## 2.1. Animal Care and Use

All animal procedures followed institutional guidelines and were approved by the Institutional Animal Care and Use Committees of Michigan State University (NIH Assurance D16-0054). Male C57Bl/6 mice (9–12 weeks old; Jackson Laboratory, Bar Harbor, ME) were group housed in a temperature- and humidity-controlled environment with a 12 hr light/dark cycle. Mice were provided *ad libidum* access to standard chow and water. Mice were euthanized by injection of pentobarbital (> 150 mg/kg i.p.) followed by decapitation.

## 2.2. Pentaplanar Reflected Image Macroscopy (PRIM) System

The PRIM System consists of four main sections: the PRIM imaging chamber, a digital camera with television lens, the lighting shroud, and the integrated control unit (Figs. 1A, B). Unless otherwise specified, all custom-designed pieces were three-dimensional printed from PETG plastic using a fused deposition modeling printer (Prusa i3 Mk3S; Prusa Research, Czech Republic). The PRIM chamber itself consists of a custom-designed ABS imaging chamber, 4 mirrors, the mounting cannula, and chamber positioner. Mirrors are fixed in position at 45° angles relative to the central specimen, which is placed on the cannula for *ex vivo* filling using a standard syringe pump. The monochrome digital camera (DMK33UX250, 5 megapixel, 3.45 µm2 pixel size; The Imaging Source, USA) and television lens (TCL1616, 16 mm focal length, F1.6-16; The Imaging Source) were mounted atop the lighting shroud roughly 12 cm above the imaging chamber on a custom camera mount that allowed for focusing and centering of t he image. The camera sat atop the shroud, which was sized to allow full illumination of the sample without inclusion of the lights themselves in the reflected image. The integrated control unit consisted of an Arduino microcontroller, Wheatstone bridge amplifier shield (Robotshop.com), PicoBuck LED driver (COM-13705, Sparkfun), in-line pressure transducer (DYNJTRANSMF, Medline) and 12V DC power supply. As designed and assembled, the integrated control unit had a pressure resolution of 0.07 mmHg that remained linear across a range from 0 – 40 mmHg. Both pressure readings and camera triggering were regulated by the Arduino microcontroller to ensure a single pressure reading was matched with each image frame, and readings were collected at 10 Hz. Pressure data were collected using *VasoTracker-DataTracker* software (courtesy Dr. Calum Wilson, University of Strathclyde; UK) for later analysis. Video images were collected using *IC Capture* software (The Imaging Source; USA). When properly aligned, 5 visual planes are recorded in a single image and each image frame correlates to a single pressure and infused volume reading. These data are then used for measurement and analysis of bladder geometry and bladder compliance.

## 2.3. Ex Vivo Bladder Filling

Urinary bladders were isolated and cannulated using a modified version of our previously described protocol (Heppner et al. 2016). Briefly, the urinary bladder with ureters and urethra was removed and placed in ice-cold Ca2+-free HEPES-buffered physiological saline solution (HB-PSS) containing [mM]: NaCl [134], KCl [6], MgCl2 [1.2], HEPES [10] and glucose [7]; pH = 7.4. The bladder and urethra were cleaned of fat and connective tissue and ureters were tied proximal to the bladder wall with 4 − 0 suture. The tissue was then moved to the PRIM chamber (also containing Ca2+-free HB-PSS), cannulated, and affixed with 4 − 0 suture. HB-PSS was then exchanged for bicarbonate-buffered PSS containing [mM]: NaCl [119], NaHCO3 [24], KCl [4.7], KH2PO4 [1.2], MgCl2 [1.2], and CaCl2 [2]. PSS buffer was bubbled externally with 5/20/75% CO2/O2/N2 to maintain pH, recirculated by peristaltic pump, and heated to 37°C using an in-line heater (Warner Instruments). Ca2+-replete PSS was infused into the bladder at a constant rate (30 µl/min) through the PRIM chamber’s cannula using a calibrated syringe pump. *Ex vivo* filling commenced simultaneously with video and pressure recording. To increase the contrast between the lumen and bladder wall, infused buffer was mixed with dark food coloring. Bladders were filled until a maximum pressure of 20–25 mmHg was reached, at which time the infusion and video/pressure recordings were simultaneously stopped. Bladders were then emptied and allowed to re-equilibrate for 5–10 minutes before the next fill. To simulate preconditioning, fill-empty cycles were repeated at least 5 times for each bladder; the final fill-empty cycle was used for all calculations.

## 2.4. Bladder Wall Thickness, Volume, and Residual Estimation

The urinary bladder was assumed to have an elastic wall of constant volume and uniform thickness, which deforms during filling and behaves as a nonlinear expanding vessel (Damaser and Lehman 1995). Here and in the following, lowercase letters will refer to the geometry of the bladder when full (deformed configuration at 20 mmHg) and uppercase letters will refer to the geometry of the bladder when empty (configuration at 0 mmHg).

To measure all dimensions required to calculate the wall volume, the first and last frames of the filling video were extracted and areas of each image plane of the bladder was measured using ImageJ software (NIH) (Fig. 2). Perimeters were manually selected by the contrast between black background and white tissue. The average area of sections 1 – 4 (representing vertical planes of the bladder) and the area of section 5 (representing a plane perpendicular to the other sections) were first measured. These measurements were collected from images at 20 mmHg (Fig. 2A) and 0 mmHg (Fig. 2B). Bladder wall thickness in the full bladder (\(t\)) was first estimated by measuring the width of the brightest section of the edge of the bladder wall in the last frame of the filling video (Fig. 2A, inset). Calculated wall thickness was 107.83±19.11 µm (N = 6) at 20 mmHg.

The bladder was next modeled as an ellipsoidal vessel. The area of section 5 was modeled as a circle of equivalent area with radius \({r}_{c}\). The average area of sections 1–4 were then modeled as an ellipse of equivalent area with radii \({r}_{c}\) and \({r}_{e}\).The hollow ellipsoid model was formed by the intersection of the circle with radius \({r}_{c}\) and an ellipse with radii \({r}_{c}\) and \({r}_{e}\) (Fig. 3A).

The outer volume of the full bladder (\({v}_{o}\)) was calculated as the volume of an ellipsoid with radii \({r}_{c}\) and \({r}_{e}\):

\({v}_{o}= \frac{4}{3}\pi {{ r}_{c}}^{2}{r}_{e}\) Eq. 1

Inner full bladder volume (\({v}_{i}\)) was calculated as the volume of an ellipsoid with radii less wall thickness, as:

\({v}_{i}= \frac{4}{3}\pi {{(r}_{c}-t)}^{2}({r}_{e}-t)\) Eq. 2

Thus, bladder wall volume (\({v}_{w}\)) was the difference between outer and inner bladder volumes, calculated as:

\({v}_{w}={v}_{o}-{v}_{i}\) Eq. 3

Residual volume (\({v}_{res}\)) was also calculated as the difference between inner volume of the full bladder and infused volume (\({v}_{inf}\)):

\({v}_{res}={v}_{i}-{v}_{inf}\) Eq. 4

Note that the value of \({v}_{res}\) is constant throughout the test as well as the analysis.

This procedure could not be replicated to estimate the wall thickness in the empty bladder due to the opacity of the tissue. For this reason, wall thickness in an empty bladder was estimated by assuming that the bladder was undergoing isochoric deformation (Ajalloueian et al. 2018; Damaser and Lehman 1995; Nagle et al. 2017; Roccabianca and Bush 2016). Thus, bladder wall thickness when empty (\(T\)) was again calculated using equations 1 and 2. Circular (\({R}_{c}\)) and elliptical (\({R}_{e}\)) radii of the empty (0 mmHg) bladder were derived from sections 1–5 of PRIM images immediately prior to the start of filling (Fig. 2B). Outer bladder wall volume when empty (\({V}_{o}\)) was calculated as:

\({V}_{o}= \frac{4}{3}\pi {{R}_{c}}^{2}{R}_{e}\) Eq. 5

Due to the hypothesis of isochoric deformation, the volume of the bladder wall must be conserved throughout pressurization; therefore, \({v}_{wall}={V}_{wall}\). The inner bladder volume can be calculated as:

\({V}_{o}-{v}_{wall}=\frac{4}{3}\pi {{(R}_{c}-T)}^{2}({R}_{e}-T)\) Eq. 6

This allows us to calculate the thickness of the empty bladder \(t\) as the real, positive solution to the third-order quadratic equation:

\({T}^{3}+\left(-2{R}_{c}-{R}_{e}\right){T}^{2}+\left({{R}_{c}}^{2}-2{R}_{c}{R}_{e}\right)t-{{R}_{c}}^{2}{R}_{e}+\frac{3}{4}\pi \left({V}_{o}-{v}_{wall}\right)=0\) Eq. 7

As a means of validating the wall thickness measurements, the residual volume when empty (\({V}_{res}\)) was calculated as above by subtracting \({V}_{o}\) from \({v}_{wall}\) and comparing this value to \({v}_{res}\) calculated in Eq. 4. If these values were within ± 10% of one another, we considered the wall thickness measurements valid.

## 2.5. Spherical Cauchy Stress Calculation

Mechanical forces acting on the bladder wall were calculated by first modeling the bladder to be a 3-dimensional pressurized spherical vessel made of elastic material (Fig. 3B), similar to previous descriptions (Nagle et al. 2017). Radius (\(\rho\)) was calculated for any given value of pressure by modeling the bladder as a sphere equal in inner volume to the sum of the residual volume (\({v}_{res}\)) and infused volume (\({V}_{inf}\)) at each value of pressure. Thus, the radius (\(\rho\)) was calculated as:

\(\rho =\sqrt[3]{\frac{3\left({V}_{inf}+{V}_{res}\right)}{4\pi }}\) Eq. 8

Stretch (\(\lambda\)) was used as a measure of deformation and was calculated as the ratio of the current radius by the undeformed (empty) radius:

\(\lambda =\rho /R\) Eq. 9

Lastly, we used the measurements derived above to calculate Cauchy stress during bladder filling:

\({\sigma }_{W}=\frac{{p}_{ves}\bullet \rho }{2\bullet {t}^{{\prime }}}\) Eq. 10

Where \({p}_{ves}\) is intravesical pressure, \(\rho\) is current spherical radius, and \(t{\prime }=T/{\lambda }^{2}\) is wall thickness in the current configuration and how it relates to the initial thickness (\(T\)) due to the assumption of isochoricity. Stress and stretch values were then plotted for each time point during *ex vivo* bladder filling. These data were also used to derive biomechanical metrics, as described previously (Zwaans et al. 2022).