# Modeling the Stress-Strain State of a Filled Human Bladder
## 1 Introduction
The Valsalva maneuver was simulated by applying pressure to the uterus and bladder from 0 to 10 kPa. The findings of the study suggest that an imbalance in abdominal pressure during obstetric surgery and on pelvic floor support structures can lead to pelvic floor prolapse in women. Currently, there are not enough works devoted to the study of the deformation of the bladder under any influence. At the same time, the creation of new valid operational techniques is impossible without the use of methods for the preoperative prediction of the results of operations. It is necessary to use mathematical models to improve the viability of medical rehabilitation after operative interventions on the bladder. Mathematical models should consider the geometric parameters and mechanical properties of structures. It is also important to consider the methods of studying and evaluating the condition of the bladder and the preoperative prediction of the present state of the bladder as a result of operation. Most of the works related to the modeling of the bladder are most often associated with the study of fluid dynamics and the behavior of the walls of the bladder during its filling and emptying [15]. For example, in [16], the relationship between changes in the basic size of the bladder and an increase in the volume of the bladder during filling was investigated. The results of finite element modeling showed that the size of the bladder increases linearly with its volume during filling. In another study [17], a three-dimensional finite element model was used to study the interactions between the bladder and the pelvic organs caused only by changes in the volume of the bladder. There are also several studies related to the development of bladder substitutes. These include the creation of bioengineered tissues and implants, as well as other innovative methods to restore bladder function. For example, [18] presents urinary bladder phantom mimicking mechanical properties and pressure during filling. The authors note that soft hollow organ phantoms can be used to complement animal experimentations for developing and validating medical devices. In [19], models of the lower urinary tract based on silicone with a fibrous structure and based on PVA were presented. Modeling using Ansys shows that the deformation of the created silicone model during urination corresponds to the normal bowl-shaped deformation of the real analog. The issue under discussion is important and has attracted the attention of scientists from all over the globe. In [20], researchers conducted experiments on simulating the filling and emptying of the bladder, considering its mechanical properties. The aim of this research was to investigate the behavior of the bladder and identify a material that could be used to replace it in cases of certain diseases. Most of the works related to the study of the bladder are devoted to the study of mechanical properties using various methods. Similar studies began in the 70s and one of the first works [21] confirmed that the bladder has viscoelastic properties. Thus, in [22], using step-by-step cytometry, the viscoelastic properties of the bladder wall tissue were analyzed. During the study, the authors obtained the modulus of elasticity and viscosity. Because a pig's bladder is similar in characteristics to a human's bladder, most studies conduct experiments on it. In [23], the viscoelastic properties of pig bladder tissue were studied using experiments on uniaxial stretching, ball bursting, and DMA. The researchers received differing information and concluded that using the results of all three methods in combination could be useful for other studies. The authors of [24] investigated the quasi-static uniaxial mechanical properties of the bladder walls. The study revealed a significant directional anisotropy of the mechanical properties of the bladder. The authors showed that the data obtained can be used to develop the most realistic computer modeling for predicting deformations in various conditions.