Preface of the Special Issue: Modeling and Simulation of Tumor Development, Treatment, and Control, Edited by Nicola Bellomo and Elena De Angelis, Volume 37, Issue 11, Pages 1121-1252, 2003, Mathematical and Computer Modelling, ISSN 0895-7177, ELSEVIE

Arlotti

Bellomo

Chaplain

De Angelis

Elena De Angelis

Hethcote

Nicola Bellomo

Nossal

Perelson

Swan

Crossref

Preface of the Special Issue: Modeling and Simulation of Tumor Development, Treatment, and Control, Edited by Nicola Bellomo and Elena De Angelis,  Volume 37, Issue 11, Pages 1121-1252, 2003, Mathematical and Computer Modelling, ISSN 0895-7177, ELSEVIE

BELLOMO, Nicola

DE ANGELIS, Elena

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEPreface [Special issue on Modeling and Simulation of Tumor Development, Treatment and Control] / BELLOMO N; DEANGELIS E.. - STAMPA. - (2003), pp. xiii-xv.OriginalPreface [Special issue on Modeling and Simulation of Tumor Development, Treatment and Control]Publisher:PublishedDOI:10.1016/S0895-7177(03)00123-7Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/1399568 since:MATHEMATICAL COMPUTER MODELLING PERGAMON Mathematical and Computer Modelling 37 (2003) xiii-xv www.elsevier.com/locate/mcm Preface Mathematical modeling and simulation of tumor growth in competition with the immune sys- tem is certainly one of the challenging frontiers of applied mathematics. The modeling generally includes also the description of therapeutical actions as well as of experiments related to under- standing the complex phenomena related to the above physical systems. Motivations are undoubtedly strong due to the fact that cancer is still one of the greatest killer in the world. It is true that mathematics cannot solve problems of immunology and medicine. However, it seems that a useful support to experiments and quantitative analysis of external actions to control the neoplastic growth can be developed by applied mathematics. Specifi- cally, models and simulations of particular behaviors of the immune competition can reduce the amount of experiments which are necessary for therapy developments. A final target, an immune- mathematical theory can be developed in order to provide a detailed description of the evolution of the system hopefully focusing phenomena which may be difficult to observe experimentally. Due to the above motivations, various scientific editions have been proposed over the last ten years. For instance, scientific journals have devoted special issues to publish scientific papers on tumor modeling. Among others, we mention the special issues edited by Bellomo [l], and Chaplain [2,3], as well as the collection of survey papers [4]. It is worth mentioning that modeling, qualitative analysis, and simulations of the physical system we are dealing with often involves quite sophisticated mathematical methods. Eventu- ally, new mathematical structures may be necessary toward a sufficiently detailed description. Therefore, applied mathematicians can find additional motivations by dealing with the above topics. This special issue reports a number of research papers which deal with different aspects of the mathematical problems which have been outlined above. These papers have been developed within the scientific activities of the European Union research and training network “Using Math- ematical Modeling and Computer Simulations to Improve Cancer Therapy”. Nevertheless, the interest in the activities is not limited to Europe as it is documented by the institutions of the authors who have contributed to this issue. The contents of this issue covers three general topics: (i) modeling cellular phenomena with special attention to the immune competition: (ii) modeling macroscopic phenomena related to condensed tumors; (iii) modeling control therapies. In detail, on the first class of models and problems, the paper by Canetta, Leyrat, and Verdier deals with experiments and modeling the dynamics of cells with special attention to microadhesion phenomena. Particular attention is focused on the adhesion between a functionalised spherical microsphere. Interest in this type of analysis to modeling condensation of tumor cells into solid forms is evident. The paper by De Angelis, Delitala, Marasco, and Roman0 deals with a bifurcation analysis 0895-7177/03/$ - see front matter @ 2003 Elsevier Science Ltd. All rights reserved. Typeset by AM-w PIT: SO895-7177(03)00123-7 xiv for a class of integro-differential equations simulating the competition between tumor ceils and immune cells in the medium of environmental cells [5]. The analysis is referred to a well-defined therapeutical action: namely the possibility of modifying the ability of neoplastic cells to inhibit the immune cells. The same framework is used by Kolev for a model of immune compet,itiorl with special attention to the role of antibodies. Also this model is developed by statistical m~thotl.~ analogous to those of the kinetic theory and is expressed in terms of a system of integro-tliffercnt,ixi equations. The mathematical framework is the one analyzed in [S]. The background framework is the one of immune competition [7]. Particularly interesting is the analysis proposed by Gobron. Saada. iuld ‘li-iolo whic:h (IW~:. with the analysis of the links between the microscopic and macroscopic, description ‘l’he paipt’r analyzes a competition-diffusion system, where populations of healthy and ill (:ells comprtc <,ti11 i move on a neutral mat.rix. Then a coupled system of nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The space dependtmt solutions show a behavior markedly different from the associated ODE system: for a. large class of initial conditions. the asymptotic behavior of the system can be described through the analysis of associated traveling waves. Referring to modeling macroscopic phenomena, the paper by Drasdo and HGhme proposes a mathematical and computer-based model on avascular tumor spheroids in-vitro. The great merit of this paper consists in the direct derivation of the model from experiments. This procedurti allows us to link the model parameters to experimental accessible biomechanical and kinetics parameters and provides a potential, at least partly quantitative, description of growing avascular tumors in stages which are not primarily determined by nutrient or oxygen supply. Interesting computer simulations are reported to visualize the formation of morphological patterns which are characteristic for the growth regime of the unperturbated cell assembly before the death process starts. The impact of this type of analysis on medical action is definitively relevant. A similar aim is in the background of the paper by Swanson, Alvord, Jr., and Murray which deals with rht analysis of a mathematical model to describe the growth and infiltration of glioma cells t,hroughout an anatomically accurate virtual human brain. The model is based on a proliferation-migratlori mechanism including the effects of the complex spatial structure and intrinsic heterogeneity of t,h(> brain tissue. The model is related to development of therapies, and in particular, on treatment b? resection. Macroscopic phenomena are analyzed by Scalerandi, Peggion, Capogrosso, Sanson~~. and Benati. who analyze cancer growth phenomena related to tumor cords. neoplasms forming cylindrical structures around blood vessels. Two papers by ForyS and Bodnar analyze the qualitative behaviour of two simple models of solid avascular tumors based on the reaction-diffusion dynamics and mass conservation 1, which reduce to ordinary differential equations. Both papers analyze the effect of time delay 0x1 the qualitative behaviour of solutions. The first paper refers specifically to stability properties of equilibrium solutions, while the second one focuses, in addition to stability analysis, also ti.1 existence of periodic solutions. The analysis is related to therapeutical actions. The last two papers art’ concerned with control problems for models described by urdinarl differential equations. The general framework for modeling is the papers by Perelson and Weis- buch [8], and Hethcote [9]; while the mathematical control theory was initiated by Swan [lo!. In detail the paper by dePillis and Radunskaya refers to a mat,hematical model of tumor growth with an immune response and chemotherapy. The qualitative analysis of the orbits generates tht desired control action. The long-term behavior of an orbit is classified according to t,he basil) 11t attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. It is shown tha,t the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once treatmenr has stopped. Numerical experiments show that an optimal control therapy is able to drive, th:b system into a desirable basin of attraction, whereas traditional pulsed chemotherapy i,s noi The paper by Swierniak, Polanski, Smieja, and Kimmel deals with the analysis of the dynarmcai properties of models of emergence of resistance of cancer cells to chemotherapy. The model of the process has a form of an infinite system of linear and bilinear state equations. The paper shows that it can be decomposed into two parts: the first one is finite-dimensional bilinear, and the second one is infinite-dimensional linear, coupled by the positive feedback. Then classical results of the theory of feedback systems are used to study the asymptotic properties of the process. The editors of this special issue hope that the contents of the above articles may be useful to applied mathematicians active in the above research field. Definitively and interesting aspects of the contents is that most papers show an active collaboration with clinicians and molecular biologists. Some of the problems generated by the articles are of great interest also on the level of analytic mathematical problems. So far, the interaction between mathematics and medicine can contribute also to the cultural development of medicine. Nicola Bellomo Elena De Angelis Guest Editors REFERENCES 1. N. Bellomo, Modeling and Simulation Problems in %mor Immune System Dynamics, Special Issue of Mathl. Camp. Modelling 23 (6) (1996). 2. M. Chaplain, Furnor Immune System Modelling, Special Issue of Math. Models Meth. Appl. Sci. 9 (4) (1999). 3. M. Chaplain, Mathematical Modelling and Simulation of Aspects of Cancer Growth, Special Issue of J. The- oretical Medicine 4 (1) (2002). 4. J. Adam and N. Bellomo, Editors, A Survey of Models on Tumor Immune Systems Dynamics, Birkhauser, Boston, MA, (1996). 5. E. De Angelis and L. Mesin, Mathematical frameworks and applications on tumors and immune system interactions, Math. Models Meth. Appl. Sci. 11, 1609-1630 (2001). 6. L. Arlotti, N. Bellomo and E. De Angelis, Generalized kinetic (Boltsmann) models: Mathematical structures and applications, Math. Models Meth. Appl. Sci. 12, 567-592 (2002). 7. G.J. Nossal, Life, death and the immune system, Scientific American 269, 53-72 (1993). 8. A. Perelson and G. Weisbuch, Immunology for physicists, Rev. Modern Phys. 69, 1219-1267 (1997). 9. H.W. Hethcote, The mathematics of infectious diseases, Siam Review 42, 599-653 (2001). 10. G.W. Swan, Role of optimal control theory in cancer chemotherapy, Math. Biosci. 101, 237-284 (1990). 

English

Preface [Special issue on Modeling and Simulation of Tumor Development, Treatment and Control]

Bellomo, Nicola

De Angelis, Elena

PORTO Publications Open Repository TOrino

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Development, Treatment and Control]
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Development, Treatment and Control]. .
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MATHEMATICAL 
COMPUTER 
MODELLING 
PERGAMON Mathematical and Computer Modelling 37 (2003) xiii-xv 
www.elsevier.com/locate/mcm 
Preface 
Mathematical modeling and simulation of tumor growth in competition with the immune sys- 
tem is certainly one of the challenging frontiers of applied mathematics. The modeling generally 
includes also the description of therapeutical actions as well as of experiments related to under- 
standing the complex phenomena related to the above physical systems. 
Motivations are undoubtedly strong due to the fact that cancer is still one of the greatest killer 
in the world. It is true that mathematics cannot solve problems of immunology and medicine. 
However, it seems that a useful support to experiments and quantitative analysis of external 
actions to control the neoplastic growth can be developed by applied mathematics. Specifi- 
cally, models and simulations of particular behaviors of the immune competition can reduce the 
amount of experiments which are necessary for therapy developments. A final target, an immune- 
mathematical theory can be developed in order to provide a detailed description of the evolution 
of the system hopefully focusing phenomena which may be difficult to observe experimentally. 
Due to the above motivations, various scientific editions have been proposed over the last ten 
years. For instance, scientific journals have devoted special issues to publish scientific papers 
on tumor modeling. Among others, we mention the special issues edited by Bellomo [l], and 
Chaplain [2,3], as well as the collection of survey papers [4]. 
It is worth mentioning that modeling, qualitative analysis, and simulations of the physical 
system we are dealing with often involves quite sophisticated mathematical methods. Eventu- 
ally, new mathematical structures may be necessary toward a sufficiently detailed description. 
Therefore, applied mathematicians can find additional motivations by dealing with the above 
topics. 
This special issue reports a number of research papers which deal with different aspects of 
the mathematical problems which have been outlined above. These papers have been developed 
within the scientific activities of the European Union research and training network “Using Math- 
ematical Modeling and Computer Simulations to Improve Cancer Therapy”. Nevertheless, the 
interest in the activities is not limited to Europe as it is documented by the institutions of the 
authors who have contributed to this issue. 
The contents of this issue covers three general topics: 
(i) modeling cellular phenomena with special attention to the immune competition: 
(ii) modeling macroscopic phenomena related to condensed tumors; 
(iii) modeling control therapies. 
In detail, on the first class of models and problems, the paper by Canetta, Leyrat, and Verdier 
deals with experiments and modeling the dynamics of cells with special attention to microadhesion 
phenomena. Particular attention is focused on the adhesion between a functionalised spherical 
microsphere. Interest in this type of analysis to modeling condensation of tumor cells into solid 
forms is evident. 
The paper by De Angelis, Delitala, Marasco, and Roman0 deals with a bifurcation analysis 
0895-7177/03/$ - see front matter @ 2003 Elsevier Science Ltd. All rights reserved. Typeset by AM-w 
PIT: SO895-7177(03)00123-7 
xiv 
for a class of integro-differential equations simulating the competition between tumor ceils and 
immune cells in the medium of environmental cells [5]. The analysis is referred to a well-defined 
therapeutical action: namely the possibility of modifying the ability of neoplastic cells to inhibit 
the immune cells. The same framework is used by Kolev for a model of immune compet,itiorl with 
special attention to the role of antibodies. Also this model is developed by statistical m~thotl.~ 
analogous to those of the kinetic theory and is expressed in terms of a system of integro-tliffercnt,ixi 
equations. The mathematical framework is the one analyzed in [S]. The background framework 
is the one of immune competition [7]. 
Particularly interesting is the analysis proposed by Gobron. Saada. iuld ‘li-iolo whic:h (IW~:. 
with the analysis of the links between the microscopic and macroscopic, description ‘l’he paipt’r 
analyzes a competition-diffusion system, where populations of healthy and ill (:ells comprtc <,ti11 i 
move on a neutral mat.rix. Then a coupled system of nonlinear parabolic equations is derived 
through a scaling procedure from the microscopic, Markovian dynamics. The space dependtmt 
solutions show a behavior markedly different from the associated ODE system: for a. large class 
of initial conditions. the asymptotic behavior of the system can be described through the analysis 
of associated traveling waves. 
Referring to modeling macroscopic phenomena, the paper by Drasdo and HGhme proposes a 
mathematical and computer-based model on avascular tumor spheroids in-vitro. The great merit 
of this paper consists in the direct derivation of the model from experiments. This procedurti 
allows us to link the model parameters to experimental accessible biomechanical and kinetics 
parameters and provides a potential, at least partly quantitative, description of growing avascular 
tumors in stages which are not primarily determined by nutrient or oxygen supply. Interesting 
computer simulations are reported to visualize the formation of morphological patterns which are 
characteristic for the growth regime of the unperturbated cell assembly before the death process 
starts. The impact of this type of analysis on medical action is definitively relevant. A similar 
aim is in the background of the paper by Swanson, Alvord, Jr., and Murray which deals with rht 
analysis of a mathematical model to describe the growth and infiltration of glioma cells t,hroughout 
an anatomically accurate virtual human brain. The model is based on a proliferation-migratlori 
mechanism including the effects of the complex spatial structure and intrinsic heterogeneity of t,h(> 
brain tissue. The model is related to development of therapies, and in particular, on treatment b? 
resection. Macroscopic phenomena are analyzed by Scalerandi, Peggion, Capogrosso, Sanson~~. 
and Benati. who analyze cancer growth phenomena related to tumor cords. neoplasms forming 
cylindrical structures around blood vessels. 
Two papers by ForyS and Bodnar analyze the qualitative behaviour of two simple models 
of solid avascular tumors based on the reaction-diffusion dynamics and mass conservation 1, 
which reduce to ordinary differential equations. Both papers analyze the effect of time delay 0x1 
the qualitative behaviour of solutions. The first paper refers specifically to stability properties 
of equilibrium solutions, while the second one focuses, in addition to stability analysis, also ti.1 
existence of periodic solutions. The analysis is related to therapeutical actions. 
The last two papers art’ concerned with control problems for models described by urdinarl 
differential equations. The general framework for modeling is the papers by Perelson and Weis- 
buch [8], and Hethcote [9]; while the mathematical control theory was initiated by Swan [lo!. In 
detail the paper by dePillis and Radunskaya refers to a mat,hematical model of tumor growth 
with an immune response and chemotherapy. The qualitative analysis of the orbits generates tht 
desired control action. The long-term behavior of an orbit is classified according to t,he basil) 11t 
attraction in which it starts. The addition of a drug term to the system can move the solution 
trajectory into a desirable basin of attraction. It is shown tha,t the solutions of the model with 
a time-varying drug term approach the solutions of the system without the drug once treatmenr 
has stopped. Numerical experiments show that an optimal control therapy is able to drive, th:b 
system into a desirable basin of attraction, whereas traditional pulsed chemotherapy i,s noi 
The paper by Swierniak, Polanski, Smieja, and Kimmel deals with the analysis of the dynarmcai 
properties of models of emergence of resistance of cancer cells to chemotherapy. The model of the 
process has a form of an infinite system of linear and bilinear state equations. The paper shows 
that it can be decomposed into two parts: the first one is finite-dimensional bilinear, and the 
second one is infinite-dimensional linear, coupled by the positive feedback. Then classical results 
of the theory of feedback systems are used to study the asymptotic properties of the process. 
The editors of this special issue hope that the contents of the above articles may be useful to 
applied mathematicians active in the above research field. Definitively and interesting aspects 
of the contents is that most papers show an active collaboration with clinicians and molecular 
biologists. Some of the problems generated by the articles are of great interest also on the level 
of analytic mathematical problems. So far, the interaction between mathematics and medicine 
can contribute also to the cultural development of medicine. 
Nicola Bellomo 
Elena De Angelis 
Guest Editors 
REFERENCES 
1. N. Bellomo, Modeling and Simulation Problems in %mor Immune System Dynamics, Special Issue of 
Mathl. Camp. Modelling 23 (6) (1996). 
2. M. Chaplain, Furnor Immune System Modelling, Special Issue of Math. Models Meth. Appl. Sci. 9 (4) 
(1999). 
3. M. Chaplain, Mathematical Modelling and Simulation of Aspects of Cancer Growth, Special Issue of J. The- 
oretical Medicine 4 (1) (2002). 
4. J. Adam and N. Bellomo, Editors, A Survey of Models on Tumor Immune Systems Dynamics, Birkhauser, 
Boston, MA, (1996). 
5. E. De Angelis and L. Mesin, Mathematical frameworks and applications on tumors and immune system 
interactions, Math. Models Meth. Appl. Sci. 11, 1609-1630 (2001). 
6. L. Arlotti, N. Bellomo and E. De Angelis, Generalized kinetic (Boltsmann) models: Mathematical structures 
and applications, Math. Models Meth. Appl. Sci. 12, 567-592 (2002). 
7. G.J. Nossal, Life, death and the immune system, Scientific American 269, 53-72 (1993). 
8. A. Perelson and G. Weisbuch, Immunology for physicists, Rev. Modern Phys. 69, 1219-1267 (1997). 
9. H.W. Hethcote, The mathematics of infectious diseases, Siam Review 42, 599-653 (2001). 
10. G.W. Swan, Role of optimal control theory in cancer chemotherapy, Math. Biosci. 101, 237-284 (1990). 


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