Breast Imaging Reporting and Data System, also known as BI-RADS is a universal system used by radiologists and doctors. It constructs a comprehensive language for the diagnosis of breast cancer. BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories. Mathematical models play an important role in the diagnosis and treatment of cancer. In this study, data of 42 BI-RADS 4 patients taken from the Center for Breast Health, Near East University Hospital is utilized. Regarding the analysis, a mathematical model is constructed by dividing the population into 4 compartments. Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk. Numerical simulations of the parameters are demonstrated. The results of the model have revealed that an increase in the lactation rate and early menopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age, the palpable mass, and family history is distinctive. Furthermore, the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined. Consequently, the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories. All things considered, with the assistance of the most effective parameters, the range of cancer risks in BI-RADS 4 subcategories will decrease.

Cancer is a serious disease that occurs as a result of an uncontrolled proliferation and growth of cells in any organ or tissue of the body. There is a requirement of building new cells in the event of cell death or damage. When the order of this formation process fails, damaged or abnormal cells can grow. The growth or proliferation of these kind of cells may result in tumors (which are sometimes called as lumps of tissues) [

According to the World Health Organization (WHO), cancer is a persuasive cause of death, vehemently prevalent in the world. In 2020, approximately 10 million people passed away because of cancer [

Cancer may begin in almost any part of the body and it is named dependent on the tissue in which it occurs. There are more than 200 types of identified cancers. The most common and mortal types of cancer include lung, stomach, liver, colon, and breast cancer. Female breast cancer is the most common cancer type with an estimated 2,3 million new cases (11.7%) around the globe [

Breast cancer generally originates from the epithelial cells of the breast ducts and glands. The most common clinical presentation is a newly formed breast lump. However, bloody nipple discharge, skin dimpling or ulceration, abnormal change in the breast size, redness or skin edema may be a sign or symptom of breast cancer. In spite of this fact, sometimes there may be a radiological abnormality during the screening but no clinical finding [

There are risk factors associated with breast cancer. To illustrate, these include age, female gender, genetic mutations, family history with ovarian or breast cancer, obesity, personal history with other types of cancer, etc. Dense breast on mammography is also a risk factor and, in this case, the diagnostic capability of mammography is relatively insufficient [

Breastfeeding, late first menstrual period and premature menopause are some of the factors that may reduce the risk of breast cancer [

In asymptomatic women, a screening mammography should be performed in order to increase the chance of successful treatment. On the other hand, in symptomatic women, the frequency of diagnostic mammography performed is higher due to the abnormality in the breast. Diagnostic mammography enables doctors to determine the exact size, location, and the shape of the lump or other pathological finding, exactly [

American College of Radiology (ACR) developed a categorization to reduce and group the variation of radiologists’ findings and descriptions for the diagnosis. Breast Imaging Reporting and Data System is given to the name of this categorization, which is also referred as BI-RADS, with initials of the name. BI-RADS system has 7 categories, starting from 0 till 6. The categorization of the BI-RADS is determined according to the obtained data from the patient’s ultrasound, mammography, etc. In the case of Category 0, further examinations are necessary in order to identify the obtained lump [

BI-RADS 4 category has a wide range of cancer probability which may portend contradictions for the doctors while diagnosis. Due to this reason, it is divided into 3 subcategories as BI-RADS 4A, BI-RADS 4B, and BI-RADS 4C. Category 4A has a relatively lower (2%–10%) malignancy rate; malignancy of Category 4B is moderate with 10%–50% and Category 4C has high suspicion of malignancy with 50%–95%. The categorization of findings may arise controversies between radiologists since their interpretations can be different [

Mathematical modelling has been widely used in the diagnosis or treatment of diseases for many years. Preventing the spread or occurrence of the tumor/cancer cells via control structures is one of the leading aims of mathematical modelling in health sciences. After identifying the problem, the population that is going to be examined should be separated into sensible number of compartments. Subsequently, with the help of parameters and variables, relationship between the compartments is constructed by means of differential equations [

For the effect of any disease, obtaining the basic reproduction number, denoted by

In [

In this paper, BI-RADS subcategories in breast radiological analyses is studied. The study includes 42 patients of Near East University Hospital, Center for Breast Health. Patients are diagnosed with BI-RADS 4 and divided into subcategories according to the findings. The principal focus of the study is to determine the effect of introduced parameters on the BI-RADS 4 subcategories and to narrow the range of cancer risk in the subcategories of BI-RADS 4.

The paper is organized as follows: First of all, the information about the used data and methods are demonstrated in

In this section, data and methods that are used during the study are explained precisely.

In this study, the data of 42 patients that are obtained in the Center for Breast Health, Near East University Hospital are used. The parameters are determined according to the obtained data.

With the help of collected data, the population is divided into 4 compartments; susceptible individuals

In this model,

In this section, the constructed model is given and the existence of the solution is proved. Afterwards, its analysis is given.

The population, denoted by

The description of variables and parameters are given in

Variables | Descriptions |
---|---|

Susceptible Individuals | |

Individuals that are diagnosed as BI-RADS 4A | |

Individuals that are diagnosed as BI-RADS 4B | |

Individuals that are diagnosed as BI-RADS 4C |

Parameters | Descriptions |
---|---|

Recruitment Rate | |

Age | |

Palpable Mass | |

Bloody Nipple Discharge | |

Lactation Rate | |

Early Menopause | |

Irregular Menstruation | |

Late Menopause | |

Family History | |

Smoking Rate of the BI-RADS 4A Individuals | |

Smoking Rate of the BI-RADS 4B Individuals | |

Natural Death Rate |

From the equality, it is clear that

The Disease Free Equilibrium Point, denoted by

It is obvious that

In this model, 3 different

Dominant eigenvalues of the matrix multiplication

Since

It is obvious that

Similarly,

In this part, sensitivity analysis of the parameters is made to see their effects on

Parameter | Value |
---|---|

Parameter | Value |
---|---|

According to the

Parameter | Value |
---|---|

In

In this section, numerical simulations for the distribution of BI-RADS 4 subcategories and sensitivity analysis are shown.

Here the idea of sensitivity analysis is to increase the values of parameters (from the obtained data) by 10% and see the trend of BI-RADS 4A, BI-RADS 4B, and BI-RADS 4C at time

In

In the

Effect of the parameters

In the

The study is constructed with the aim of reducing the huge range of cancer risk for BI-RADS 4 subcategories. In the analysis of the model, disease-free equilibrium

Simulation of the BI-RADS 4 subcategories, given in

Sensitivity analysis applied to the parameters of the model in

An increase in the lactation rate has a positive effect on all BI-RADS 4 subcategories, because it causes an expressive decrease in diagnosis. The results of an increase in the percentage of lactation rate are given in

Early menopause is also an important parameter so that women have fewer chance to be diagnosed as BI-RADS 4 (especially BI-RADS 4B and BI-RADS 4C) if they go through menopause earlier. The graph of this result is given in

The numerical results of the model showed that family history is another important parameter for the BI-RADS 4. An increase in the members with cancer history develops an inclination towards BI-RADS 4 diagnosis. This result is shown in

In

The negative effects of late menopause on BI-RADS 4C is shown in

In conclusion, the results showed that being non-smoker, increasing the lactation rate and regular controls (especially for the people with family history) are some of the significant parameters that can be controlled by people themselves. With this way and with the use of screening methods, people can reduce the risk of being cancer since they enable early diagnosis and so treatment.

In addition, the model revealed that BI-RADS 4 subcategories will be divided into 2 compartments in time. This may lead to a meaningful decrease in the range of cancer risk in future with the control of studied parameters. For further studies, a non-standard finite difference scheme can be introduced into systems as in [