteoblasts, osteoclast, and cancer cells are analyzed via numerical simulations.
Naoya Hatanaka, Mitsuru Futakuchi, Takashi Suzuki
Signaling Networks Involved in the Malignant Transformation of Breast Cancer
Abstract
Breast cancer stem cells (CSCs) are involved the malignant transformation of breast cancer, including metastasis, because they are more stress-resistant and have higher tumorigenicity than the surrounding breast cancer cells (non-CSCs). We aimed to elucidate the various signaling networks involved in the transformation of mammary epithelial cells into tumor cells based on literature review. We found that constitutive activation of the NF-\({\upkappa}{\text{B}}\) pathway maintains CSCs in basal-like breast cancer, a subtype of triple-negative breast cancer, where NF-\({\upkappa}{\text{B}}\)-mediated induction of JAG1 in non-CSCs results in the stimulation of Notch signaling in CSCs. On the other hand, epithelial-mesenchymal transition (EMT) and its reverse reaction, mesenchymal-epithelial transition (MET), are thought to be involved in breast cancer cell metastasis, which makes elucidating their regulatory mechanisms essential. We identified HCC38, a basal-like breast cancer cell line, as a suitable model to investigate such mechanisms, because EMT and MET are in intratumoral equilibrium with each other in HCC38. In the HCC38 study, we found that multiple signaling pathways between epithelial and mesenchymal cells are involved in the regulation of the dynamic equilibrium between EMT and MET. Mathematical simulation of these intracellular and intercellular signaling networks involved in the malignant transformation of breast cancer could lead to the elucidation of the mechanisms of tumor malignant transformation and the development of therapeutic targets.
Mizuki Yamamoto, Jun-ichiro Inoue

Data Science

Frontmatter
Cell-Free Based Protein Array Technology
Abstract
Cell-free protein production technology can easily produce recombinant proteins from cDNA temples, because it is synthesized in a tube without cell culture. We developed a wheat cell-free protein production system from washed wheat embryos. Since our cell-free system is based on eukaryotic translational machinery, it is very suitable for synthesis of eukaryotic proteins such as human protein. Using this system, recently we made a protein array technology consisting of proteins synthesized in 384-well formatted plates, and then constructed human protein array consisting of more than 20,000 recombinant human proteins (20K-HuPA). In addition, combinations with AlphaScreen or magnetic plate technology promotes development of a new high-throughput and high-sensitive approach for identification of protein–protein or protein–antibody interaction. Herein, we demonstrate the results of protein interactomes and antibody validation by using protein array.
Ryo Morishita, Hirotaka Takahashi, Tatsuya Sawasaki
Omics Data Analysis Tools for Biomarker Discovery and the Tutorial
Abstract
Given the current progress in next-generation sequencing and mass spectrometry, considerable attention has been given to omics approaches and biomarker discovery to understand heterogeneous diseases. However, it is difficult to analyze them in the biological experimental community because the analysis processes are complicated. To address this problem, we have introduced and explained in this chapter the tools used for omics data analysis and how they are used.
Yosui Nojima, Yoshito Takeda
Integrative Network Analysis of Cancer Cell Signaling by High-Resolution Proteomics
Abstact
Post-translational modifications (PTMs), such as phosphorylation, ubiquitination and acetylation, are known to be widely involved in the regulation of various biological processes through extensive diversification of each protein function at the cellular network level. Previous functional analyses of cancer cell signaling under a variety of experimental conditions revealed many of the key molecules and their associated protein modifications in relation to each type of cancer. In order to systematically discover critical modulators from diversified signaling molecules, we have developed a high-resolution mass spectrometry-based proteomics platform for integrative identification and quantification of multiple post-translational modifications from various types of cancer cells. In this chapter, we would like to highlight the potential impact of computational network dissection based on PTM-directed proteomic data towards systematic understanding of cellular signaling principles.
Masaaki Oyama, Hiroko Kozuka-Hata
Distance-Matrix-Based Extraction of Motility Features from Functionally Heterogeneous Cell Populations
Abstract
It has recently been recognized that seemingly identical cell populations can exhibit functional heterogeneity in vivo. However, the unsupervised extraction of features to understand such heterogeneous cell behaviors has been a challenging task. Here, we present a novel, data-driven method to visualize cell heterogeneity as a set of points in a low-dimensional Euclidean space, based on a distance matrix between individual cells. The axes of this space serve as a guide for finding the characteristic features in the population. By using cell motility as an example, we show that our visualization can distinguish three types of simulated cell movements as separate clusters, without knowing a priori the mathematical models they follow. By applying our method to time-lapse two-photon imaging data of neutrophils, we successfully extract critical features that characterize different types of cell motility. We expect that our method would be applicable to other cellular phenotypes.
Naotoshi Nakamura, Ryo Yamada
Data Analytic Study of the Genetic Mechanism of Ovarian Carcinoma Using Single-Cell RNA-Seq Data
Abstract
This study aims to elucidate the underlying genetic mechanism for ovarian carcinoma using single-cell RNA-seq data. We propose a unique data-driven approach to understand the nature of the data as it is as far as possible. Precisely, we draw a scatter plot, called distance-direction expression pattern, and show it presents several channels of progresses of gene interactions. Then we apply it to the above data. As a result, we found that two channels are presented in the pattern, one for moderate exacerbation of TGF-\(\beta \) and the other for TGF-\(\beta \)-induced highly expressed genes that are more directly connected to cancer growth.
Shuji Kawasaki, Hiroatsu Hayashi, Yoko Tominaga
Backmatter
Metadata
Title
Methods of Mathematical Oncology
Editors
Prof. Takashi Suzuki
Prof. Clair Poignard
Prof. Mark Chaplain
Prof. Vito Quaranta
Copyright Year
2021
Publisher
Springer Singapore
Electronic ISBN
978-981-16-4866-3
Print ISBN
978-981-16-4865-6
DOI
https://doi.org/10.1007/978-981-16-4866-3

Premium Partner

    Image Credits