Paper Citation Record · LEDGER

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

As of 8 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 2 inbound Pith citation observations for arXiv:2505.22580.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.22580 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

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measured 48 of 48 standing notices

One-hop event checks from named stored sources.

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measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T14:24:54.724459Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

46 of 46 outbound references displayed

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External citation measurements

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Outbound references

Observation 9ee890c2-007c-4056-9ebc-e682008f004f · outbound

This paper cites Environment-mediated drug resistance: a major contributor to minimal residual disease.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Environment-mediated drug resistance: a major contributor to minimal residual disease

Reference 1

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Observation 08a3b003-3f07-445c-a3c8-884595685c03 · outbound

This paper cites The mathematics of cancer: integrating quantitative models.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment The mathematics of cancer: integrating quantitative models

Reference 2

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Observation 5e5411cc-2cd8-46a7-a388-fda0d59f5634 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A review of mathemat- ical models for tumor dynamics and treatment resistance evolution of solid tumors

Reference 3

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Observation 734269f4-7757-46f7-a692-b8f12741153f · outbound

This paper cites Integrating models to quantify environment- mediated drug resistance.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Integrating models to quantify environment- mediated drug resistance

Reference 4

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Observation c7f3a2b8-fdab-4b45-86e7-a51282a1dac4 · outbound

This paper cites Mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment

Reference 5

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Observation 166dcc43-760d-4cee-aaec-1d5b531ba8d7 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Optimization of dosing for egfr-mutant non–small cell lung cancer with evolutionary cancer modeling

Reference 6

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Observation 3ef8a22c-71fe-45d7-a1fb-7b4c3a61aab6 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy

Reference 7

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Observation 6fc94b1c-f593-44cb-8441-54b47cef0fde · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy

Reference 8

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Observation 869aad6f-f6b8-46bd-aca2-2e5b0a17842a · outbound

This paper cites Angiogenesis and chemotherapy resistance: Optimizing chemotherapy scheduling using mathematical modeling.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Angiogenesis and chemotherapy resistance: Optimizing chemotherapy scheduling using mathematical modeling

Reference 9

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Observation c9899cab-f3c4-4bc7-b30e-e6c1dddf07eb · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Mathematical modeling of therapy-induced cancer drug resistance: connecting cancer mechanisms to population survival rates

Reference 10

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Observation 2b0a42f5-44c8-4e4f-b7d9-c490c2f94297 · outbound

This paper cites Mesoscopic and continuum modelling of angiogenesis.

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

Reference 11

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Observation a39a0f13-bfa1-4618-acc0-c531e22ca308 · outbound

This paper cites A mathematical model of tumour-induced capillary growth.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A mathematical model of tumour-induced capillary growth

Reference 12

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Observation 7dbd44ef-9434-49fe-a6ff-b27c1c9406b7 · outbound

This paper cites Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions

Reference 13

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Observation c6d62697-37f4-4978-be6f-509beb722469 · outbound

This paper cites Modeling angiogenesis: A discrete to continuum description.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Modeling angiogenesis: A discrete to continuum description

Reference 14

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Observation fc62996d-7198-4455-90b7-dcfae8a172de · outbound

This paper cites Continuous and discrete mathematical models of tumor-induced angio- genesis.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Continuous and discrete mathematical models of tumor-induced angio- genesis

Reference 15

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Observation cb6d61ac-24b8-484b-b42d-ff3eaf8298e9 · outbound

This paper cites The mathematical modeling of cancer growth and angiogenesis by an individual based interacting system.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment The mathematical modeling of cancer growth and angiogenesis by an individual based interacting system

Reference 16

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Observation fb0e8bd6-ec2c-4165-9c59-90c84e29cb8e · outbound

This paper cites Agent-based modeling in molecular systems biology.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Agent-based modeling in molecular systems biology

Reference 17

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Observation faf42908-c8c5-414a-aa35-06a9f7fd6f46 · outbound

This paper cites Simulating cancer growth with multiscale agent-based modeling.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Simulating cancer growth with multiscale agent-based modeling

Reference 18

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A hybrid multiscale model of solid tumour growth and invasion: evolution and the microenvi- ronment

Reference 19

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Observation ce5f0896-e279-474e-8ca4-5fa8dc59e9a7 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Emergence of anti-cancer drug resistance: exploring the importance of the microenvironmental niche via a spatial model

Reference 20

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Observation 15ab250e-a341-420d-a2e5-691abf579422 · outbound

This paper cites The role of environmentally mediated drug resistance in facilitating the spatial distribution of residual disease.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment The role of environmentally mediated drug resistance in facilitating the spatial distribution of residual disease

Reference 21

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Observation 27f3828d-9c36-4dd7-bb89-7a68e76d5a67 · outbound

This paper cites Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis

Reference 22

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Observation 72831e1a-7e61-455c-b343-4abb29573915 · outbound

This paper cites Molecular mechanisms and clinical applications of angiogenesis.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Molecular mechanisms and clinical applications of angiogenesis

Reference 23

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Observation af1005b3-a4ae-4f0d-b923-dd860b3d5b5e · outbound

This paper cites Evolutionary dynamics: exploring the equations of life.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Evolutionary dynamics: exploring the equations of life

Reference 24

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Source-reported events for the cited work

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This paper cites A quantitative measurement of the human somatic mutation rate.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A quantitative measurement of the human somatic mutation rate

Reference 25

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Observation 3d3d619e-51aa-4ceb-80ce-7c6f2d7d2da7 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Oncogenic activity of epidermal growth factor receptor kinase mutant alleles is enhanced by the t790m drug resistance mutation

Reference 26

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Observation c00e38e4-84b9-4cd5-a84c-edb29b157977 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Epidermal growth factor receptor mutants from human lung cancers exhibit enhanced catalytic activity and increased sensitivity to gefitinib

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:54.359012Z

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Observation 6c4a807c-7b64-4881-9ef0-7f8e7b5ca320 · outbound

This paper cites Tumor angiogenesis and vascular patterning: a mathematical model.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Tumor angiogenesis and vascular patterning: a mathematical model

Reference 28

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Observation b3a87dd7-c72c-4354-8040-d1bf9a8e30c8 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Met amplification occurs with or without t790m mutations in egfr mutant lung tumors with acquired resistance to gefitinib or erlotinib

Reference 29

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This paper cites Met inhibitors for targeted therapy of egfr tki-resistant lung cancer.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Met inhibitors for targeted therapy of egfr tki-resistant lung cancer

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:53.683000Z

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

Reference 31

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Effect of hydraulic conductivity and permeability on drug distribution, an investigation based on a part of a real tissue

Reference 32

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This paper cites Interstitial fluid flow and drug delivery in vascularized tumors: a computational model.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Interstitial fluid flow and drug delivery in vascularized tumors: a computational model

Reference 33

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Real-time visualization and quantitation of vascular permeability in vivo: implications for drug delivery

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:53.004886Z

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Observation ae41dc71-488c-4a5d-b65d-c1d4b33b0142 · outbound

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A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Numerical solution of partial differential equations: an introduction

Reference 35

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Observation eaf87de6-6bbf-4b20-8ff1-0032f2fafb2d · outbound

This paper cites The three steps to cancer: a new concept of cancerigenesis.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment The three steps to cancer: a new concept of cancerigenesis

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:52.467270Z

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Observation a3d7a161-28ff-4f69-a56c-50f90c96a5c2 · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Differential binding of vegf isoforms to vegf receptor 2 in the presence of neuropilin-1: a computational model

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:52.191459Z

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Observation c6e3a23c-d81c-43c6-b705-1c6340faa7b6 · outbound

This paper cites A simple mechanistic model of sprout spacing in tumour-associated angiogenesis.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

Reference 38

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Observation 5f8e4e08-a5e1-4fd2-b0d9-ffdf52d2130b · outbound

This paper cites A spatial model of tumor-host interaction: application of chemotherapy.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment A spatial model of tumor-host interaction: application of chemotherapy

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:51.676995Z

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This paper cites Oxygen consumption rate of tissue measured by a micropolarographic method.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Oxygen consumption rate of tissue measured by a micropolarographic method

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:51.436070Z

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Observation d68df497-6ce2-45a2-8fa7-b2eb2322c8b4 · outbound

This paper cites Heterogeneous response of individual multicellular tumour spheroids to immunotoxins and ricin toxin.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Heterogeneous response of individual multicellular tumour spheroids to immunotoxins and ricin toxin

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:51.147100Z

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment The exponential-gompertzian tumor growth model: Data from six tumor cell lines in vitro and in vivo

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:50.976125Z

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Observation e331e487-8ec9-4f7b-bd88-26a78dfbe3d4 · outbound

This paper cites Response to chemotherapy of emt6 spheroids as measured by growth delay and cell survival.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Response to chemotherapy of emt6 spheroids as measured by growth delay and cell survival

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:50.717486Z

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Observation 7c5517cd-332c-4796-af14-c2f5e58b7aa7 · outbound

This paper cites Cell kinetics of human squamous cell carcinomas in the oral cavity.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Cell kinetics of human squamous cell carcinomas in the oral cavity

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:50.547372Z

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Observation ef92e691-c11a-443d-9937-232c06ddd862 · outbound

This paper cites Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry.

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:50.398417Z

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Observation a759edcd-ee76-494c-a218-44669365e8fd · outbound

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

A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment Estimating the growth kinetics of experimental tumors from as few as two determinations of tumor size: implications for clinical oncology

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:50.197673Z

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Pith citing papers

Observation 06122912-0244-47ad-800d-b0398c4ef7c6 · inbound

Multiplier Sensitivity in Isoperimetric Optimal Control cites this paper.

Multiplier Sensitivity in Isoperimetric Optimal Control A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment

Reference 90

Resolution: unresolved; no resolver link, observed 2026-07-14T14:24:54.724459Z

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

Reflected Optimal Stopping with a Max-Type Payoff: Measure-Valued Stopping Gains and Killed Resolvent Representation A hybrid PDE-ABM model for angiogenesis and tumour microenvironment with application to resistance in cancer treatment

Reference 73

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