AGE-RELATED DYNAMICS OF ELASTICITY OF DEEP DORSAL VEIN OF HUMAN PENIS ACCORDING TO RESULTS OF DIRECT MEASUREMENTS

Обоснование. Венозной системе полового члена отводится важная роль в механизме развития и поддержания эрекции. В то же время, диагностика и хирургическая коррекция нарушенного венозного оттока оказывается успешной далеко не во всех случаях. Частота нарушений эрекции связана с различными факторами, но прогрессивно растет с увеличением возраста. Цель. Определить в прямом эксперименте возрастную динамику упругости основного магистрального венозного сосуда полового члена – глубокой дорсальной вены. Материалы и методы. Исследования проводились на образцах глубокой дорсальной вены, полученных при аутопсии 30 лиц мужского пола, погибших внезапно от травм или острых заболеваний в возрасте от 18 до 83 лет. Глубокую дорсальную вену полового члена выделяли острым путём без окружающих тканей. Фрагмент вены длиной около 2,5-3,5 см выделяли дистальнее поддерживающей связки, служившей ориентиром. В процессе экспериментов образцы вен подвергались воздействию дискретно возрастающей растягивающей силы в продольном направлении с фиксацией соответствующих абсолютных приращений их длины на специально спроектированной установке по оригинальной методике. Результаты. Математический анализ результатов прямых измерений упругих свойств исследуемой вены, позволил выявить существенное – около 20% – уменьшение упругости вены в исследуемом возрастном диапазоне 18 лет – 83 года от α0 = 6,2∙10 -8 м/Н до α0 = 5,0∙10 -8 м/Н. С увеличением силовой нагрузки среднее значение упругости вены быстро убывает, асимптотически приближаясь к установившемуся значению порядка α = 1,4∙10 -8 м/Н. При этом сохраняется возрастная тенденция к снижению упругости при различной степени функциональной нагрузки. Заключение. Выявленные закономерности снижения упругости отражают изменения стенки глубокой дорсальной вены с возрастом и могут играть роль в возрастном увеличении частоты эректильной дисфункции. Примененный метод определения упругости может быть использован для определения упругости сосудов другой локализации, а также ряда других биологических тканей в норме и при патологии. Ключевые слова: глубокая дорсальная вена, прямое измерение упругости, математический анализ, эректильная дисфункция.

The venous system of penis is assigned an important role in the mechanisms of development of and supporting erection [1]. The diagnostics and surgical correction of pathological venous outflow is not always successful [2]. The rate of erectile disorders is associated with different factors, but it progressively grows with age. Changes in the venous vessels of different localization in norm and in pathology were studied in several works [3,4]. However, among numerous research works in the field of phlebology there are no publications concerning direct measurements of the elasticity of veins with quantitative evaluation of this parameter [5].
In works [6,7] the authors propose a physical model of a biological tissue and a method of its mathematical description permitting to determine reduction in the elasticity of the fibrous tunic and cavernous arteries of penis with age. The aim of our research is experimental study of age-related dynamics of elasticity of the major venous vessel of penisthe deep dorsal vein (DDV).

Materials and Methods
Research was conducted on samples of DDV received in autopsy of 30 male individuals who suddenly died from traumas or acute diseases at the age of 18 to 83 years. The DDV of penis was isolated by acute method without surrounding tissues from a standard incision used in autopsy. A fragment of vein 2.5-3.5 cm in length was isolated distally to the retaining ligament served as a landmark. The obtained material was transported with strict observance of the temperature and humidity requirements. The period from the moment of death to the study did not exceed 18 hours.
In the experiment the samples of veins were subject to discretely increasing stretching force F in the longitudinal direction with record of the corresponding absolute increments of the length Δl on a specially designed setup [6,7].
Subsequent mathematical processing of experimental results consisted in transformation of the mass of discrete data into analytical dependences of the kind: (1) where l and Sinitial length and crosssectional area of the samples.
Transformation was carried out using the general approximating function [6]: where a, b and cconstant coefficients characterizing the properties of a specific sample.
According to the definition of elasticity α, its numeric value equals the slope of the curve to dependence (2) and, consequently, is determined by the expression: Thus, after differentiation of the Equation (2), we receive: As it is seen, the value of elasticity is not a constant since it considerably depends on force load F/S. Therefore, it is possible to speak only about its initial value α 0 as some limit to which α tends at F →0.
Results and Discussion Processing of experimental data was performed using the extension package Curve Fitting Toolbox of the computational environment Matlab, and consisted in determination of coefficients a, b and c in equation (2). The results of approximation, with indication of the age are given in Table 1. The values of reliability of approximation R-square given in the Table, evidence practically ideal coincidence of experimental results with their presentation in the analytical form using approximating function (2). This also confirms the correctness of the ratio following from it (4) that considerably extends possibilities of the analysis of the experimental results.
Thus, use of coefficients a and b permits to calculate the initial (maximal) value of the elasticity of the samples α 0 and to determine its dependence on age. The results of calculations by formula (4) are given in Figure 1.
No less informative is the parameter of dependence of the average value of elasticity ᾱ 0 on the force load F/S (Fig. 2) calculated by formula (4)    It should be noticed that the results of the calculations well agree with the results of the direct experiments. In particular, they demonstrate a rather rapid transition of relative increments of length Δl/l at low force loads and their subsequent decline with a smooth transition to practically linear dependence on the mechanical tension F/S.
Veins are referred to capacitance vessels that accommodate the most part of circulating blood and provide its return to the heart. This explains a high elasticity of a venous vessel at the beginning of its filling and smooth reduction in the elasticity with increase in the load. Nevertheless, with high loads, a vein can withstand high pressure in it [3,4]. The data obtained by us also confirm this regularity.
Mathematical analysis of the results of direct measurements of the elastic properties of DDV revealed a considerableabout 20% reduction in the elasticity of vein in the studied age range 18-83 years from α 0 = 6,2·10 -8 m 2 /N to α 0 = 5,0·10 -8 m 2 /N. With increase in the functional load on the vein the elasticity rapidly decreases at the initial stage and then practically does not change having achieved a certain level of saturation. With this, the age-related tendency to reduction in the elasticity with different extent of functional load is preserved.
The revealed regularities of reduction in the elasticity reflect changes in the venous walls with age that may play a certain role in age-related increase in erectile dysfunction. The obtained data enrich our knowledge about peculiarities of elastic properties of veins, and also about age-related changes in their functional properties.
The used method of quantitative evaluation of the elasticity of vein can be used in study of other problems of scientific and clinical medicine. Conclusion 1. A direct measurement of the elasticity of the deep dorsal vein of human penis (elasticity with low force loads) revealed a decline of the initial elasticity of the vein in the age range of 18-83 years from α 0 = 6,2·10 -8 m 2 /N to α 0 = 5,0·10 -8 m 2 /N. With increase in the functional load on the vein elasticity rapidly decreases in the initial stage, then it reaches a certain level and after that practically does not change.
2. The proposed method can be used for determination of elasticity of vessels of other localization, and of other biological tissues in norm and pathology.