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Updated: Feb 15, 2026

Staining and High-Resolution Imaging of Three-Dimensional Organoid and Spheroid Models
Published on: March 27, 2021
Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues
Aleksandra Karolak1, Dmitry A Markov2,3, Lisa J McCawley2,3
1Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA.
Abstract:
A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.
Insights
Mathematical oncology uses computational models to predict optimal cancer therapies for individual patients. This review explores 3D tumor models for personalized treatment strategies and virtual clinical trials.
Area of Science:
- Computational oncology
- Mathematical modeling in medicine
- Bioinformatics and computational biology
Background:
- Precision medicine aims to tailor treatments to individual patients.
- Mathematical and computational oncology provides tools for predicting optimal drug, dose, and timing.
- Spatial tumor architecture is crucial for understanding tumor development and treatment response.
Purpose of the Study:
- To review mathematical models that incorporate the spatial architecture of 3D tumors.
- To demonstrate the application of these in silico models to patient-specific data for assessing therapeutic strategies.
- To introduce the concept of virtual clinical trials for personalized medicine.
Main Methods:
- Survey of mathematical models focusing on spatial tumor architecture (e.g., spheroids, organoids, multi-component tissues).
- Discussion of how these models simulate tumor development, progression, and response to treatment.
- Integration of patient-specific data, medical imaging, and organ-on-chip experiments with computational models.
Main Results:
- Mathematical models offer efficient and cost-effective simulations for evaluating numerous treatment schedules.
- In silico models can be adapted to patient-specific data to predict the most effective therapeutic strategies.
- Virtual clinical trials represent a novel approach to personalized treatment determination.
Conclusions:
- Mathematical modeling, particularly incorporating spatial tumor architecture, is vital for advancing precision medicine in oncology.
- In silico approaches enable the prediction of personalized treatment strategies, optimizing drug selection and dosage.
- The integration of computational models with experimental data and patient information facilitates the development of virtual clinical trials for personalized cancer care.
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