Mini-Workshop: Mathematical Models for Cancer Cell Migration
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Tumour cell invasion is an essential hallmark in the progression of malignant cancer. Thereby, cancer cells migrate through the surrounding tissue (normal cells, extracellular matrix, interstitial fluid) towards blood or lymph vessels which they penetrate and thus access the blood flow. They are carried by blood circulation to distant locations where they extravasate and develop new tumours, a phenomenon known as metastasis. The invasive spread of cancer cells is highly complex – it involves several mechanisms, like diffusion, chemotaxis and haptotaxis; these in turn are conditioned by and influence the subcellular dynamics. Mathematical models offer a powerful tool to gain insight into the complicated biological processess connected to tumour invasion and have also stimulated advanced mathematical research. Some of the new developments in the field of biomedical oncology were inspired by such models. A significant challenge arises due to the interactions of cancer cells with a complicated and structured microenvironment of healthy tissue. Many of the models of cancer cell migration are based on partial differential equations (PDEs) including spatial heterogeneity, orientational tissue structure, tissue stiffness and deformability. Specific settings relate to reaction-diffusion equations, transport equations, continuum equations, and to their multi-scale analysis, to local and global existence and uniqueness, to pattern formation, blow-ups and invasions. A further approach involves agent-based models providing a characterisation of cell migration by way of simulating the (inter)actions of autonomous agents (individual cells, collective dynamics) and aiming for assessing their effects on the entire system. In this meeting we covered the full spectrum between macroscopic PDE models and microscopic individual based models with the common goal of modelling cancer cell migration. Of particular interest was the derivation of macroscopic properties from microscopic details. Similar multiscale models have been used in other contexts (such as chemotaxis for example), and we gained some significant insight from the collaborations in this workshop. In this one week meeting we posted nine open ended problems (outlined below), which will form the seed for new collaborations going far beyond this workshop.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it