Development of a novel mesh model to define a new index “amount of stone” to evaluate calculus and predicting the lithotripsy time

Urolithiasis incidence has kept rising worldwide [1]. More than 90% of urinary calculi can be treated by endoscopy. Large staghorn calculi can be cleared away by percutaneous nephrolithotomy [2, 3]. However, it remains unsolved about how to evaluate the stone size quickly and accurately before operation to reduce intraoperative complications, such as infection and bleeding, and guide surgical procedures.

No standards for preoperative evaluation of stone size have been established. Common indicators include maximum diameter, maximum cross-sectional area, volume and surface area. Among them, volume, which can be calculated by 3D technology, has been attached with high clinical value [4]. However, the complexity in calculation limits its wide use in clinic. Maximum diameter is also being used, but unscientific. In real-time surgery, clinicians are mainly concerned with the difficulty in breaking a stone to pieces of favorable sizes, rather than the simple maximum diameter, volume and other indicators.

Therefore, the author tries to establish a mesh model and use it to define a new index to evaluate stones.

Here are two questions to be resolved before the study.

Fracture theory is the most widely used in establishing a stone-crushing model. Using this theory, we regarded stone fragmentation as a process making enough cracks in the stone to fragment it into pieces with the target size. We established a mathematical model to calculate the minimum number of cracks for crushing.

Considering that non-contrast CT, usually at a spacing of 5 mm, is commonly used for preoperative stone examination, we defined the target size as 5 mm in diameter, and a cubic-shaped stone with edges of 5 mm (on x, y, z axes, respectively) as a target stone unit. A stone was divided into multiple target stone units with a 5 mm mesh in three directions. The bottom surface of each target stone unit was defined as the target cross-sectional area (5 mm × 5 mm = 0.25 mm², expressed in u), then the number of target cross-sections between two units was calculated, and the total number of cross-sections (Q) of each stone was obtained as the theoretical minimum of cross-sections.

Each level is measured with the orthogonal method. The x and y values at each level of CT are measured. x is the maximum diameter and y is the maximum diameter perpendicular to the x-axis. The x and y values are graded by 5 mm: 0 mm < x < 5 mm is expressed as 1; 5 mm ≤ x < 10 mm as 2; 10 mm ≤ x < 15 mm as 3. The same method is used for y. The measurement results are expressed by (x₁, y₁), (x₂, y₂), (x₃, y₃), and so on. Then, the number of cracks perpendicular to the z-axis (n_1-2) is expressed as the product of x and y. The number of cracks parallel to the z-axis (n₁) = x₁(y₁ − 1) + y₁(x₁ − 1), n₂ = x₂(y₂ − 1) + y₂(x₂ − 1), n₃ = x₃(y₃ − 1) + y₃(x₃ − 1), and so on. The total number of cross-sections of the stone is called the amount of the stone: Q (u) = n₁ + n_1-2 + n₂ + n_2-3 + n₃ + …. (Fig. 1). If there are multiple stones, the Q of each stone is calculated and summed up. The Q is the theoretical minimum cost.

Next, we verified the reliability of this index from three points.

1. The mathematical basis of the model

The foundation of the model is that the stones are supposed to be regular. Because most of the stones are irregular, errors are inevitable. Some scholars believe that the elliptical formula can be used to calculate the cross-sectional area of stones [10], while others believe that the elliptical formula is inaccurate [11]. Therefore, we summed the cross-section areas of the stone measured layer-by-layer orthogonally, multiplied by the spacing, and compared the results with the CT 3D reconstruction volume, to verify whether the influence of the stone shape on the model was within the acceptable range.

We designed a prospective study to resolve the above three points. Since the stones with a diameter less than 5 mm can only be washed out directly through a channel of about 18F under the percutaneous nephroscope, we used percutaneous nephrolithotomy to verify the effectiveness of our new method. During the operation, the channels with a diameter of 18F and holmium laser were selected. Holmium laser is a solid-state pulsed laser using rare element as the excitation medium. The mechanism is that after the activation of the Holmium laser, the stone and its surrounding water absorbs the laser energy, causing the temperature to rise and the stone to undergo a thermochemical reaction. At the same time, the water around the stone generates plasma bubbles (or steam bubbles), and uses the shock wave generated in the expansion or crushing process to smash the stone [12].

A total of 198 patients who had received PCNL in our hospital from March 2021 to December 2022 were recruited and 112 eligible were included.

112 patients included 73 men (65.1%) and 39 women (34.9%). Their age was between 23 and 68 years, with a mean of 49.92 ± 11.36 years. The height was between 150 and 186 cm, with a mean of 166.56 ± 8.04 cm. The weight was between 47 and 105 kg, with a mean of 71.06 ± 12.43 kg. The BMI was between 18.73 kg/m² and 32.05 kg/m², with a mean of 25.51 ± 3.37 kg/m². The stones appeared in the left side of 51 cases (45.5%), and the right side in 61 cases (54.5%). A KUB examination was carried out for all patients before the operation, confirming that they were all positive.

Puncture channels of PCNL were all single channels with 18F. Double J tubes and nephrostomy tubes were retained after surgery. The constant-speed pressure limiting pump was used as the water source during the surgery. The pump speed was 680 ml/min and the pressure limit was 700 mmHg. The model of the holmium laser surgery system used was Auriga XL (StarMedTec GmbH Company) produced on August 19, 2016. During lithotripsy, the core diameter was 600 um, the lithotripsy mode was used, and the frequency was 12 Hz. The energy of a single pulse was 3500 mJ. After lithotripsy, the number of pulses, lithotripsy time (s), and lithotripsy energy (mJ) were read from the memory of the holmium laser machine. The surgery was performed by two doctors independently. The surgery was performed by Wang Yunyan in 69 cases, (61.6%) and by Ji Lu in 43 cases (38.4%).

All patients received CT urography (CTU) examination before surgery. In CTU, the distance of 0.7 mm and the plane thickness of 1 mm were set as references. The stones were measured by two experienced clinicians, each measuring the calculi once. The results were averaged. The Q was measured using a CTU non-contrast sequence with the following methods. From top to bottom, the first level of the stone was recorded as 1 and the second level as 2. The 7th (4.9 mm), 14th (9.8 mm), 21st (14.7 mm), and other levels of the whole stole were measured, respectively. Then, the levels were measured again from bottom to top with this method, and the results of both times of measurement were averaged. In the plain CT scan, the levels of each visible stone were directly measured. If there were multiple stones, each of them was measured and calculated, and the results were summed. If a stone has several discontinuous surfaces at the same level, the results on these surfaces should be added; and if the stone disappeared before the 7th level, only the maximum cross-section was recorded. If its maximum cross-sections x and y edges were less than 5 mm in length, the stone was ignored.

The HU values were measured by selecting the circular area of interest within the largest section of the stone on the CT scan image and reading its average HU value. The HU values were between 375 and 1653 HU, with a mean of 1162.51 ± 176.63 HU. HU values less than or equal to 677.5 are considered as soft stone types, HU values greater than or equal to 970 are considered as hard stone types, and those between 677.5 and 970 are considered as mid-hard stone types [13, 14]. There were 90 cases (80.4%) of hard stones, 13 cases (11.6%) of mid-hard stones and 9 cases (8.0%) of soft stones.

The non-contrast CT images in the CTU examination and images obtained from the ordinary non-contrast CT were imported into Mimics21 software. The region of interest was selected in the bone interval of CT value for 3D reconstruction, and the volume, surface area, and other data were read directly from the reconstructed model.

The statistical software SPSS26.0 was used, and the measurement data were expressed as x ± s. The difference was statistically significant when p < 0.05.

We multiplied the x and y values measured by the orthogonal measurement method, and then multiplied both by 0.49 mm. After layer-by-layer accumulation, we calculated the linear regression between both values and stone volume in 3D-reconstructed model: regression coefficient B = 0.715, R² = 0.900, p < 0.001 (Tables 1, 2, Figs. 2, 3).

The results showed that 90.0% of the stones could be measured using the x/y layer-by-layer orthogonally. The final volume could be calculated by multiplying the cumulative volume by the regression coefficient k. The coefficient of these stones was k = 0.715, near to π/4, indicating that 90.0% of the stones were ellipse-shaped. This model could be considered as reliable.

The results in showed that there was no statistical difference between the two groups (p > 0.05) (Table 3). It was found that the bias from the cross-section selection during the non-contrast CT had not influence on the results of the model.

Bleeding and infection are the most common surgical complications of percutaneous nephrolithotomy [15]. A long-time lithotripsy may cause infection, bleeding and other adverse events [16]. The risk of infection increases obviously if the lithotripsy time in percutaneous nephrolithotomy exceeds 90 min [17]. Our study confirmed that amount of stone, measured by the mesh model, is accurate in predicting the lithotripsy time before the operation. Moreover, its accuracy was significantly superior than that of stone volume and maximum diameter measured by the 3D reconstruction.

The time of percutaneous nephrolithotomy includes not only the lithotripsy time, but also the extraction time. The number of targeted stone units directly affected the extraction time, as shown by our mesh model. The eliminate speed of smaller stone fragments through 18F is faster than that of 5 mm, so there maybe an optimal balance point between the size of gravel and sheath. No obvious evidence could confirm the relationship between the number of the targeted units and the extraction time in the present study, which will be revealed by the follow-up study.

The stone volume recommended by the previous scholars has a limited application in clinic, because the measurement requires specific 3D imaging software. The amount of stone in our study can be measured based on the non-contrast CT. Although the model formula looked complicated, the calculation of the results is relatively simple. For example, a stone with a very big size of about 4 × 4 cm can be seen on 8 levels of CT, the (x_n, y_n) are (22.63,18.08, (19.73,19.80), (17.39,16.81), (18.15,12.36), (30.41,17.15), (35.78,18.08), (36.42,18.21), and (27.21,16.97), it only takes within 3 min to measure it. After unitization with 5 mm as the standard (that is, rounding after 2 times), they are (5, 4), (4, 4), (4, 4), (4, 3), (7, 4), (8, 4), (8, 4), and (6, 4), The calculation is (4 × 4 + 5 × 3) + 4 × 4 + (3 × 4 + 4 × 3) + 4 × 4 + (3 × 4 + 4 × 3) + 4 × 3 + (4 × 2 + 3 × 3) + 4 × 3 + (7 × 3 + 6 × 4) + 7 × 4 + (7 × 4 + 8 × 3) + 8 × 4 + (7 × 4 + 8 × 3) + 6 × 4 + (5 × 4 + 6 × 3) = 423 u, it only takes within 5 min to calculate it and it is more efficient to calculate small stones.

The mesh model can also applied to calculate the amount of stones reduced into target size when the channel of percutaneous nephrolithotomy is less than 18F. Meanwhile, reducing the spacing of preoperative CT scans to the corresponding size is necessary to make the accurate measurement. The lithotripsy time of different channels can be successfully predicted by quantifying different target sizes of stones, which can provide reference for selecting the intraoperative channel size.

Many scholars have proposed many other scoring systems to quantify stones, but their usage is restricted due to lack of unified standards and theoretical evidence. For example, the S.T.O.N.E scoring system proposed by Okhunov [18], where the character S represents the maximum cross-sectional area of calculi, was not only difficult to operate but also was inaccurate.

In the process of lithotripsy, the single energy often spills over, which may explain that there was no obvious correlation between the operation time and stone type and single energy in this study.

Due to the small number of cases included in our study, the optimal single energy could not be calculated, which should be resolved by further large-sample studies.

Our study was a single-center study with a small number of cases, which may lead to the selective bias and have a certain impact on the analysis of the results.

The powder lithotripsy and the popcorn technology are often applied in the rigid ureteroscopy and the flexible ureteroscopy [19, 20], which leads to ineffective pulses during the operation, so it is not suitable to use this method for research. We collected some data of ureteroscopic holmium laser lithotripsy, but failed to obtain the effective results.