To fabricate the silicone wall, we followed a procedure similar to that described by Cerussi et al. [16]. Briefly, 0.585 g of titanium IV dioxide (TiO2, 248576, Sigma Aldrich, St. Louis, MO, USA) was weighed out into an empty beaker. Into the same beaker, we added 60 mL of P4 silicone activator (Eager Plastics, Chicago, IL, USA), then placed it in a sonicator (Branson 3800; Sigma Aldrich) for 3 hours. During sonication, we added 1 mL of 1.5 g/L nigrosin ink (198285, Sigma Aldrich) and 2 mL of 1.5 g/L NIR979W dye (QCR Solutions, Port St. Lucie, FL, USA) to 600 mL of P4 silicone base (Eager Plastics). We blended the contents with a handheld mixer until fully homogenized. The silicone activator with TiO2 was then slowly introduced into the silicone base with stirring until completely homogenized. The mixture was placed inside a vacuum chamber to de-aerate before being transferred to a silicone mold. The filled mold was placed back into the vacuum chamber until no bubbles remained. Finally, the silicone was allowed to cure for 24 hours.

For the construction of the SG wall, 700 g of clear gelatin (Humimic Medical, Greenville, SC, USA) was cut into approximately 3-cm cubes and placed inside a 1,000 mL beaker. A mechanical oven (Heratherm OS630, Thomas Scientific, Swedesboro, NJ, USA) was preheated to 125°C. The beaker containing the gelatin was then placed in the oven until the SG was completely melted, which took approximately 3 hours. After melting, the SG was poured into a deep aluminum pan. Subsequently, a custom 3D-printed frame constructed from acrylonitrile butadiene styrene (ABS) was immersed in the pan to ensure that the thickness of the SG, once set, would match that of the silicone wall. The frame was then left in the pan to cure overnight.

After curing both the silicone and SG walls, the phantom assembly commenced. The silicone wall was positioned, and silicone glue was meticulously applied to all junctions between the silicone and the box. Likewise, sealant was applied to the SG frame. A 3D-printed ring was inserted into the neck of the balloon to secure the tubing. Subsequently, the balloon was positioned over the box’s bottom hole and sealed. The completed phantom’s overall dimensions were 16×17×11.5 cm.

A 70% fat-to-water content emulsion was prepared as the filling medium, following a procedure similar to that described by Ohmae et al. [18]. In a 1,000 mL beaker, 965 g of food-grade pure soybean oil was mixed with 15 g of lecithin emulsifier (Daejung Chemicals & Metals Co., Ltd., Siheung, Korea) and heated on a hotplate to 60°C until the lecithin had completely dissolved. Concurrently, 420 g of water was heated to the same temperature in another 1,000-mL beaker. The 2 liquids were then combined using a high-speed vacuum blender (i8800, Jiaxiang Electric Co., Ltd., Dongguan, China), employing a preset blending routine that lasted for a total of 2 minutes and 30 seconds. After blending, the emulsion was allowed to cool for 5 minutes before being poured into the phantom.

The reproducibility of the phantom, specifically the ability to inflate the balloon consistently in the same position and manner using the syringe’s labeled guidance, was evaluated using imaging techniques. In this experiment, the phantom was filled with clear water, and the balloon was incrementally inflated from 50 mL to 350 mL, which is the syringe’s maximum capacity, in 50 mL increments. At each increment, the balloon was imaged by looking through the transparent SG wall. This procedure was then replicated twice. Additionally, careful attention was given to maintaining the camera and phantom in identical positions for each imaging step. Variations in the balloon’s size and position were assessed by calculating the percentage difference on a pixel-by-pixel basis.

DOS, a quantitative optical modality that operates in the nearinfrared spectrum, was utilized to measure our phantom [21-24]. In brief, DOS is capable of estimating the optical properties of turbid media, specifically absorption (μa) and reduced scattering (μs’). It fundamentally integrates 2 techniques: the frequency domain (FD), which relies on laser light captured by a photodetector, and the continuous wave (CW), which uses white light detected by a spectrometer. The construction and description of a DOS-based device have been extensively detailed in previous studies [14,15].

For our experiment, a probe was 3D-printed with a sourceto-detector distance of 30 mm. This probe was subsequently mounted to ensure consistent positioning on the silicone side of the hybrid SG phantom for the duration of the experiment.

To estimate bladder volume using optical signals data collected from a DOS-based device were analyzed with machine learning models employing multiple linear regression (MLR). MLR is a supervised learning method that uses multiple independent variables to predict a single dependent variable [25]. Seven MLR models were used, each based on different types of optical signals gathered by the FD and CW components. These signals varied from basic detector outputs, such as amplitude, phase, and reflectance, to more processed signals, namely absorption coefficient (μa) and reduced scattering coefficient (μs’). The models were trained on data from a single inflation set ranging from 100 mL to 300 mL, in increments of 100 mL. We predicted bladder volume using each MLR model as the phantom bladder was repeatedly filled and emptied, with volumes ranging from 100 mL to 350 mL in 50 mL increments. Data analysis was conducted using MATLAB 2020b.

In this study, we used a commercial ultrasound device (Biocon-1100, Mcube Technology Co., Ltd., Seoul, Korea) as the gold-standard reference. We validated the expected volume of the balloon with ultrasound measurements ranging from 100 mL to 350 mL, increasing in 50-mL increments. This validation served 2 purposes: (1) to confirm that our phantom could provide adequate contrast for ultrasound imaging, and (2) to ensure the accuracy of the volume delivered by the syringe. In accordance with the manufacturer’s recommendations, we performed 3 ultrasound measurements at each increment and selected the maximum volume from these 3 measurements for use.

Based on photographic analysis, as depicted in Fig. 2, we noted variations in the balloon’s position and shape when inflated to only 50 mL. The minimal internal pressure at this volume led to a partial collapse and wrinkling of the balloon’s surface, which varied with each inflation. However, when the balloon was further inflated to 100 mL and then to a maximum of 350 mL, we observed a more consistent reproducibility in terms of the balloon’s position, shape, and size. Consequently, for subsequent experiments involving ultrasound and DOS, we omitted the 50 mL inflation step and employed only volumes exceeding 100 mL.

Different types of data captured by the DOS were categorized into separate MLR models. The R2 and mean absolute volume error for each model were calculated to evaluate their performance, as presented in Table 1. If R2 is deemed the most critical parameter, then model 1 and model 6 would be regarded as the top-performing models. Conversely, if one prioritizes the lowest mean absolute error, model 5 and model 6 emerge as the best. Predictions of bladder volume based on the MLR models with the highest R2 are illustrated in Fig. 3. The trends are remarkably consistent, especially as the balloon volume was cycled between 100 mL and 350 mL. The most significant error occurred at the final volume increment to 350 mL.

The expected balloon volume, as indicated by the syringe labeling, was validated through ultrasound imaging. We found an average absolute volume difference of 8.3 mL when compared to the anticipated volume, as depicted in Fig. 4. This degree of absolute volume error aligns with the manufacturer’s data [26].