Combining Morphometry and Computational Mathematics to Predict Bone Metastasis in Breast Cancer

by Christos Evangelou, MSc, PhD – Medical Writer and Editor

In a recent study, scientists at the Carol Davila Clinical Nephrology Hospital, University of Medicine and Pharmacy Carol Davila, and the National University for Science and Technology Politehnica of Bucharest investigated whether nuclear morphometry and spatial mapping of tumor cells could identify characteristic differences between breast cancers that do or do not metastasize to the bone.

The team identified morphometric characteristics of breast cancer cells that could help discriminate tumors that metastasize to the bones from those that are unlikely to form bone metastases.1 By combining morphometry and computational mathematics, the researchers have developed a method that could help identify high-risk patients, potentially informing treatment strategies and improving prognosis.

“Breast cancer bone metastases are responsible for lower life expectancy and decreased quality of life. Development of morphometric and molecular techniques that would allow the selection of high-risk patients can lead to a more personalized treatment plan for them, thus preventing the development of metastases,” said Alexandru Adrian Bratei, M.D.Eng., the corresponding author of this study.

The report was published in the journal Diagnostics (Basel).


Unmet Need: Predicting Bone Metastasis in Breast Cancer

Breast cancer is one of the most common cancers worldwide, and metastasis is a complication that significantly affects patient survival and quality of life. Over 70% of breast cancer metastases occur in the bone, causing pain, fractures, and other debilitating complications.1

Although certain tumor subtypes have a greater likelihood of osteotropic spread, predicting which patients are at a high risk of developing bone metastasis remains a clinical challenge. Early identification of high-risk cases could improve outcomes through frequent monitoring and targeted treatment.

“Our aim was to find out morphometrical aspects that would correlate with an aggressive behavior of breast carcinomas and would lead to a higher metastatic potential,” noted Dr Bratei.

He explained that each tumor has its own features, which until now have been evaluated mostly qualitatively. “It is time to evaluate the tumor with a mathematical and more quantitative view,” he said.



The researchers retrospectively analyzed archived tumor samples from 41 patients with invasive breast carcinoma of no special type, including seven patients with histopathologically confirmed bone metastases.1 They scanned tumor specimens using an Olympus VS200 slide scanner and analyzed digitized slides using QuPath software. Using digital pathology tools, the team analyzed 60–100 tumor cell nuclei per sample for size, shape, and spatial parameters.

“We decided to combine classical morphometry with mathematical modeling to not only evaluate classical dimensions but also develop variables and algorithms to evaluate geometric parameters such as the mean distance between nuclei,” said Dr Bratei.

The team measured various morphometric parameters of the tumor cells, such as nuclear area, nuclear volume, nucleus-to-cytoplasm ratio, long axis, small axis, acyclicity grade, anellipticity grade, and mean internuclear distance.1 These parameters provide a comprehensive morphometric profile of the tumor cells, offering unique insights into their metastatic potential.

“By analyzing representative areas using QuPath, we conducted measurements on tumor cells, and we obtained some measurements which were lately used for mathematical modeling,” Dr Bratei explained.

Commenting on the novelty of this approach, he said that this is the first time a mathematical model based on the geometry and morphometry of nuclei was used to evaluate the metastatic potential of breast cancer.


Smaller, More Elongated Nuclei Associated With Bone Metastasis

Compared with the tumor cells in patients without bone metastases, tumor cells from bone metastases had smaller nuclear area, smaller long axis, smaller small axis, smaller mean nuclear volume, and lower mean internuclear distance. In addition, tumor cells from bone metastases had higher nucleus-to-cytoplasm ratio, higher axis ratio, higher acyclicity grade, and higher anellipticity grade than the tumor cells from patients without bone metastases. These findings suggest that small nuclear size, high nucleus-to-cytoplasm ratio, elongated nuclear shape, high nuclear dysmorphism, and dense nuclear packing could be potential predictors for the evaluation of bone metastatic potential of breast cancer cells.

The researchers proposed cut-off values for each morphometric parameter and created a morphometric panel that can help differentiate between high-risk and low-risk patients for developing bone metastases. Specifically, they proposed an algorithm with eight criteria to categorize patients as high risk (≥6 criteria), intermediate risk (3–5 criteria), or low risk (<3 criteria) of developing bone metastases.

The proposed morphometric algorithm categorized samples as high risk for bone metastasis with 83%–100% accuracy and reliably stratified risk using only a tumor biopsy sample, assigning over 85% of bone metastasis patients to the high-risk category. These findings suggest that this morphometric panel could help reduce morbidity from bone metastases by enabling clinicians to tailor therapies based on a patient’s individual risk profile and to identify patients needing targeted screening and treatment.


Future Perspectives

This study provides preliminary evidence to support the potential of computational morphometry to assess the risk of bone metastasis in patients with breast cancer, opening new avenues for improving patient prognosis and personalizing treatment strategies.

Although the study’s findings are promising, the researchers acknowledge its limitations, including the small sample size and its retrospective design. Future research is needed to validate these findings in larger cohorts with diverse breast cancer subtypes and staging and to explore the underlying mechanisms linking these morphometric parameters to bone metastasis. This could lead to the development of more accurate predictive models and potentially novel therapeutic targets.

“We would like the readers of our report to remember that mathematical and quantitative evaluation in pathology can be more useful for tumor characterization and for patients’ management than the common qualitative evaluation,” Dr Bratei said.



  1. Duca-Barbu SA, Bratei AA, Lisievici AC, et al. A novel algorithm for evaluating bone metastatic potential of breast cancer through morphometry and computational mathematics. Diagnostics (Basel). 2023;13(21):3338. Published 2023 Oct 30. doi:10.3390/diagnostics13213338

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