Pith. sign in

REVIEW 4 major objections 6 minor 2 cited by

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Tumour blood-vessel networks and early mutations jointly drive drug resistance in a hybrid PDE-agent model.

desk verdict Plausible hybrid model with suggestive results, but single-run evidence and hand-tuned parameters leave the central claims unestablished. read the letter →

arxiv 2505.22580 v1 pith:QZCSNGXX submitted 2025-05-28 math.NA cs.NA

Louis Shuo Wang , Jiguang Yu , Zonghao Liu This is my paper
classification math.NAcs.NA MSC 92C5065M0635Q92
keywords drugresistanceangiogenesishybriddiscrete-continuousmodelagent-basednon-smallcelllungcancerT790Mmutationtumourmicroenvironmentmutation-selectionfeedback
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that angiogenesis, the growth of new blood vessels into a tumour, does more than feed the tumour: it shapes how drug resistance evolves. Using a hybrid model in which reaction-diffusion equations describe oxygen, drug, and tumour-angiogenic-factor fields while agent-based rules track individual tumour and endothelial cells, the authors simulate two resistance scenarios. With pre-existing resistant cells, newly formed vessels create perivascular sanctuaries where oxygen-driven proliferation outweighs drug damage, letting resistant cells persist. With spontaneous mutation, earlier and more frequent mutations give the tumour a larger survival advantage, and a positive feedback loop emerges: faster proliferators mutate more often, and the drug selects the more resistant survivors, so high proliferation and high resistance come to dominate together. The authors claim this loop resolves conflicting experiments on the T790M second-site EGFR mutation in non-small cell lung cancer, one showing a growth disadvantage and the other showing synergistic oncogenic activity.

What carries the argument

The engine of the argument is a hybrid discrete-continuous (HDC) model: reaction-diffusion PDEs for tumour angiogenic factor, oxygen, and drug concentration are solved on a grid with finite-difference and alternating-direction implicit methods, while tumour cells and endothelial tip cells are agents with rules for movement, branching, anastomosis, proliferation, apoptosis, and mutation. The load-bearing new component is the consecutive random mutation algorithm, in which each mutation multiplies a cell's death threshold, oxygen consumption rate, and proliferation rate by independent random factors drawn from $U[0.7,1.7]$ (bounded to $[0.5x,4x]$), producing gradual, non-directional trait changes. The feedback loop the authors identify is the mechanism that carries the biological conclusion: proliferation rate controls mutation frequency at a fixed mutation rate, and resistance controls survival under drug, so the two traits reinforce each other under selection and eventually yield dominance of cells carrying both.

What would settle it

Run the same agent-based simulation with the mutation rate decoupled from proliferation, for example as a fixed per-cell probability per time step rather than per division, and check whether high proliferation and high resistance still co-dominate; if they do not, the proposed feedback mechanism is not necessary for the result. Alternatively, in spatial data from EGFR-TKI-resistant non-small cell lung cancer, test whether resistant and fast-proliferating clones preferentially colocalise near vessels, since a uniform distribution would contradict the perivascular sanctuary claim.

Watch

Extended reading notes

Core claim

In the paper's own terms, the central discovery is that tumour-induced angiogenesis produces a microenvironment that enhances both pre-existing and mutation-induced drug resistance, and that spontaneous resistance is governed by a mutually reinforcing coupling between proliferation rate and resistance. In the pre-existing case, vessels supply oxygen near the tumour, and because oxygen-driven division halves cellular drug damage at each generation while drug damage accumulates linearly, the region around vessels becomes a sanctuary where resistant cells survive low-dose treatment. In the spontaneous case, a consecutive random mutation algorithm lets daughter cells alter death threshold, oxygen consumption, and proliferation rate by random factors; selection under drug pressure then favours cells with both elevated resistance and elevated proliferation, because at fixed mutation rate more divisions mean more mutation opportunities, and the resistant survivors keep proliferating. The paper identifies this feedback as the reason that cells combining high proliferation with high resistance eventually dominate, and it presents the early-time mutation accumulation window as the period when treatment can still succeed.

Load-bearing premise

The qualitative conclusions, such as the perivascular sanctuary, the earlier-mutation advantage, and the proliferation-resistance feedback, are assumed to survive changes in the hand-set parameters (TAF source $k=5$, oxygen supply $S_o=3.5$, adjusted TAF production $\eta=1000$) and in the ad hoc $U[0.7,1.7]$ mutation multiplier, but no sensitivity analysis or ensemble statistics are reported to verify this.

Editorial extensions

If this is right

  • If the perivascular sanctuary mechanism is right, tumour cells nearest to newly formed vessels should be the hardest to eliminate with low-dose continuous therapy, and vessel-rich regions should be the first site of resistance-driven recurrence.
  • If earlier and more frequent mutations confer greater survival advantage, then delaying resistance by reducing mutation opportunities, for example by cytostatic control of proliferation, should measurably improve treatment outcome rather than merely delaying regrowth.
  • The model's resolution of the T790M conflict implies that the growth-disadvantage and growth-advantage phenotypes are not contradictory states of the same mutation but different evolutionary outcomes: the resistance mutation alone can slow growth, while co-selected additional alterations produce aggressively proliferating resistant clones.
  • The optimal-scheduling comparison in the paper implies that pulsed high-dose and continuous low-dose regimens with equal total dose differ in which resistance mechanism they fail against, so treatment choice should depend on whether resistance is pre-existing or mutation-driven.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension would be to make the mutation rate itself a function of local drug concentration and proliferation state rather than a fixed per-division constant, and to ask whether the high-proliferation/high-resistance correlation strengthens or weakens under that rule.
  • If the feedback loop is general, then any therapy that decouples division from mutation, such as drugs that slow cycling without killing, should suppress the emergence of dual-trait dominance; this could be checked in agent-based models before clinical translation.
  • The perivascular sanctuary prediction could be tested against spatial transcriptomics or multiplex imaging of EGFR-TKI-resistant lung tumours: resistant and highly proliferative clones should colocalise near vessels, whereas the model would be undermined if they are uniformly distributed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a hybrid PDE–agent-based model of tumour-induced angiogenesis and drug resistance, coupling reaction–diffusion equations for TAF, drug, and oxygen with agent-based tumour and endothelial cells, including stochastic branching, anastomosis, and a consecutive random mutation algorithm. The numerical study reports that pre-existing resistant cells create a perivascular sanctuary that sustains the tumour under continuous low-dose treatment; that spontaneous mutation at higher rates confers a survival advantage; that high proliferation and high resistance traits appear to reinforce each other and lead to dominance of cells carrying both traits; and that these findings explain conflicting experimental observations on the T790M EGFR mutation in NSCLC. The paper also compares continuous versus pulsed drug-delivery strategies.

Significance. If the reported findings are robust, the model would be a valuable in silico platform for studying how angiogenesis and the tumour microenvironment shape both pre-existing and acquired drug resistance, and it could motivate testable hypotheses about perivascular sanctuary sites and the co-selection of proliferation and resistance traits. The model has several strengths: it integrates a well-established angiogenesis framework (Anderson–Chaplain) with stochastic agent dynamics; it calibrates vascularization time to the 14-day experimental benchmark in Section 3.1; it includes a detailed parameter table and a flowchart in Appendix C; and Section 5(iv) explicitly acknowledges a real limitation (vessel-wall permeability). However, the central qualitative claims currently rest on single stochastic trajectories with hand-tuned parameters, and the clinical interpretation is analogical; unless these gaps are closed, the paper can only support a weaker, hypothesis-generation claim.

major comments (4)
  1. [Section 3.6 (Figs. 7, 9–12)] The central qualitative claim—that high proliferation rate and high resistance are mutually reinforcing and culminate in the simultaneous emergence and final dominance of cells carrying both traits—is supported only by individual simulation runs. The model is heavily stochastic (Brownian motion for cell positions, U[0.7,1.7] mutation multipliers, random daughter-cell placement, Poisson branching, random anastomosis choices), yet no ensemble statistics, confidence intervals, or even the number of repeated runs are reported. Section 3.1 mentions 'extensive simulations (results not shown)' without giving the ensemble size or a summary statistic. Because the four-mutation-rate comparison and the spatial-overlap claims in Figures 7–12 could arise from a single atypical trajectory, the robustness of the central claim is unverified. Please report means and variances over repeated runs, and quantify the spatial and temporal co-occurrence of high-proliferation and high-resistance cells.
  2. [Section 2.4 and Section 3.6(ii)] The proposed 'mutually reinforcing relationship' is partly built into the model by construction. Section 2.4 states that mutations occur 'when tumour cells divide,' and Section 3.6(ii) then reasons that higher proliferation rates, at fixed mutation rates, lead to promoted mutation frequencies. Since mutation events are tied to division, a higher proliferation rate necessarily produces more mutation opportunities per unit time; the resulting positive feedback between proliferation and resistance is therefore a consequence of the mutation algorithm rather than an emergent property of the tumour–microenvironment interactions. To support the claim as an emergent finding, the authors should either decouple the per-unit-time mutation rate from the division rate (for example, by allowing division-independent mutational events and repeating the analysis) or explicitly state that the reinforcement is an assumption of the model.
  3. [Section 3.7, Table 1] Table 1 is missing the reported success/failure outcomes. The text states that check/cross symbols 'indicate the success and failure of treatment,' but the corresponding table entries are blank for all seven strategies and for both pre-existing and spontaneous resistance. As a result, the paper's comparative claim about treatment strategies—and any inference about optimal dosing—is not supported as printed. Please supply the complete table with the outcome of each strategy, and indicate the criterion used to define success (for example, extinction of the tumour within a specified time horizon). Ideally, report outcomes over an ensemble of stochastic runs rather than a single trajectory.
  4. [Section 4 and Appendix B] The claimed explanation of the T790M paradox is analogical rather than mechanistic. The model tracks generic 'proliferation rate' and 'death threshold' traits and contains no EGFR allele, no TKI, and no T790M; the link from the simulated co-dominance of fast-growing, drug-resistant cells to the conflicting clinical observations of T790M growth disadvantage versus advantage is asserted rather than derived. At minimum, the manuscript should change 'explain' to 'is consistent with a generic mechanism and predicts ...' and specify a clinical or experimental prediction that would distinguish the hypothesis. In addition, the parameter-reporting inconsistencies in Appendix B prevent reproduction of the calibration: the text states that eta is adjusted to 10^3 and that Do=0.35 and rho_o=0.57 are used, but Table B.2 lists eta=6.2669e3, Do=0.64, rho_o=34.3881, and the cell-cycle time is described in the text as 8 hours while Table B.2 gives M_age ~ U[0.9,1.1] days with non-dimensional values 9/16–11/16. These values should be reconciled, and a sensitivity analysis over k=5, S_o=3.5, and the mutation multiplier interval U[0.7,1.7] should be reported.
minor comments (6)
  1. [Section 2.1] The text announces random diffusion, chemotaxis, and haptotaxis, but the flux J_n contains only diffusion and chemotaxis; haptotaxis is never defined.
  2. [Section 2.1 / Appendix A / Section 6] The PDE discretization is described inconsistently: Section 2.1 says forward Euler finite differences are used for all PDEs, while Appendix A.2 introduces an ADI scheme and Section 6 says the ADI method was used; Appendix A.1 only details the endothelial-cell equation. Please clarify which scheme was used for each equation.
  3. [Appendix C] The flowchart refers to updating 'Fibronection' concentrations, but no fibronectin field appears in the model equations; the flowchart should be aligned with the model.
  4. [Section 2.4 / Section 3.6] The mutation intensity mu is called a Poisson intensity per time step, but Section 3.6 cites the biological rate per replication as 10^-6–10^-2 and then uses mu up to 10^-1; the relationship between the per-replication rate and the time-step intensity should be stated, and the use of values above the cited biological range should be justified.
  5. [Section 3.7] The term 'optimal' in the Introduction and Section 3.7 is not supported because only seven fixed strategies are compared and no objective function is defined; consider replacing 'optimal' with 'comparative' unless a formal optimization is performed.
  6. [Introduction and Section 3.1] There is a typo in the Introduction ('formulalted' in the sentence about Pillay et al.) and inconsistent spelling of 'brush border' ('brush board' in Section 3.1); please proofread.

Circularity Check

3 steps flagged · score 6.0 of 10

Partial circularity: the mutual-reinforcement and synchronized co-emergence claims restate the per-division simultaneous-trait mutation rule, and the 14.08-day vascularization and carrying-capacity results are calibration targets reported as findings.

  1. self definitional [Section 2.4 (Mutation); Section 3.6 (Spontaneous Mutation, item (ii), Figures 9-12)]
    "When tumour cells divide, daughter cells may acquire mutations... higher proliferation rates at fixed mutation rates lead to promoted mutation frequencies, thereby boosting the likelihood of producing cells that are more resistant to treatment. As a result, high proliferation rates and high resistance traits reinforce each other... the appearance and prevalence of cells with increased proliferation rates appear to be in sync with those exhibiting enhanced resistance traits."

    The paper presents the proliferation-to-resistance channel as a finding, but the channel is the model's per-division mutation rule restated: mutations occur only 'when tumour cells divide' (Section 2.4), so a faster-proliferating lineage necessarily draws more mutation multipliers, and resistance is defined as a higher death threshold that mutations can raise. The claimed synchronized appearance of high-proliferation and high-resistance cells is likewise forced by construction: one mutation event simultaneously multiplies death threshold, oxygen consumption, and proliferation rate in the same cell, so any cell becoming resistant changes its proliferation rate at the same instant.

  2. fitted input called prediction [Section 3.1 (Initial TAF Field)]
    "We must choose the value of k so that our vascular growth is in agreement with some existing experimental data. In [12], 14 days is a typical value in many experiments for the time required to complete vascularization... After trial and error, we find that the appropriate value for k is k = 5, under which the time to complete vascularization in our simulation is 14.08 days, and the final pattern of vessels in Figure 1 is qualitatively similar to the result in Fig. 11 of [15]."

    k = 5 is the fit: it is chosen 'after trial and error' specifically so that the simulated vascularization time matches the 14-day experimental value quoted from [12]. Reporting '14.08 days' as the model's output is then reporting the calibration target back as agreement with data; the agreement is forced by construction and carries no independent predictive content at that point of the argument. The qualitative brush-border comparison to [15] is likewise a post hoc pattern match within the fitted regime.

1 more flagged steps
  1. fitted input called prediction [Appendix B (Parameter Estimation); Section 3.3 (Vascularization)]
    "When So is small, that is, So = 3, the tumour will experience hypoxia and cease to expand. In contrast, a high supply rate, that is, So = 5, facilitates enough access of tumour cells to oxygen, causing exponential tumour growth. We choose an intermediate value So = 3.5, which triggers the tumour to expand and eventually reach a new carrying capacity... the tumour population reaches a new carrying capacity... this is the mature stage of tumour development."

    The carrying-capacity behaviour presented in Section 3.3 as a model result is the exact criterion used in Appendix B to select So: So = 3.5 is chosen because it 'triggers the tumour to expand and eventually reach a new carrying capacity.' The finding that the population reaches a 'mature stage' carrying capacity whose steady state is set by the supply rate is therefore the fitting target restated as an emergent outcome. The parameter table does label So 'calibrated,' but the narrative in Section 3.3 presents the resulting behaviour as a discovery rather than as the imposed selection criterion.

full rationale

I examined all six circularity patterns. There are no author self-citations in the reference list (references [1]-[46] are external), so the self-citation, uniqueness-import, and ansatz-smuggling patterns do not apply; the passive/active adaptation distinction is a classification of two mechanisms already encoded, not a renamed empirical result presented as new. Three constructive reductions were found. First, the central claim of mutual reinforcement between high proliferation and high resistance rests on the assertion that higher proliferation leads to higher mutation frequency, which is exactly the Section 2.4 rule that mutations occur upon division; and the synchronized appearance of the two traits is forced because each mutation event updates all three trait values in the same cell. Second, the vascularization time of 14.08 days is the calibration target for k = 5, then reported as agreement with experiment. Third, reaching a carrying capacity is the calibration target for So = 3.5, then reported as the model's mature-stage behaviour. The final dominance of dual-trait cells and the resistance-versus-mutation-rate ordering retain genuine emergent content from the agent-based dynamics (drug selection, hypoxia, crowding), and no parameter is fitted to the resistance conclusions themselves, so the paper is not wholly circular. The absence of ensemble statistics and sensitivity analysis is a robustness concern, not circularity, and is excluded per the review rules. Overall: partial circularity, score 6.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on several domain assumptions borrowed from prior models, plus hand-chosen parameters and an ad hoc mutation rule. No new physical or biological entities are introduced. The model's qualitative behavior is tuned through calibration, and the robustness of the main conclusions to these choices is not demonstrated.

free parameters (4)
  • TAF source amplitude k = 5
    Set by trial and error to match vascularization time of 14 days (Section 3.1).
  • Oxygen supply rate So = 3.5
    Calibrated to produce a tumor that expands then reaches carrying capacity (Appendix B).
  • TAF production rate eta (adjusted) = 1000
    Adjusted because the non-dimensional value led to unreasonable results (Appendix B).
  • Mutation multiplier interval = U[0.7, 1.7] with clipping [0.5x, 4x]
    Chosen by hand as part of the consecutive random mutation algorithm, without biological calibration (Section 2.4).
assumptions (4)
  • domain assumption The Anderson-Chaplain hybrid discrete-continuous framework is a valid description of tumor angiogenesis.
    The model adopts the equations and rules from [15] without re-derivation (Section 2).
  • ad hoc to paper The consecutive random mutation algorithm with U[0.7,1.7] multipliers approximates biological mutation.
    Introduced to avoid abrupt trait changes, but no biological calibration is provided (Section 2.4).
  • domain assumption The T790M mutation is representable by generic increases in death threshold, proliferation and oxygen consumption traits.
    The model does not include EGFR or T790M-specific mechanisms; Section 4 draws the analogy.
  • ad hoc to paper The calibrated parameters (k, So, eta) can be varied without changing the qualitative conclusions.
    No sensitivity analysis is provided, so the invariance of the central claims is assumed (Sections 3.1, 3.6, Appendix B).

how reviews work

0 comments
Cite this review

Pith. "Pith review of A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment." pith.science (2026). https://pith.science/paper/QZCSNGXX

@misc{pith2026250522580,
  author       = {Pith},
  title        = {Pith review of: A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QZCSNGXX}},
  note         = {Machine review of arXiv:2505.22580}
}
read the original abstract

The main obstacle to effective cancer treatment is the development of drug resistance, which can be divided into two categories: spontaneous and acquired drug resistance. Non-small cell lung cancer (NSCLC) is the main cause of cancer-related deaths worldwide. A subset of lung cancer, adenocarcinomas, is characterised by mutations in the epidermal growth factor receptor (EGFR) gene. Treatment of EGFR-mutated lung adenocarcinomas has become less effective over time due to drug resistance development, which is associated with a second mutation in the EGFR gene. An important factor in the development of cancer is angiogenesis, which is the formation of blood vessels from the existing vasculature. These newly formed blood vessels provide oxygen and nutrients to tumour cells to maintain tumour growth and proliferation. We applied a hybrid discrete-continuous (HDC) model to capture the dynamic vasculature in the tumour microenvironment (TME). In the case of pre-existing resistance, the formation of angiogenic networks creates a microenvironment that supports tumour survival and enhances drug resistance. In the case of spontaneous mutation-induced resistance, earlier and more frequent mutations confer a greater survival advantage to the tumour population. There is also a mutually reinforcing relationship between a high proliferation rate and high resistance characteristics. These findings explain two conflicting experimental results about the second mutation in NSCLC.

Figures

Figures reproduced from arXiv: 2505.22580 by the authors.

Figure 1
Figure 1. Vascular network up to t = 23.04 9 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Vascularization 11 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Tumor number under vascularization 12 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: No resistance 3.5. Pre-existing Resistance If a small fraction of resistant cells are present before treatment, continuous low-dose treatment is ineffective in removing the tumour, and the tumour population survives. We define the declining point to be the first time t…
Figure 5
Figure 5. Figure 5: pr = 0.2, 0.3, 1 14 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: pr = 0.2, 0.3, 1 15 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Spontaneous mutation case with µ = 10−1 , 10−2 , 10−3 , 10−4 17 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Spantaneous mutation case with µ = 10−1 , 10−2 , 10−3 , 10−4 20 [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Temporal evolution of oxygen consumption rate and proliferation rate distributions [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: Spatial distribution of oxygen consumption rate [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 11
Figure 11. Figure 11: Spatial distribution of proliferation rate [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: Spatial distribution of resistance trait [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reflected Optimal Stopping with a Max-Type Payoff: Measure-Valued Stopping Gains and Killed Resolvent Representation

    math.AP 2026-07 conditional novelty 6.0 of 10

    For reflected diffusion optimal stopping with G=x1∨αx2, the gain Γ is a signed measure with singular diagonal part −(n⊤an)/(2√(1+α²))σΔ, and V=G−R_C^r Γ (killed at first entry to the stopping set).

  2. Multiplier Sensitivity in Isoperimetric Optimal Control

    math.AP 2026-07 accept novelty 6.0 of 10

    Under stated convexity and attainability conditions, the isoperimetric Pontryagin multiplier is the negative supergradient of the constrained value function, and this sensitivity can survive when the modified control-...

Reference graph

Works this paper leans on

46 extracted references · 45 canonical work pages · cited by 2 Pith papers

  1. [22]

    Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis

    Heng Yang, Haofeng Lin, and Xiaoqiang Sun. Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis. Computational and Structural Biotechnology Journal , 21:5285–5295, 2023

    work page 2023

  2. [1]

    Environment-mediated drug resistance: a major contributor to minimal residual disease

    Mark B Meads, Robert A Gatenby, and William S Dalton. Environment-mediated drug resistance: a major contributor to minimal residual disease. Nature reviews cancer, 9(9):665–674, 2009

    work page 2009

  3. [2]

    The mathematics of cancer: integrating quantitative models

    Philipp M Altrock, Lin L Liu, and Franziska Michor. The mathematics of cancer: integrating quantitative models. Nature Reviews Cancer, 15(12):730–745, 2015

    work page 2015

  4. [3]

    A review of mathemat- ical models for tumor dynamics and treatment resistance evolution of solid tumors

    Anyue Yin, Dirk Jan AR Moes, Johan GC van Hasselt, Jesse J Swen, and Henk-Jan Guchelaar. A review of mathemat- ical models for tumor dynamics and treatment resistance evolution of solid tumors. CPT: pharmacometrics & systems pharmacology, 8(10):720–737, 2019

    work page 2019

  5. [4]

    Integrating models to quantify environment- mediated drug resistance

    Noemi Picco, Erik Sahai, Philip K Maini, and Alexander RA Anderson. Integrating models to quantify environment- mediated drug resistance. Cancer research, 77(19):5409–5418, 2017

    work page 2017

  6. [5]

    Mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment

    James M Greene, Jana L Gevertz, and Eduardo D Sontag. Mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment. JCO clinical cancer informatics , 3:1–20, 2019

    work page 2019

  7. [6]

    Optimization of dosing for egfr-mutant non–small cell lung cancer with evolutionary cancer modeling

    Juliann Chmielecki, Jasmine Foo, Geoffrey R Oxnard, Katherine Hutchinson, Kadoaki Ohashi, Romel Somwar, Lu Wang, Katherine R Amato, Maria Arcila, Martin L Sos, et al. Optimization of dosing for egfr-mutant non–small cell lung cancer with evolutionary cancer modeling. Science translational medicine, 3(90):90ra59–90ra59, 2011

    work page 2011

  8. [7]

    A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy

    Fr´ ed´ erique Billy, Benjamin Ribba, Olivier Saut, H´ el` ene Morre-Trouilhet, Thierry Colin, Didier Bresch, Jean-Pierre Boissel, Emmanuel Grenier, and Jean-Pierre Flandrois. A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy. Journal of theoretical biology,...

    work page 2009

Show all 46 references
  1. [8]

    A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy

    Trachette L Jackson and Helen M Byrne. A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Mathematical biosciences, 164(1):17–38, 2000

    2000

  2. [9]

    Angiogenesis and chemotherapy resistance: Optimizing chemotherapy scheduling using mathematical modeling

    Mariusz Bodzioch, Piotr Bajger, and Urszula Fory´ s. Angiogenesis and chemotherapy resistance: Optimizing chemotherapy scheduling using mathematical modeling. Journal of Cancer Research and Clinical Oncology , 147(8):2281–2299, 2021

    2021

  3. [10]

    Mathematical modeling of therapy-induced cancer drug resistance: connecting cancer mechanisms to population survival rates

    Xiaoqiang Sun, Jiguang Bao, and Yongzhao Shao. Mathematical modeling of therapy-induced cancer drug resistance: connecting cancer mechanisms to population survival rates. Scientific reports, 6(1):22498, 2016

    2016

  4. [11]

    Mesoscopic and continuum modelling of angiogenesis

    Fabian Spill, Pilar Guerrero, Tomas Alarcon, Philip K Maini, and Helen M Byrne. Mesoscopic and continuum modelling of angiogenesis. Journal of mathematical biology , 70:485–532, 2015

    2015

  5. [12]

    A mathematical model of tumour-induced capillary growth

    D Balding and DLS McElwain. A mathematical model of tumour-induced capillary growth. Journal of theoretical biology, 114(1):53–73, 1985

    1985

  6. [13]

    Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions

    Helen M Byrne and Mark AJ Chaplain. Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions. Bulletin of mathematical biology , 57(3):461–486, 1995

    1995

  7. [14]

    Modeling angiogenesis: A discrete to continuum description

    Samara Pillay, Helen M Byrne, and Philip K Maini. Modeling angiogenesis: A discrete to continuum description. Physical Review E, 95(1):012410, 2017

    2017

  8. [15]

    Continuous and discrete mathematical models of tumor-induced angio- genesis

    Alexander RA Anderson and Mark AJ Chaplain. Continuous and discrete mathematical models of tumor-induced angio- genesis. Bulletin of mathematical biology , 60(5):857–899, 1998

    1998

  9. [16]

    The mathematical modeling of cancer growth and angiogenesis by an individual based interacting system

    Franco Flandoli, Marta Leocata, and Cristiano Ricci. The mathematical modeling of cancer growth and angiogenesis by an individual based interacting system. Journal of Theoretical Biology , 562:111432, 2023

    2023

  10. [17]

    Agent-based modeling in molecular systems biology

    Mohammad Soheilypour and Mohammad RK Mofrad. Agent-based modeling in molecular systems biology. BioEssays, 40(7):1800020, 2018

    2018

  11. [18]

    Simulating cancer growth with multiscale agent-based modeling

    Zhihui Wang, Joseph D Butner, Romica Kerketta, Vittorio Cristini, and Thomas S Deisboeck. Simulating cancer growth with multiscale agent-based modeling. In Seminars in cancer biology , volume 30, pages 70–78. Elsevier, 2015

    2015

  12. [19]

    A hybrid multiscale model of solid tumour growth and invasion: evolution and the microenvi- ronment

    Alexander RA Anderson. A hybrid multiscale model of solid tumour growth and invasion: evolution and the microenvi- ronment. In Single-cell-based models in biology and medicine , pages 3–28. Springer, 2007

    2007

  13. [20]

    Emergence of anti-cancer drug resistance: exploring the importance of the microenvironmental niche via a spatial model

    Jana L Gevertz, Zahra Aminzare, Kerri-Ann Norton, Judith P´ erez-Vel´ azquez, Alexandria Volkening, and Katarzyna A Rejniak. Emergence of anti-cancer drug resistance: exploring the importance of the microenvironmental niche via a spatial model. In Applications of dynamical sys...

    2015

  14. [21]

    The role of environmentally mediated drug resistance in facilitating the spatial distribution of residual disease

    Noemi Picco, Amy Milne, Philip Maini, and Alexander Anderson. The role of environmentally mediated drug resistance in facilitating the spatial distribution of residual disease. 2024

    2024

  15. [23]

    Molecular mechanisms and clinical applications of angiogenesis

    Peter Carmeliet and Rakesh K Jain. Molecular mechanisms and clinical applications of angiogenesis. Nature, 473(7347):298–307, 2011

    2011

  16. [24]

    Evolutionary dynamics: exploring the equations of life

    Martin A Nowak. Evolutionary dynamics: exploring the equations of life . Harvard university press, 2006

    2006

  17. [25]

    A quantitative measurement of the human somatic mutation rate

    David J Araten, David W Golde, Rong H Zhang, Howard T Thaler, Lucia Gargiulo, Rosario Notaro, and Lucio Luzzatto. A quantitative measurement of the human somatic mutation rate. Cancer research, 65(18):8111–8117, 2005

    2005

  18. [26]

    Oncogenic activity of epidermal growth factor receptor kinase mutant alleles is enhanced by the t790m drug resistance mutation

    Nadia Godin-Heymann, Ianthe Bryant, Miguel N Rivera, Lindsey Ulkus, Daphne W Bell, David J Riese, Jeffrey Settleman, and Daniel A Haber. Oncogenic activity of epidermal growth factor receptor kinase mutant alleles is enhanced by the t790m drug resistance mutation. Cancer resea...

    2007

  19. [27]

    Epidermal growth factor receptor mutants from human lung cancers exhibit enhanced catalytic activity and increased sensitivity to gefitinib

    Roseann Mulloy, Audrey Ferrand, Youngjoo Kim, Raffaella Sordella, Daphne W Bell, Daniel A Haber, Karen S Anderson, and Jeffrey Settleman. Epidermal growth factor receptor mutants from human lung cancers exhibit enhanced catalytic activity and increased sensitivity to gefitinib...

    2007

  20. [28]

    Tumor angiogenesis and vascular patterning: a mathematical model

    Rui DM Travasso, Eugenia Corvera Poir´ e, Mario Castro, Juan Carlos Rodrguez-Manzaneque, and Aurora Hern´ andez- Machado. Tumor angiogenesis and vascular patterning: a mathematical model. PloS one , 6(5):e19989, 2011

    2011

  21. [29]

    Met amplification occurs with or without t790m mutations in egfr mutant lung tumors with acquired resistance to gefitinib or erlotinib

    James Bean, Cameron Brennan, Jin-Yuan Shih, Gregory Riely, Agnes Viale, Lu Wang, Dhananjay Chitale, Noriko Motoi, 32 Janos Szoke, Stephen Broderick, et al. Met amplification occurs with or without t790m mutations in egfr mutant lung tumors with acquired resistance to gefitinib...

    2007

  22. [30]

    Met inhibitors for targeted therapy of egfr tki-resistant lung cancer

    Qiming Wang, Sen Yang, Kai Wang, and Shi-Yong Sun. Met inhibitors for targeted therapy of egfr tki-resistant lung cancer. Journal of hematology & oncology , 12:1–11, 2019

    2019

  23. [31]

    Andrew Mckenzie, Aaron Cranston, Phil Mallinder, Nektaria Papadopoulou, Simon Jiang, Kerry Moakes, Yinfei Yin, David Onion, Anna Grabowska, Martin Page, et al. In vivo generation of egfr-tki resistance in a patient-derived xenograft (pdx) with an activating egfr mutation (l858...

    2013

  24. [32]

    Effect of hydraulic conductivity and permeability on drug distribution, an investigation based on a part of a real tissue

    Masod Sadipour, Mohammad Masoud Momeni, and Majid Soltani. Effect of hydraulic conductivity and permeability on drug distribution, an investigation based on a part of a real tissue. arXiv preprint arXiv:2304.06273 , 2023

    2023 arXiv

  25. [33]

    Interstitial fluid flow and drug delivery in vascularized tumors: a computational model

    Michael Welter and Heiko Rieger. Interstitial fluid flow and drug delivery in vascularized tumors: a computational model. PloS one , 8(8):e70395, 2013

    2013

  26. [34]

    Real-time visualization and quantitation of vascular permeability in vivo: implications for drug delivery

    Desmond BS Pink, Wendy Schulte, Missag H Parseghian, Andries Zijlstra, and John D Lewis. Real-time visualization and quantitation of vascular permeability in vivo: implications for drug delivery. PloS one , 7(3):e33760, 2012

    2012

  27. [35]

    Numerical solution of partial differential equations: an introduction

    Keith W Morton and David Francis Mayers. Numerical solution of partial differential equations: an introduction . Cam- bridge university press, 2005

    2005

  28. [36]

    The three steps to cancer: a new concept of cancerigenesis

    Meyer M Melicow. The three steps to cancer: a new concept of cancerigenesis. Journal of Theoretical Biology, 94(2):471– 511, 1982

    1982

  29. [37]

    Differential binding of vegf isoforms to vegf receptor 2 in the presence of neuropilin-1: a computational model

    Feilim Mac Gabhann and Aleksander S Popel. Differential binding of vegf isoforms to vegf receptor 2 in the presence of neuropilin-1: a computational model. American Journal of Physiology-Heart and Circulatory Physiology , 288(6):H2851– H2860, 2005

    2005

  30. [38]

    A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

    B Addison-Smith, DLS McElwain, and PK Maini. A simple mechanistic model of sprout spacing in tumour-associated angiogenesis. Journal of Theoretical Biology , 250(1):1–15, 2008

    2008

  31. [39]

    A spatial model of tumor-host interaction: application of chemotherapy

    Peter Hinow, Philip Gerlee, Lisa J McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M Graham, Bruce P Ayati, Jonathan Claridge, Kristin R Swanson, et al. A spatial model of tumor-host interaction: application of chemotherapy. Mathematical biosciences and engineer...

    2009

  32. [40]

    Oxygen consumption rate of tissue measured by a micropolarographic method

    GH Takahashi, I Fatt, and TK Goldstick. Oxygen consumption rate of tissue measured by a micropolarographic method. The Journal of general physiology , 50(2):317, 1966

    1966

  33. [41]

    Heterogeneous response of individual multicellular tumour spheroids to immunotoxins and ricin toxin

    Roberto Chignola, R Foroni, A Franceschi, M Pasti, C Candiani, C Anselmi, Giulio Fracasso, Giuseppe Tridente, and Marco Colombatti. Heterogeneous response of individual multicellular tumour spheroids to immunotoxins and ricin toxin. British journal of cancer , 72(3):607–614, 1995

    1995

  34. [42]

    The exponential-gompertzian tumor growth model: Data from six tumor cell lines in vitro and in vivo

    Romano Demicheli, Graziella Pratesi, and Roberto Foroni. The exponential-gompertzian tumor growth model: Data from six tumor cell lines in vitro and in vivo. estimate of the transition point from exponential to gompertzian growth and potential cinical implications. Tumori Jour...

    1991

  35. [43]

    Response to chemotherapy of emt6 spheroids as measured by growth delay and cell survival

    PR Twentyman. Response to chemotherapy of emt6 spheroids as measured by growth delay and cell survival. British journal of cancer , 42(2):297–304, 1980

    1980

  36. [44]

    Cell kinetics of human squamous cell carcinomas in the oral cavity

    Junko SAKUMA. Cell kinetics of human squamous cell carcinomas in the oral cavity. The Bulletin of Tokyo Medical and Dental University , 27(1):43–54, 1980

    1980

  37. [45]

    Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry

    GD Wilson, NJ McNally, S Dische, MI Saunders, C Des Rochers, AA Lewis, and MH Bennett. Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry. British journal of cancer , 58(4):423–431, 1988

    1988

  38. [46]

    Estimating the growth kinetics of experimental tumors from as few as two determinations of tumor size: implications for clinical oncology

    Roberto Chignola and Roberto Israel Foroni. Estimating the growth kinetics of experimental tumors from as few as two determinations of tumor size: implications for clinical oncology. IEEE transactions on biomedical engineering , 52(5):808– 815, 2005. 33

    2005

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.