Research

Mathematics as a leverage point for cancer care

Four connected programs, one through-line: innovative mathematical models that turn patient and disease variability into more precise, less toxic treatment.

Program 01 · Mathematical Oncology Initiative

Geometry and optimal transport for the structure of cancer

Multimodal cancer datasets — genomics, computational pathology, radiomics — are high-dimensional and noisy, and conventional correlation-based analyses poorly capture the geometric structure needed to define clinically meaningful cancer subtypes. The Mathematical Oncology Initiative applies advanced, innovative mathematics to this problem, adapting optimal mass transport (OMT) and graph-based methods to cluster samples, integrate multi-omic networks, and surface therapeutic targets.

The initiative has a deliberate second goal: to mentor and train talented fellows and junior faculty in these methods. It is supported by the Breast Cancer Research Foundation and the Simons Foundation.

Patient subtyping

OMT / Wasserstein-distance clustering to define subtypes across breast, ovarian, sarcoma, melanoma, and lung cancers.

Network geometry

Curvature and geometric analysis of gene-interaction networks to find fragile points and candidate drug targets.

Target discovery

Hypothesis generation — e.g., pregnancy-specific glycoproteins as candidate lung-cancer drug targets.

Program 02 · ECHO

Automated, clinically optimal treatment planning

Intensity-modulated radiotherapy planning is a high-dimensional optimization problem (more than 10,000 variables) that trades tumor coverage against sparing many normal tissues. Conventional weighted-sum methods give planners poor, unintuitive control over the resulting trade-offs. ECHO (Expedited Constrained Hierarchical Optimization) solves the most clinically critical objectives first, then admits lower-priority objectives as constraints that preserve what has already been achieved — yielding explicit, reproducible, clinically deliverable plans.

ECHO is now used to help plan roughly 23% of all patients treated at MSK and was recognized with 2021 INFORMS Franz Edelman Laureate honors for impact in applied analytics. It was refined and implemented clinically with optimization expert Masoud Zarepisheh, PhD.

Program 03 · Proton & particle radiobiology

Modeling response across radiation modalities

Proton and particle therapies deposit dose with a physics profile very different from conventional photons, which changes how tumors and healthy tissues respond. The lab builds mechanistic models of how dose, timing, and tumor biology combine to determine response and toxicity across modalities; our tumor-control models reproduce key clinical observations under both photon and carbon-ion irradiation, giving a quantitative basis for comparing modalities and personalizing prescriptions. This is a long thread — the lab's very first NIH award funded a computer-simulation system for proton radiotherapy.

Program 04 · Digital twins

A simulatable model of each patient's tumor

A "digital twin" is a computational model of an individual patient's tumor that can be simulated forward in time. Building on a parsimonious, mechanistic "energy-budget" model of tumor control developed with Jeho Jeong, the lab combines multimodality imaging (FDG-PET and MRI) with tumor biology to forecast how a given tumor will respond to radiation — and to flag likely non-responders early, while treatment can still be adapted. Related efforts synthesize hypoxia information from routine PET and forecast normal-tissue toxicity at the level of individual image voxels.

Methods & open tools

A multimodal toolkit to probe cancer and treatment response

The lab develops reusable methods and software — from optimal transport and network geometry to mechanistic radiobiology and open-source imaging platforms. The software itself (CERR/pyCERR, ORCO, NetFlow, ViSPACE, FocusNexus, and the AI auto-segmentation models) is collected under Tools for Cancer Research.

CERR / pyCERR

Open-source platform for imaging, dose, and radiomics analysis; now native Python.

MATLAB / PythonOpen source
View repository →

NetFlow

Framework for topological representations of high-dimensional biomedical data.

MethodsPreprint 2025
Read the preprint →

Dynamic network curvature

Geometry that measures how robust or fragile parts of a gene network are, revealing candidate targets.

MethodsSci Rep 2024
Read the paper →

Jeho TCP model

A parsimonious "energy-budget" model of tumor control, extended into radiobiological digital twins.

RadiobiologyClin Cancer Res 2017
Read the paper →

urOMT

Unbalanced, regularized optimal-mass-transport that recovers flow and transport from dynamic imaging and networks — applied from brain glymphatics to breast-cancer DCE-MRI.

MethodsSci Rep 2024
Read the paper →

NIH ROBIN consortium

Radiation Oncology-Biology Integration Network

ROBIN is a National Cancer Institute network (RFA-CA-21-040) of U54 centers created to apply new biological knowledge to optimize radiation therapy in combination with systemic drugs, immunotherapy, and other agents. The lab is part of the ImmunoRad ROBIN center, led by Weill Cornell Medicine, the University of Chicago, and Memorial Sloan Kettering (U54CA274291; multiple-PIs Silvia Formenti, Ralph Weichselbaum, and Joseph Deasy), which studies how radiation therapy interacts with the immune system — anchored in a rectal cancer bio-repository of tumor, blood and stool samples collected before and after standard treatment. Dr. Deasy also leads the center's Data Sharing and Integrative Analysis core.

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ImmunoRad ROBIN center

The consortium site: aims, teams, cross-training core, research opportunities, and the didactic curriculum.

immunorobin.org →
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NCI ROBIN program

The National Cancer Institute's overview of the network, its member centers, and structure.

dctd.cancer.gov →

ROBIN didactic talks — "Fundamentals of Radiation and Immunity"

A bimonthly primer designed by the ImmunoRad ROBIN Cross-Training Core so that immunologists, radiation and cancer biologists, radiation oncologists, and medical physicists share a common foundation. Recordings are hosted on the consortium site; each year below links to the page with the videos.

20255 talksWatch on immunorobin.org ↗
  • Jan 8Gilmer ValdesAssessing causal effects of radiation toxicities on overall survival
  • Jan 22Ralph WeichselbaumRadiotherapy and immunotherapy: what determines success or failure
  • Feb 19Rachael PhillipsTargeted learning: the bridge from machine learning to statistical and causal inference
  • Mar 5Dan NguyenIntroduction to artificial intelligence in radiation oncology
  • Mar 19Gaorav GuptaPARP7 is a targetable suppressor of radio-immunotherapy synergy
202415 talksWatch on immunorobin.org ↗
  • Jan 10William McBrideProteasome in radiation responses and radiovaccination
  • Jan 24Florian GretenTargeting cancer-associated fibroblasts in rectal cancer
  • Feb 6Mary Helen Barcellos-HoffCapitalizing on TGFβ's complexity in cancer
  • Feb 21Luigi MarchionniA hitchhiker's guide to big-data-based biomarkers — lessons learned over two decades
  • Mar 6Jason LukeExploring the abscopal intersection of SBRT and immune checkpoint blockade
  • Apr 17Marie-Catherine VozeninPre-clinical studies with FLASH — what do we know?
  • May 1Aditya JulooriRadiation/immunotherapy clinical trials: what do we know (so far)?
  • May 15Tian LiuMinimizing radiation side effects: ultrasound strategies for predicting and monitoring normal-tissue toxicities
  • Jun 26Scott BratmanUtility of circulating tumor DNA in radiation oncology
  • Sep 18Jamie HoneychurchOverview of innate and adaptive immunity: a foundation for tumor immunology
  • Oct 2Famke SchneidersRadio-immunotherapy combinations and the effect of RT on lymph nodes
  • Oct 16Ibrahim HatipogluFundamentals of tumor immunology
  • Nov 6Kevin HarringtonEnhancing the effects of tumour irradiation through microenvironmental conditioning and optimized adjuvant therapy
  • Nov 13Jonathan SchoenfeldImmunotherapy and radiation: a clinical/translational perspective
  • Dec 18Keyur ShahFrom data to decisions: the role of radiation sciences in radiation oncology
202314 talksWatch on immunorobin.org ↗
  • Jan 18Encouse GoldenClinical management of rectal cancer in 2023
  • Feb 2Cristina MontagnaChromosome instability, aneuploidy and tumorigenesis
  • Mar 15Kathryn BealInnovations in radiation for brain metastases
  • Mar 29Laura SantambrogioUnderstanding the plasticity of the MHC II immunopeptidome
  • Apr 26Omar MianPersonalizing therapy for cancers of the genitourinary tract
  • May 24Lorenzo GalluzziMitochondrial apoptosis in the immune response to radiation therapy
  • Jun 7Phuoc TranClinical radiobiology basics
  • Jun 21Sean PitrodaIntegrated molecular subtyping to define the spectrum of metastatic disease
  • Sep 6Philip ConnellTargeting DNA repair in oncology
  • Oct 4Sadna BudhuTargeting phosphatidylserine enhances the anti-tumor response to local radiation therapy in a preclinical model of melanoma
  • Oct 18Xiaofeng YangAI-based medical image analysis for precision radiotherapy
  • Nov 1Julie SchwarzUsing imaging and genomics to improve outcomes for patients with cervical cancer
  • Nov 15Timothy ChanMutation, DNA damage repair, and mechanisms underlying immunotherapy efficacy
  • Dec 6Eric DeutschIntegrated imaging and biological approaches for next-generation immuno-radiotherapy combinations

Curriculum overview: immunorobin.org/curriculum/fundamentals-of-radiation-and-immunity. Titles are as listed on the consortium schedule.

Milestones

Selected milestones

Papers, awards, grants, and program launches over time.

  1. 2024Consortium

    VALIDATE consortium formed

    ~25 institutions, to directly validate published toxicity-prediction models using patient-specific data.

  2. 2022Grant

    ROBIN U54 center launched

    NIH ImmunoRad center on tissue and immune responses to irradiation in rectal cancer (U54CA274291).

  3. 2021Award

    INFORMS Franz Edelman Laureate

    Recognition for ECHO's real-world impact in applied analytics.

  4. 2017Grant

    Mathematical Oncology Initiative begins

    Continuous Breast Cancer Research Foundation support for mathematical methods in cancer.

  5. 2010Milestone

    Chair of Medical Physics at MSK

    Joins Memorial Sloan Kettering; holder of the Enid A. Haupt Endowed Chair in Medical Physics.

Funding

Who supports this work

The lab has been supported by Varian/Siemens, The Breast Cancer Research Foundation, Cycle for Survival, Enid A. Haupt, Richard and Clara Weyergraf-Serra, and multiple NIH grants — currently including the ROBIN U54 (multiple-PI) and NCI R01 projects on brain-metastasis prediction, radiogenomic toxicity models, and AI-guided lung radiotherapy.