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Updated: Jan 10, 2026

Using Computer-based Image Analysis to Improve Quantification of Lung Metastasis in the 4T1 Breast Cancer Model
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Mathematical Pathological Approach as a Novel Tool for Prognosis in Breast Cancer.

Sana Ahuja1, Neha Singh1, Amit Kumar Yadav1

  • 1Department of Pathology, Vardhman Mahavir Medical College and Safdarjung Hospital, New Delhi, India.

Indian Journal of Surgical Oncology
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PubMed
Summary

Mathematical pathology

Keywords:
Breast cancerDiffusion penetration lengthMathematical model

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Area of Science:

  • Oncology
  • Mathematical Pathology
  • Breast Cancer Research

Background:

  • Breast cancer is a leading global cancer in women.
  • Mathematical pathology offers novel patient-specific tumor growth predictors.
  • Diffusion penetration length quantifies chemotherapeutic agent spread in tumors.

Purpose of the Study:

  • To assess diffusion penetration length in invasive ductal carcinoma.
  • To correlate this metric with histopathological features and molecular subtypes.
  • To explore its potential as a prognostic indicator.

Main Methods:

  • Histopathology and immunohistochemistry (ER, PR, Her2neu, Ki67, cleaved caspase-3).
  • Calculation of proliferative and apoptotic indices.
  • Mathematical modeling using mammographic tumor dimensions to compute diffusion penetration length.

Main Results:

  • Diffusion penetration length was higher in Grade III vs. Grade II tumors (not significant).
  • No significant correlation found with tumor size, nodal status, or stage.
  • A significant correlation was observed between diffusion penetration length and surrogate molecular classification.

Conclusions:

  • Diffusion penetration length shows a significant link with breast cancer's molecular subtypes.
  • It may not be an independent prognostic factor but holds utility in invasive ductal carcinoma evaluation.