Quantitative Predictions of Neoadjuvant Chemotherapy Effects in Breast Cancer by Individual Patient Data Assimililation

Research Article

Ann Hematol Oncol. 2021; 8(5): 1345.

Quantitative Predictions of Neoadjuvant Chemotherapy Effects in Breast Cancer by Individual Patient Data Assimililation

Castorina P1,2*, Carco D1, Colarossi C1, Mare M1,5, Memeo L1, Pace M2,3,4, Puliafito I1 and Giuffrida D1

1Department of Experimental Oncology, Mediterranean Oncology Institute, Italy

2National Institute of Nuclear Physics, Italy

3Department of Medical Physics, University of Catania,Italy

4Sicilian Center for Nuclear Physics and Structure of Matter, Italy

5Department of Biomedical and Dental Sciences of Morphological and Functional Images, University of Messina, Italy

*Corresponding author: Castorina Paolo, Department of Experimental Oncology, Mediterranean Oncology Institute, 95029 Viagrande, Italy

Received: February 15, 2021; Accepted: April 14, 2021; Published: April 21, 2021


Neoadjuvant chemotherapy has been used for breast cancer aiming at downgrading before surgery. In this article we propose a new quantitative analysis of the effects of the neoadjuvant therapy to obtain numerical, personalized, predictions on the shrinkage of the tumor size after the drug doses, by data assimilation of the individual patient. The algorithm has been validated by a sample of 37 patients with histological diagnosis of locally advanced primary breast carcinoma. The biopsy specimen, the initial tumor size and its reduction after each treatment were known for all patients. We find that: a) the measure of tumor size at the diagnosis and after the first dose permits to predict the size reduction for the follow up; b) the results are in agreement with our data sample, within 10% to 20%, for about 90% of the patients. The quantitative indications suggest the best time for surgery. The analysis is patient oriented, weakly model dependent and can be applied to other cancer phenotypes.


In the era of personalized oncology, mathematical models are a useful tool for a better understanding of the clinical effects of therapy.

The expected individual response to tumor therapies is generally based on a set of indices, defined with large quantitative variability. For example, for neoadjuvant chemotherapy for locally advanced breast cancer, aiming at downgrading before surgery, one usually considers the subtypes classification according to the expression of hormone receptors, Estrogen (ER) and Progesterone (PR), of the Human Epidermal Growth Factor Receptor 2 (HER2), the proliferation index ki67, the inizial tumor size and cellularity. Indeed, these clinical informations may have a prognosis value similar to that of multigene prognostic score [1].

The tumor progression during neoadjuvant chemotherapy [2,3], described by previous (and others) predictive factors, gives direct informations on the response to the therapy. By those analyses one gets semi-quantitative results following the standard classification: tumor size (median and range), T stage, Node stage, JACC stage, Lymphovascular invasion and other parameters.

A complementary strategy could be obtained by more quantitative informations, based on numerical approaches which, by single patient data assimilation, enhance the level of reliability of forecasts on the individual response.

Here we discuss an algorithm which, starting from the measure of the tumor size (radius) at the diagnosis and after the first dose, is able to predict, essentially without free parameters, the shrinkage of the tumor in the sequence of treatments. The proposed method is, by itself, patient oriented since the first size reduction and the initial cellularity take into account the specific initial condition.

The numerical predictions agree, within 10% to 20%, for more than 90% of the observed data of our sample of 37 patients.

Mathematical Formulation of the Diagnostic Algorithm

The breast tumor growth is described by the Gompertz law [8,9], solution of the differential equation

(1/ N)dN / dt = - k ln(N / N8 ), (1)

where N is the cell number at time t, k is a constant and N8 is the maximum number of cells (N8=3.1×1012, according to ref. [9]).

The modification of the specific growth rate due to chemotherapy, during the time interval of a single treatment, is obtained by introducing a function c(t) in the previous equation [10-13], i.e.

(1/ N)dN / dt = - k ln(N / N8 ) c(t), (2)

where c(t) has a negligible value after the interval, t, between two timeline doses (t=3 weeks). In other terms, chemoterapy effects start, periodically, at the beginning of each drug dose but almost completely decline after t=3 weeks and, therefore, the function c(t) has a discontinuity on the days of treatment. By solving the previous eq. (2) (see appendix A) for homogeneous, spherical symmetric configurations, the size reduction after n doses is given by

where Rn+1 is the tumor radius after n+1 doses and, for each patient, the constant k is determined by the initial cellularity (the second term in the growth law in eq. (1) is the fraction of duplicating tumor cells).

In the final result, (eq. 3), the function c(t) does not explicitely appear: its contribution is hidden in the (measured) size after the first dose R1(t). In this respect, the approach is independent on the model describing the chemotherapy effects.


Validation: Patients and Therapy

Patients: This is a retrospective single centre study. Thirtyseven women, aged 36 years to 78 years, with histolog- ically proven operable breast cancer were evaluated. All tumours were tested for Estrogen Receptor (ER), Progesterone Receptor (PgR), HER 2 and ki 67. Thirty-six patients showed positivity for ER (range 2% to 90%) and PgR (range range 2% to 90%), HER2 3+ was present in 5/37 patients. Ki 67 was variable from 5 to 30%. Median diameter of tumour, defined by imaging, was 43, 5 mm (range 21 mm to 72 mm). Four patients had clinical positivity for axillary nodes. Pregnant women were ex-cluded. ECOG-PS of all patients was 0 or 1. All patients had adequate haematological, renal and haepatic function. All patients had a normal left ventricular ejection fraction (LVEF >50%).


Neoadjuvant chemotherapy corresponds to the use of a systemic treatment applied before locore- gional treatment (surgery and / or radiotherapy) in order to obtain a more frequent conservating surgery, downgrading the tumour size. Major drugs used for breast cancer patients included anthra- cyclines and taxanes [4]. Patients evaluated in our study received a median of five cycles (range 4 to 6) of every -3-week (q3w) ET (epirubicin 80 mg/m², paclitaxel 175 mg/m²) [5,6]. Seven patients having HER2 3+ received integrate treatment with trastuzumab 6 mg/kg (8 mg/kg as loading dose). At the first follow up, after one chemotherapy administration, all patients had a tumour diameter reduction variable from 10% to 70%. At the second follow up, after second chemotherapy administration, all patients showed a further diameter reduction included between 10% and 30%. At the third follow up, 14/37 patients continued to respond to treatment while the others showed a stable disease. At the fourth follow up, only one patient showed a futher tumour diameter reduction, the others continued to have a stabilization of disease and this was persisting at the remaining follow up [7].

Results and Discussion

The estimate of the tumor shrinkage in the dose sequence follows immediately from eq.(3) and from the determination of R1(t). In Figure 1,2 the numerical results are compared with data for the second and the third treatment for all patients. The radius measurements had a 2% to 3% statistical error and the error propagation has been taken into account. For the second dose, the ratio between predictions and data is within the prudential interval 1 ± 0.1 (1 indicates a perfect agreement) for 31 patients of the entire sample (84%) and the agreement is within 1 ± 0.2 (Figure 1) for 34/37 (92%). For the third dose, in 29/37 and 32/37 cases the agreement is within the fiducial 1 ± 0.1, 1 ± 0.2 intervals (Figure 2) respectively.