News

Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia

by Daniel R. Bergman, Kerri-Ann Norton, Harsh Vardhan Jain & Trachette Jackson

Read the paper

This paper presents a novel computational framework that constrains high-dimensional ABM parameter space with multidimensional real-world data.  We accomplish this by extending and validating a first-of-its-kind method that leverages explicitly formulated surrogate models to bridge the computational divide between ABMs and experimental data.  We show that Surrogate Modeling for Reconstructing Parameter Spaces (SMoRe ParS) can constrain high-dimensional ABM parameter spaces using unidimensional (single time-course) data.  We then demonstrate that it can constrain parameter spaces of more complex ABMs using multidimensional data (multiple time courses at different biological scales).  To validate our method, we compared the SMoRe ParS-inferred ABM parameter space with ABM parameters inferred by an often computationally expensive direct comparison with experimental data.  A strength of SMoRe ParS is that it allows for exploring ABM parameter space even at points that are not directly sampled and where ABM output was never generated.   Computationally efficient methods to connect ABMs with multidimensional data are timely and important as ABMs are a natural platform for capturing heterogeneity and predicting emergent behavior in multiscale systems.  SMoRe ParS is a robust and scalable computational framework that can explore the uncertainty within multidimensional parameter spaces associated with ABMs representing complex biological phenomena.

Caption: The schematic diagram for using SMoRe ParS to infer ABM input parameters from experimental data via a surrogate model. The solid arrows connecting the Experimental Data and Agent-based Model boxes to the Surrogate Model box represent the direction of information flow in the first few steps of SMoRe ParS. Green (control), yellow (0.75μM oxaliplatin), and red (7.55μM oxaliplatin) colors in the Experimental data box refer to the dosing regimens that generated the experimental data.

Brief description of the roles of the authors (e.g. student, group-leader etc):

Daniel R. Bergman, postdoc

Kerri-Ann Norton,  computational modeling collaborator, and developer of SMoRe Pars

Harsh Vardhan Jain, co-senior author and co-developer of SMoRe Pars

Trachette Jackson, co-senior author and co-developer of SMoRe Pars

Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia

by Luke Pierik, Patricia McDonald, Alexander R.A. Anderson & Jeffrey West. 

Read the paper

Second order effects describe changes in a system which result from introducing variability or fluctuations in a system’s input. Quantifying second-order effects relies on an understanding of the convexity of an underlying function determining system output, and this has been effectively used in several fields, notably financial risk management. Previously, the vocabulary of fragile or antifragile has been used: fragile systems are harmed by variability while antifragile systems benefit from variability. The key insight here is that oncologists can control the input variability of treatment schedules, and therefore it is critical to define the fragility (or antifragility) of tumors. In cancer, second-order effects have been studied through dose response curves, which are ubiquitous theoretical and clinical tools in the field. However, these curves do not incorporate knowledge about how long dosages remain near the tumor (i.e. pharmacokinetics), which influences treatment outcomes. In this paper, we explore this relation between second-order effects and pharmacokinetics through standard mathematical models as well as a previously parameterized tumor model with 5-fluorouracil. By studying second-order effects with pharmacokinetics, more efficient treatment schedules may be devised which utilize the underlying convexity of dose response to produce greater patient outcomes.

Nonlinear Regression Modelling: A Primer with Applications and Caveats

by  Timothy O'Brien & Jack Silcox

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In their applied studies, researchers often find that nonlinear regression models are more applicable for modelling various biological, physical, and chemical processes than are linear ones since they tend to fit the data well and since these models – and especially the associated model parameters – are usually more scientifically meaningful.  For example in relative potency, drug synergy, and similar compound interaction modelling, key model parameters aid researchers in making important decisions regarding comparisons of drugs or compounds and/or whether combinations of these substances would enhance effects.

These researchers may be at a loss for how best to perform this nonlinear modelling, including choosing between various growth models or binary logistic models, how these work and which analysis methods are best and why.  Working through several key examples, this paper provides a gentle yet informative hands-on introduction to nonlinear modelling, provides key R code which can be easily adapted to fit ones own nonlinear models, and underscores key caveats regarding often-problematic Wald confidence intervals and p-values as well as the lack of penalizing for overfitting in a certain large-sample likelihood-based approach.

About the Authors: Tim O’Brien is a professor of Mathematics and Statistics (with a joint appointment in Environmental Sustainability) at Loyola University Chicago.  Jack Silcox is a postdoctoral researcher in the Department of Psychology at the University of Utah.

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

by  Alexander Browning, Thomas Lewin, Ruth Baker, Philip Maini, Eduardo Moros, Jimmy Caudell, Helen Byrne and Heiko Enderling

Read the paper

Mathematical models have the potential to revolutionise clinical practise by providing real-time insights that guide decision-making and predict patient responses. Challenges associated with the application of mathematical models are perhaps, however, most acute for single-patient clinical data of cancer tumour progression. Data are often noisy, sparse, and simplistic; patient responses are often highly variable; and mathematical models may be necessarily complex.

In this work, we develop and present a novel, simple, mathematical model of tumour volume progression in response to radiotherapy that can capture a full gamut of patient responses observed in the clinic. To maximise the utility of data collected from a large clinical cohort whilst accounting for significant patient-to-patient variation, we present alongside the model a Bayesian statistical method that allows for real-time clinical predictions to be drawn throughout a patient's course of treatment.

All model parameters vary between patients, with prior parameter knowledge for new patients informed by a weighted mixture of posterior parameter knowledge from previously observed patients. We demonstrate the ability of our model and statistical framework by considering a subset of patients for which predictions are continuously updated throughout their course of treatment.

The research was led by Alexander Browning (from 2023), a research fellow, and Thomas Lewin (until 2022), a DPhil student.

Caption: Data from a cohort of training data are used to calibrate population-level posterior distributions that account for patient-to-patient variability. Individual-level predictions are then drawn and then updated throughout a patients’ course of treatment

Models for implant-induced capsular contracture post breast cancer surgery

by Cheryl Dyck, Kathryn V. Isaac, and Leah Edelstein-Keshet

Read the paper

Surgical breast reconstruction can play an important role in the emotional and psychological outlook of a breast cancer patient.  Unfortunately, a common complication of implant-based reconstruction is capsular contracture (CC), formation of a painful and often disfiguring scar-tissue around the implant. Treatment for CC generally requires surgical capsule excision and implant replacement.  CC etiology is poorly understood, limiting the ability for determining a patient's risk profile, treatment, and prevention. Here we examine the early stages of CC development with a hierarchy of mathematical models for interacting macrophages, fibroblasts, myofibroblasts, and collagen. A simplified "toy" model provides insight suggesting parameter regimes that lead to either a stable state with a non-pathological thin capsule, a stable state with a pathological thick capsule, and a bistable range in between.  A fold bifurcation can exist with the full model with outcome determined by genetic and health profile (parameter values) and inflammatory state (initial conditions.) These results predict some patients are resistant to CC, some are destined to have CC, whereas a susceptible population could develop CC as a result of inflammatory insult.  Further examination and clinical study of the parameters of interest may yield risk factors and preventative and therapeutic targets.

Cheryl Dyck MAsc (SFU) is a Mathematical Biology Consultant. Kathryn V. Isaac MD FRCSC MPh, is a Plastic and Reconstructive Surgeon with Vancouver Coastal Health and Providence Health Care, an Assistant Professor, Department of Surgery, Faculty of Medicine, University of British Columbia, Canada and P. Clugston Chair of Breast Reconstruction.  Dr. Edelstein-Keshet is a Professor in the Department of Mathematics, University of British Columbia, is the author of "Mathematical Models in Biology (2005) SIAM", and a former president of the Society for Mathematical Biology.

Caption: Schematic diagram for a model of the early phases of tissue recovery around a breast implant (capsule formation.) The implant surgery initiates an immune response that eventually recruits collagen-producing cells. The collagen affects tissue stiffness, and feeds back on the balance between fibroblasts and their activated phenotype, myofibroblasts, further influencing collagen production.  Model analysis and simulations predict whether patients are resistant, susceptible, or prone to developing capsular contracture, a painful and disfiguring deformation of the reconstructed breast. Scheme made with Biorender

Alys Clark (University of Auckland), Sara Loo (Johns Hopkins University), Fiona R. Macfarlane (University of St Andrews), and Thomas Woolley (Cardiff University).

1. In Memory: Torcom Chorbajian, Long-time Volunteer and SMB Officer
   
2. News – updates from: 
   • SMB Subgroups
   • Upcoming Conferences and Workshops
   • Updates from Royal Society Publishing
3. People – An interview with Professor Jae Kyoung Kim, who will be a plenary speaker at the Joint Annual Meeting of the Korean Society for Mathematical Biology and Society for Mathematical Biology in Seoul this year.
4. Editorial – on 'A look forward to KSMB - a chat with Dr Yangjin Kim' on the upcoming SMB-KSMB conference.
5. Featured Figure – Highlighting the research by early career researcher Ryan Murphy, University of Melbourne.

To see the articles in this issue, click the links at the above items.

Contributing Content

Issues of the newsletter are released four times per year in Spring, Summer, Autumn, and Winter. The newsletter serves the SMB community with news and updates, so please share it with your colleagues and contribute content to future issues.

If you have any suggestions for content or on how to improve the newsletter, please contact us at any time. We appreciate and welcome feedback and ideas from the community. The editors can be reached at newsletter@smb.org.

We hope you enjoy this issue of the newsletter!

Alys, Sara, Fiona, and Thomas

In Memory: Torcom Chorbajian: Long-time Volunteer and SMB Officer

Contributed by Lou Gross, Ray Mejia and John Jungck

The Society lost a tremendous long-standing leader and volunteer on January 19, 2024 when Torcom Chorbajian passed away in Lafayette, Colorado.  Without any paid staff members, except for those associated with the Bulletin, SMB has functioned over its history due to the dedicated efforts of many volunteers. Torcom was exemplary as the volunteer Treasurer and Board member for nearly forty years. He had tremendous knowledge of the history of the Society and had direct personal connections with the leadership over the first decades, by far attending more Board meetings than anyone else in our history. 

As the person who managed membership records, dealt with all financial aspects of the Society and handled interactions with the various publishers of the Bulletin,  Torcom devoted untold hours to Society business. He was the one who corresponded with our far-flung membership for decades, handling all kinds of membership and subscription challenges. He took personal interest in our members, particularly those outside North America who relied on their subscriptions to stay informed of the latest research in the time before electronic connections were prevalent. Many were the times he called the current Society President to discuss challenges faced by one of our members and to express concern about sometimes delayed responses from the various publishers. He knew our membership far better than anyone else in the leadership and had attended all of our Annual Meetings for many years. For many meetings, he would manage the display of collections of books to provide our members an opportunity to see the latest texts from various publishers. He handled the distribution of travel funds for many, many students over the years who benefited from the Society’s Landahl awards to enable them to attend meetings (see the photo attached from the 2010 Rio meeting of Torcom writing a check for a student attendee). Torcom also designed the three-sided pens (see photo) handed out at many meetings that are still cherished by members due to the way they sit so comfortably in your hand. 

    

Torcom’s contributions were celebrated in 2008 with the first Torcom Chorbajian Lecture at the Annual Meeting at the University of Toronto.  As then-President Gerda de Vries noted in the January 2013 SMB Newsletter “I want to thank Torcom Chorbajian for serving as Treasurer for almost 40 years. Torcom has been a member of the SMB since its inception in the 1970s and was appointed Treasurer two years later. Torcom has accepted the title of Honorary Treasurer of the SMB.” Tocom is remembered as a friend and tireless steward of the SMB and its members.

News Section

By Fiona Macfarlane

SMB Subgroups Update

Cell and Developmental Biology Subgroup

The Cell and Developmental Biology (CDEV) subgroup was active (with minisymposia, contributed talks, posters, a subgroup business meeting, and a group dinner) at the 2023 SMB Annual Meeting in Columbus, OH, and we're looking forward to the 2024 SMB Annual Meeting in Seoul, Korea!

In addition to our activities at the annual meetings and our blog-post series (https://smb-celldevbio.github.io/blog/) highlighting researchers in our community, we started two new virtual initiatives in the last year. First, we held mentored mock virtual interviews for students and postdocs preparing for the academic job market (thanks to all who participated as mentors and mentees!). Second, we are holding our first virtual micro-conference “Virtual Cell and Development Festival Week” from March 18–21, 2024. The schedule features plenary talks on research and professional development topics, several minisymposia, and two panels (focused on industry careers and the future of models and software platforms). Each day of the festival week has about 2 hours of programming, with a range of times selected to fit many timezones. Please see https://smb-celldevbio.github.io/cdevfestival/ for more information and registration details (registration is free). All are welcome and encouraged to attend our first virtual CDEV festival week!

Immunobiology and Infection Subgroup

The Immunobiology and Infection subgroup is excited to host four outstanding speakers in its annual minisymposium at the joint Annual Meeting of the KSMB and SMB, in addition to the many excellent sessions being organized by our members. Join us for talks by Reginald McGee, Wasiur Khuda Bukhsh, Adrianne Jenner, and Past Chair Stanca Ciupe. Hope to see you in Seoul!

At last year’s SMB Annual Meeting at Ohio State University, together with SMB and the National Institute of Allergy and Infectious Diseases (NIAID), our subgroup co-organized a half-day workshop Bridging multiscale modeling and practical clinical applications in infectious diseases. This event brought together top experts in multiscale mathematical modeling with experimentalists and clinicians working at the frontier of immunity and infectious diseases to share their research and discuss challenges and opportunities for future work. We were thrilled to see the high level of interest from conference attendees and are looking forward to organizing a future iteration of the event.  If you missed it, or want to relive the fun, the organizing team wrote a summary article which will be forthcoming in the Bulletin of Mathematical Biology, keep an eye out and we will send around when it is published. Thank you to the co-organizers, speakers, and participants.

Mathematical Epidemiology and Mathematical Oncology Subgroups

The Mathematical Epidemiology (MEPI) and Mathematical Oncology (ONCO) subgroups hosted SMB MathEpiOnco 2024, a joint virtual mini-conference February 18-20. Over 150 registered participants from 22 countries attended the three-day meeting. The conference featured plenary talks by Marisa Eisenberg (University of Michigan, USA), Claudia Pio Ferreira (São Paulo State University, Brazil), and Natalia Komarova (U.C. San Diego, USA) as well as a panel discussion of Opportunities at the Interface of Mathematical Epidemiology and Oncology with panelists Hanna Dueck (National Institutes of Health, USA), Zhilan Feng (National Science Foundation and Purdue University, USA), and Ami Radunskaya (Pomona College, USA) and a tutorial session on Stochastic Processes in Epidemiology and Oncology led by Linh Huynh (Dartmouth College, USA) and Pujan Shrestha (Texas A&M, USA). In addition, the conference featured 22 contributed talks for SMB members working on problems in mathematical epidemiology, mathematical oncology, and the intersection of the two fields.

The conference prompted important discussions about similarities in approaches to studying problems in oncology and epidemiology with a mathematical lens and highlighted areas for research growth in questions that are relevant to both fields.  Furthermore, the conference underscored important links between infectious disease and cancer that leave open a number of interesting questions that mathematical biologists can explore. The conference closed with a period of discussion in working groups with goals such as Connecting within-host dynamics with population level incidence and transmission dynamics, Investigating the role of models in studying infectious diseases that lead to cancer, and Connecting models and parameters across different types of model structures. Participants in working groups made plans for future projects and mini-symposia to be organized for future scientific meetings. 

SMB MathEpiOnco 2024 was organized by Jason George (Texas A&M), Meredith Greer (Bates College, USA), Linh Huynh (Dartmouth College), Harsh Jain (University of Minnesota Duluth, USA), and Michael Robert (Virginia Tech, USA). For more information, visit the conference website:https://seminar.math.vt.edu/SMB-MEPI-ONCO/schedule.html

Upcoming Conferences and Workshops

Society for Mathematical Biology Annual Meeting

From 30^th June - 5^th July Friday 2024, the joint annual meeting of the Korean Society for Mathematical Biology and the Society for Mathematical Biology will be held at KonKuk University, Seoul, Republic of Korea. Early bird registration will be open until 30^th April 2024, for more details check the conference website: https://smb2024.org/

Royal Society Publishing

The following Royal Society theme issue has been highly cited, downloaded and is FREE to access online: ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’ compiled and edited by Dr Jasmina Panovska-Griffiths, Dr William Waites, and Professor Graeme J Ackland - see https://royalsocietypublishing.org/toc/rsta/2022/380/2233

The COVID-19 pandemic has highlighted the importance of mathematical modelling in informing and advising policy decision making. Via a collection of sixteen papers, this issue showcases how the Royal Society coordinated efforts of diverse scientists to help model the coronavirus epidemic and overcome a number of technical challenges. Different papers address the utilisations of different technical modelling frameworks and how different techniques are combined, show how modelling of different scenarios can give informed scientific advice, discuss how to correctly quantify the uncertainty of the model parameters and projections, and flag up the importance of transparency and robustness of models and numerical code to ensure reproducibility of the results. Read more in a blog post by one of the Guest Editors: https://royalsociety.org/blog/2022/08/modelling-epidemics-ramp/

We are also looking for new theme issues and that if you are interested in submitting a proposal, please visit the website https://royalsocietypublishing.org/rsta/guest-editors or contact the Editorial Office for more information - philtransa@royalsociety.org.

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People

By Alys Clark

We interviewed Professor Jae Kyoung Kim, Chief Investigator of the Biomedical Mathematics Group at the Institute for Basic Science, Republic of Korea and an academic staff member in Mathematics at the National University in Daejeon, Republic of Korea, find out more here.

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Editorial

By Sara Loo

A look forward to KSMB – a chat with Dr Yangjin Kim

As the year continues to tick quickly on and winter comes to an end, we can look forward to many exciting things. Not least of these is the upcoming Korean Society of Mathematical Biology – Society of Mathematical Biology joint meeting in July. In the lead up to this summer’s conference, and as submissions for minisymposia and contributed talks come streaming in, I met with Yangjin Kim, co-chair of the meeting’s organising committee to get to know a bit more about KSMB and what we can expect in Seoul in July.

On a wintery evening over Zoom, we chatted about the history of KSMB. Founded in 2005, its co-founders quickly established bridges across disciplines – one of the founders, Tae-Soo Chon is a biologist. This quickly and firmly founded the society within the biological science community, as well as in its natural habitat in the mathematical sciences. This led to many natural and fruitful collaborations. Starting from very small numbers, the society now draws in over 150 participants at their annual meetings. Beyond this, the society has been a strong advocate for the field in the Asia region, convening the China-India-Japan-Korea Conference on Mathematical and Theoretical Biology last year in Jeju Island, South Korea.

Having been a part of SMB since early in his research career, Yangjin speaks fondly of his experiences at SMB conferences. His passion for creating a similar environment for others across many different regions is evident. “I grew up with SMB”, he mentions. He has only missed two meetings since his first in Raleigh in 2005, and as a PhD student he earned himself a Landahl Travel Grant in 2006. These influences are long-reaching, and throughout our conversation he is reminded of how beneficial the society has been to him – “I always feel comfortable when I attend the SMB meeting every year… having a chance to talk to people in my research area and getting [to meet] mentors.” He has encouraged his students to attend the yearly meetings and “it has been wonderful for them, they say.”

He tells me how fruitful his interactions with SMB members have been. He has worked with many mentors and peers throughout his career and time as an SMB member – his thesis advisor Hans Othmer, Avner Friedman, Mark Chaplain, amongst others. Being a part of a community of like-minded peers and receiving advice, feedback and, even, criticisms from others in the society have marked his career. In some sense, he “[sees] it as the center of [his] career.” 

This sort of environment is something he values greatly, and something he seeks to share with researchers all over the world. I ask him what he hopes the conference will be like, or something he hopes it may achieve. “I want it to be really international”, he says. Though Yangjin trained in the US and spent 13 years there in his early career, his position at Konkuk University in South Korea has allowed him to grow and cultivate excitement and interest for the field in Asia. Throughout Asia, other regional societies of mathematical biology have popped up, and are starting to grow – the Phillipine Society for Mathematical Biology was launched earlier this year, and the CIJK conference last year was its eighth iteration. Holding KSMB-SMB in Seoul will be a great foundation for these smaller societies to gain support and interact with members of our larger community, stimulating ongoing research in the region. Already, they have seen a range of diverse abstracts from many Asian countries and young scientists.

So what else can we look forward to in Seoul in July? Yangjin mentions excellent food, beautiful modern and traditional buildings, some K-pop, a beautiful campus and perhaps some drone flying is on the cards. Beyond that, take a moment to be thankful for the joint meeting and the commitment of the organising committee in pulling this off. This was originally planned for 2022 and though it was inevitably postponed, here we are 2 years later. “It is a long time coming, [we] almost got exhausted from asking ‘when are we going to have this!’”, Yangjin laughs. It took many years of preparation, discussions have seen multiple SMB presidents, and ongoing commitment from the SMB board and members of KSMB. 감사합니다 See you in July!

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Featured Figure

By Thomas Woolley 

Early Career Feature - Ryan Murphy, University of Melbourne

In this issue, we feature the article “Formation and growth of co-culture spheroids: New compartment-based mathematical models and experiments”. This research was performed by Ryan J. Murphy (University of Melbourne), Gency Gunasingh (University of Queensland), Nikolas K. Haass (University of Queensland), and Matthew J. Simpson (Queensland University of Technology).

Tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. In our previous studies, we have connected the seminal Greenspan mathematical model to monoculture tumour spheroid growth data for the first time, leading to practical experimental design recommendations and quantification of the time evolution of spheroid structure (necrotic core, proliferation-inhibited intermediate region, proliferating rim). By considering time-dependent oxygen conditions, we also revealed that tumour spheroids can experience surprising necrotic core dynamics and transient reversal of growth phases that had been well-characterised for over fifty years.

In this study, we consider co-culture tumour spheroid growth experiments. Co-culture spheroid experiments are challenging to interpret as they are comprised of two or more cell types that may have different characteristics, such as differing proliferation rates or responses to nutrient availability. The dynamics are further complicated by multiple biological processes occurring on overlapping timescales. As Greenspan’s model has been valuable in analysing monoculture spheroid data, we first connect Greenspan’s model to co-culture data for the first time. We find that parameter estimates are consistent for co-culture spheroids seeded with different initial proportions of two cell types. However, since the model assumes all cells behave identically, it cannot capture experimentally observed internal dynamics of growing co-culture spheroids.

For greater insights, we generalise a class of compartment-based mathematical models previously restricted to spheroids composed of one cell type, such as Greenspan’s model, so that they can be applied to spheroids consisting of multiple cell types. It is then straightforward to develop and explore multiple natural two-population extensions to Greenspan’s seminal model, where the populations may differ with respect to their proliferation rate, death rate, response to nutrients, or migration preferences. By connecting these new models to data, we reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well suited to analyse spheroids grown with multiple cell types, and the new class of ordinary differential equation-based mathematical models provide opportunities for further mathematical and biological insights.

You can find out more about this research here: https://link.springer.com/article/10.1007/s11538-023-01229-1

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Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments

by  Ryan J. Murphy (University of Melbourne), Gency Gunasingh (Frazer Institute, University of Queensland), Nikolas K. Haass (Frazer Institute, University of Queensland), Matthew J. Simpson (Queensland University of Technology)

Read the paper

Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and develop anti-cancer therapies. However, they are challenging to interpret as they are composed of two or more cell types that undergo multiple biological processes on overlapping timescales. In this study, we interpret new co-culture spheroid experimental data using Greenspan’s seminal monoculture model and multiple new and natural two-population extensions of Greenspan’s model. This allows us to reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. The mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types. Further, the new class of compartment-based mathematical models, which includes Greenspan-type models as a special case, provide opportunities for further mathematical and biological insights. 

Dr Ryan J. Murphy performed the mathematical and statistical modelling. Ms Gency Gunasingh performed the experimental work. Professor Nikolas K. Haass and Professor Matthew J. Simpson contributed equally.

VisualPDE: Rapid Interactive Simulations of Partial Differential Equations

by Benjamin J. Walker, Adam K. Townsend, Alexander K. Chudasama & Andrew L. Krause

Read the paper

Mathematical biology and other areas of science are employing increasingly complex models that take the form of partial differential equations. Such models can exhibit a rich set of behaviours, including those that defy intuition, such as diffusion-driven pattern formation. In this paper we present VisualPDE, a web-based tool enabling  real-time interactive exploration of such models. We feel that such interactive 'play' is an incredibly important and under-utilized way to develop intuition and build deep understanding of these models.

The paper opens by saying that a reader should simply go and play on the website, VisualPDE.com, themselves. It then outlines our rationale for developing this tool, some of the technical and design issues we faced, as well as some of the examples and use-cases we have already explored. The structure of this paper supplements the 'living' website with things we think a reader might find interesting, particularly around the wider context and technical aspects of designing the website. We hope it helps the wider community deepen our understanding of PDE models, and rethink how we teach and do research using mathematics more generally.

Image caption: This is an interactive simulation on the website which can also be viewed at https://visualpde.com/sim/?preset=BMB . It uses spatial heterogeneity to force a reaction-diffusion system to exhibit both a complex prepattern and emergent spot-like patterns in different parts of the domain.

Scalable Gromov-Wasserstein Based Comparison of Biological Time Series

by Natalia Kravtsova, Reginald L McGee and Adriana T Dawes

Read the paper

In this paper, we introduce a rigorous and powerful method for comparing time series data using a novel and computationally efficient modification of the Gromov-Wasserstein optimal transport distance. In brief, our method, which we denote GW$_{\tau}$, views each trajectory as a separate metric space and compares these metric spaces via optimal transport. This feature of our method makes it exceptionally flexible in the types and size of data sets that can be compared, including data sets that occur on different time scales, are missing measurements, or even lie in spaces of different dimensions. Its rigorously demonstrated properties show a clear increase in efficiency and accuracy over other methods and using a variety of data. Using our method, we show that averaging time series using recently proposed Fused Gromov-Wasserstein barycenters provides more reliable average trajectories compared to the most commonly used mean trajectories. Our easily implemented and fast GW$_{\tau}$ method can be applied to a wide range of time series data, from cell biology to ecology, and allows for new comparisons and quantifications that preserve key features in the data sets.

Natalia Kravtsova, a student author, led the research in this paper, including formal analysis, methodology, and visualization. Prof. McGee and Prof. Dawes provided supervision. All three authors contributed to the formulation and conceptualization of the research, and manuscript preparation.

Alys Clark (University of Auckland), Sara Loo (Johns Hopkins University), Fiona R. Macfarlane (University of St Andrews), and Thomas Woolley (Cardiff University).

1. People – Interviews with Dr Adrianne Jenner and Dr Michael Watson.
2. Editorial – on 'Research that is worth a thousand words: Visualising a conference' on the theme of conference illustration.
3. Featured Figures – Highlighting the research by early career researcher Chloé Colson and highlighting the most accessed paper from the Bulletin of Mathematical Biology August 2023 issue.

People

By Sara Loo

We interviewed Dr Adrianne Jenner, lecturer at Queensland University of Technology, find out more here.

 

We interviewed Dr Michael Watson, lecturer in Applied Mathematics at the University of New South Wales in Sydney, Australia and co-chair of the Cardiovascular Modelling subgroup, find out more here.

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Editorial

By Thomas Wooley

Research that is worth a thousand words: Visualising a conference

Conferences, workshops, and study groups serve as critical hubs for innovative discussions and interdisciplinary collaborations. Yet, the traditional format of these gatherings has remained steadfast – talks, slides and projectors. Unfortunately, the insights shared during these talks often prove to be as transient as a fading dream, slipping away quickly, leaving us with fleeting memories.

Taking notes during lectures can help, and if the speaker is willing, you can supplement them with presentation slides. However, more often than not, we find ourselves returning from these events with notebooks filled with intricate spider diagrams and hastily scribbled ideas that seem more at home on a conspiracy theorist's corkboard.

The most recent innovation has been recorded talks; you can literally relive the presentation. However, spotty connection issues, poor sound recording and non-existent video editing aside, surely, we must be able to make memory recall more… fun?

While lectures and presentations will always be the core of these gatherings, there's an untapped approach that could revolutionise the conference experience – conference illustration. Illustrations are not only visually captivating, making even the most mundane topics intriguing, but they also provide tangible outputs that can be used to showcase current and future work, satisfy funding requirements, and elevate audience engagement.

An illustrated talk by Maria Abou Chakra on the presentation The Climate Game.

My introduction to this practice occurred during the COVID-19 pandemic when Maria Abou Chakra's remarkable work began circulating on Twitter. I wholeheartedly encourage you to explore her talents in mathematical biology and artistry by following her on Twitter, @MariaAbouChakra, (yes, I refuse to call it X) and visiting her collection of sci-sketches on her website (http://individual.utoronto.ca/abouchakra/sci-sketchnotes/). Her work is both beautiful and highly informative. She truly is a renaissance woman with a foot both in the science and the aesthetic!

I've had the privilege of presenting for Maria at the "Modelling Cell Development and Regeneration Discussion Group," and I've consistently used her illustrations to convey my work to academic and lay audiences. They're undeniably more appealing than a slew of equations and technical jargon.

Maria’s illustration of my talk about putting stochasticity, or “noise”, in biological patterning systems.

• During a recent conversation with Maria, she explained how illustrating talks helped her retain information, focusing on the core concepts rather than minutiae. She generously shared some valuable tips for those aspiring to follow in her footsteps:

• 1)     Organize your sketch space, decide where elements like titles, conclusions, and key ideas should be placed. Preparation is key, as space can fill up quickly.

• 2)     Technology is not a prerequisite; a pen, pencil, and paper can be a great starting point.

• 3)     If you prefer technology, consider using software like Autodesk SketchBook (free) or Procreate.

• 4)     Familiarize yourself with the features and brushes of your chosen app.

• 5)     Practice. Skills are honed over time through effort and dedication.

However, for those without the time, skills, or inclination for such artistry, consider hiring an illustrator for your next conference. It's important to acknowledge that while these artists may not come cheap, their work holds immense value. In an era where AI produces "art", we must not underestimate the genuine skill of condensing and presenting information in a visually curated manner. We should be willing to compensate those with artistic talents, ensuring that such skills don't become lost, or devalued, in the face of automation.

If you're working with a tight conference budget, I understand that this may not be your top priority. However, if you have some flexibility in your finances, take a moment to explore the pool of talented illustrators available. You may be pleasantly surprised by the options at your disposal. Posting a message on Twitter, or Facebook could yield enthusiastic responses from skilled illustrators.

In a recent conference on interdisciplinary IVF challenges, https://thefertilitynetwork.wixsite.com/infer,  conducted with my colleague Dr Katerina Kaouri and funded by GW4, https://gw4.ac.uk/, we were fortunate to have some extra funds available. After evaluating our options, we decided to engage a local artist, Eleanor Beer (https://www.eleanorbeer.com/), as our conference illustrator.

Eleanor readily admitted she wasn't an IVF expert, but this was precisely the point. She focused on capturing the big ideas and overarching themes of the conference, not on mining details for her next research paper.

Eleanor Beer’s illustration of our recent “Interdisciplinary Challenges in IVF” conference.

Unsurprisingly, both the delegates and the organizing committee were thrilled with Eleanor's work. She provided us with a piece of art that we eagerly anticipate displaying in our department. It stands as a constant reminder of our funding success and the continuing scientific challenges that need to be addressed.

As we uncover the potential of incorporating illustrators into conferences, it becomes clear that their contributions have the power to revolutionize how we disseminate and absorb information. Their work transcends language barriers and kindles our scientific creativity. The benefits are substantial, and it is high time to recognize and embrace the visualization of conferences.

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Featured Figures

By Fiona Macfarlane

Early Career Feature - Chloé Colson, University of Oxford, UK

In this issue, we highlight research from Chloé Colson, a PhD student at the University of Oxford (UK) working with Philip Maini and Helen Byrne. We asked Chloé to tell us a little more about their paper `Investigating the Influence of Growth Arrest Mechanisms on Tumour Responses to Radiotherapy’:

Cancer is a heterogeneous disease, with tumours of the same type exhibiting large variation at the genotypic and phenotypic levels. These differences can have a significant influence on tumour sensitivity to treatment and, more generally, on patient prognosis. Improving our understanding of the mechanisms underpinning cancer is, therefore, essential for the development of effective patient-specific therapeutic protocols. In this paper, we aim to assess how two distinct mechanisms of growth control may affect tumour responses to radiotherapy (RT), an established cancer treatment used to treat more than 50% of cancer patients.

In previous work (Colson et al. 2022), we developed a novel ordinary differential equation model of solid tumour growth which distinguishes between growth arrest due to nutrient insufficiency, when cell proliferation and death rates balance, and due to contact inhibition, when the cell proliferation rate converges to zero, with no cell death. While it has been shown that both of these mechanisms can be simultaneously active in vitro in 2D monolayer and 3D spheroid assays (Helmlinger et al. 1997), most models of tumour growth only describe a single growth control mechanism. By considering both nutrient and space limited growth, our model exhibits three distinct regimes: nutrient limited (NL), space limited (SL) and bistable (BS), where both mechanisms of growth arrest coexist.

In the present work, we extend our tumour growth model to include time-dependent responses to RT and systematically study RT response in the three growth regimes introduced above. We construct three virtual populations of NL, SL and BS tumours, and, for each population, we initially consider tumour responses to a conventional fractionation schedule consisting of 5x2 Gy fractions per week for 8 weeks. We determine average responses and explore how values of key parameters (i.e., the tumour oxygen consumption rates (q₁, q₃) and the vascular volume) generate extreme (i.e., strongly positive and negative) behaviour. We find that tumour responses to RT are regime-dependent, with tumours in the SL cohort responding positively and tumours in the BS cohort responding poorly. We also identify the biological processes that may explain positive and negative treatment outcomes in each regime. For instance, as shown in the Figure, we find that increased RT efficacy for SL tumours may be due to limited tumour regrowth and/or RT cell kill. Finally, by studying the impact of the total dose and dosing frequency on tumour response, we elucidate how dosing strategies that maximise the reduction in tumour burden vary between regimes; higher doses applied at higher frequency are beneficial for SL tumours, whereas lower doses applied at lower frequency can be more effective for NL and BS tumours.

Subject to the validation of our findings with experimental data, we believe that our modelling framework has the potential to help guide patient-specific treatment protocol design and, thus, contribute to improving patient prognosis.

You can find out more about this interesting work here: https://link.springer.com/article/10.1007/s11538-023-01171-2

Most accessed article in the Bulletin of Mathematical Biology in August 2023

The article entitled “Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?” was the most accessed article in the August edition of the Bulletin of Mathematical Biology. This article was written by Georgia Weatherley, Robyn P. Araujo, Samantha J. Dando and Adrianne L. Jenner from the Queensland University of Technology.

In this paper, the authors review the existing mathematical efforts to understand multiple sclerosis (MS), a neuroimmunology disease affecting the brain and spine. The goal with this review was to highlight the opportunities for mathematicians to have major impact on MS, both in terms of diagnosis, prognosis and improving treatment design.

MS is a neurodegenerative disease where myelin, which surrounds and protects neurons in the brain and spine, is degraded by an overactive immune system. The loss of myelin causes a range of physical and cognitive impairments for which there is currently no cure. Existing mathematical models of MS, while limited in volume in comparison to diseases such as leukemia or malaria, are diverse and insightful. Modelling works range from non-spatial deterministic models (ODEs) to spatially deterministic models (PDEs) and spatially stochastic models (ABMs).

The authors summarise, to the best of their knowledge, all existing mathematical efforts to capture MS across the four major disease scales: population, systemic, CNS and molecular (cellular). As such, this review serves as a foundation for future modelling works in MS.

The modelling techniques developed by mathematical oncologists and immunologists are readily translatable to MS and could provide much needed answers to open problems in this complex, profoundly heterogeneous disease. This review is a call to arms for the mathematical biology community, complete with a list of open problems that could benefit from a mathematical approach.    

You can find out more about this interesting work here: https://link.springer.com/article/10.1007/s11538-023-01181-0

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