Aug 2026· Bulletin of Mathematical Biology· Vol 88· 53 references
Mathematical Biology Tumor Growth
Abstract
Abstract Intra-tumor heterogeneity in proliferation rates fundamentally influences cancer progression and treatment resistance. To investigate how continuous phenotypic variation shapes eco-evolutionary dynamics, we develop a phenotype-structured partial differential equation framework that explicitly models proliferation heterogeneity as a dynamic trait. Our model integrates three key biological principles: (1) phenotypic diffusion capturing heritable variation in proliferation rates, (2) global resource competition enforcing density-dependent growth constraints, and (3) an experimentally grounded life-history trade-off linking elevated proliferation to increased mortality. Using adaptive dynamics, we derive the optimum proliferation rate in a growing tumor, showing that the optimal phenotype dynamically shifts toward slower proliferation as tumors approach carrying capacity under control condition. We perform in silico treatment simulations for four different treatment regimes (pan-proliferation, low-, mid-, and high-proliferation targeting) to show how therapeutic selective pressures reshape fitness landscapes. While all treatments slow down tumor growth, they induce divergent evolutionary trajectories. We connect these dynamics with changes in mean proliferation rates during and after treatment. Our work establishes a predictive, evolutionarily grounded framework for understanding how therapy reshapes tumor proliferation landscapes, offering a mechanistic basis for designing strategies that anticipate and counteract adaptive resistance.
The results are packaged in the Greenfield Startup Model (GSM), which explains the priority of startups to release the product as quickly as possible, and the need to shorten time-to-market, by speeding up the development through low-precision engineering activities.
Carmine Giardino, Nicolò Paternoster, M. Unterkalmsteiner et al.· IEEE Transactions on Softwar...· 178 citations· ⚡14
Software startup companies develop innovative, software-intensive products within limited timeframes and with few resources, searching for sustainable and scalable business models.
M. Unterkalmsteiner, P. Abrahamsson, Xiaofeng Wang et al.· e-Informatica Software Engin...· 157 citations· ⚡17
This study conducts a case survey study based on the secondary data of the major pivots happened in 49 software startups, and demonstrates that customer need pivot is the most common among all pivot types.
Sohaib Shahid Bajwa, Xiaofeng Wang, Anh Nguyen-Duc et al.· Empirical Software Engineeri...· 127 citations· ⚡15
The comparison of adopter and non-adopter sample reveals three potential adoption inhibitor, security, data privacy, and portability, which underlines the importance of the technical and security perspectives for research investigating the adoption of technology.
Nattakarn Phaphoom, Xiaofeng Wang, S. Samuel et al.· Journal of Systems and Softw...· 111 citations· ⚡8
This study investigates how Lean internal startup facilitates software product innovation in large companies and identifies its enablers and inhibitors, and shows the potential of the method-in-action framework to investigate the Lean startup approach in non-startup context.
Henry Edison, Nina M. Smørsgård, Xiaofeng Wang et al.· Journal of Systems and Softw...· 78 citations· ⚡6
The application of agile software methods and more recently the integration of Lean practices contribute to the trend of continuous improvement in the software industry. One such area warranting proper empirical evidence is a project’s operational efficiency when using the Kanban method. This short paper takes a new an...
Marko Ikonen, Petri Kettunen, Nilay V. Oza et al.· EUROMICRO Conference on Soft...· 67 citations· ⚡9
Related blog posts
MIT News · Artificial Intelligence· news.mit.eduOct 18, 2026
A new computational approach reveals how cells communicate to assemble into tissues. This could accelerate stem cell engineering, improve disease models, and inform therapies.