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Morphological parameters of biological material are extremely informative in diagnostic studies, in particular, to determine the species, sex, time of death, the term of burial. The most informative object for these tasks is the skeleton, because changes in the bones are stored for a long time, while soft tissue is subjected to rotting. Bone tissue is the most durable, but at the same time, it is very labile and reacts to all metabolic processes in the body. The object of the study was proximal phalanx, medial phalanx and ungular bone of the pelvic limb of cattle ranging in age from newborn to 12 years old. Radiography of the proximal phalanx, medial phalanx and ungular bones of the pelvic limb was performed on the Arman apparatus. The bones were subjected to X-ray in the lateromedial projection. The inner and outer sections of the tubular bone were determined. The mathematical modeling of the interaction of X-rays and the cortical layer of bones of fingers (proximal phalanx, medial phalanx and ungular) of cattle was carried out in this work. It is established that this process is described by Bouger's law. The physico-mathematical model of proximal phalanx, medial phalanx and ungular bones has been calculated, on the basis of which it was possible to calculate the X-ray densitometric indices of these bones of cattle. The age features of dynamics of X-ray densitometric indices of the proximal phalanx, medial phalanx and ungular bones were established and a method of determining the age of cattle according to this criterion was proposed. A mathematical model for the proximal phalanx, medial phalanx and ungular bones of the pelvic limbs of cattle that can be applied in X-ray densitometry uses: for the average third proximal phalanx – section of heterogeneous tubular structure modeled by a semicircle; for a medial phalanx bone – a section of a triangular shape; for the ungular bone – a heterogeneous structure, the plantar surface is inscribed in a rectangle. The process of interaction of X-rays with the bone structure of the examined pelvic limb bones can be described by Bouguer's law. The developed mathematical modeling of this interaction and the algorithm for its analysis is the basis for determining the age of cattle for X-ray densitometric indices of the proximal phalanx, medial phalanx and ungular bones of pelvic limbs. By X-ray densitometry of the proximal phalanx and medial phalanx bones of the pelvic limbs extremities one can diagnose the age of bovine animals from birth to 5 years, but according to ungular bones – from birth to 10 years. X-ray densitometry of medial phalanx and ungular bones of pelvic limbs can be used for diagnosing bovine cattle in a complex with other morphological, chemical and physical methods of investigation.

regulatory mechanisms in biosystems

X-ray densitometric indices of proximal phalanx, medial phalanx and ungular pelvic limb bones as criteria for age diagnosis of cattle in forensic veterinary expertise