New formula for predicting standard liver and spleen volumes in Chinese adults

The liver volume and spleen volum are useful index for cirrhosis patients with esphageal varices. But the calculation of the volume is time-consuming and boring. To solve the problem, we successfully established the liver and spleen volume formula using the body surface area. We compared the liver volume formula with other four formulas, which be proved with highest accuracy and lowest error. Until now, except for the new spleen volume formula in the research, there are few reports about it. To obtain a reference range of morphological indices, and to establish a formula to accurately predict the standard liver and spleen volumes in Chinese adults.


Introduction
The liver volume has been proven to correlate with liver function and it is a morphological index that is widely used in patients undergoing liver transplantation [1,2] . The accurate estimation of liver volume is very important during pre-transplantation assessment. In patients with cirrhosis, the volumes of the liver and spleen change due to the presence of portal hypertension [3,4] . The liver and spleen volumes have proven to be useful indices to evaluate the severity of esophageal varices and the bleeding risk [5][6][7] .
Because the liver and spleen both are irregular organs, measuring their volumes is usually very difficult. The water overflow method was considered the gold standard to calculate the volume of irregular organs, but it is difficult to implement in human beings, and now it is only used intra-operatively and during autopsies [8,9] . However, with the development of medical imaging technology, many techniques are available to measure the volumes of the liver and spleen, such as computed tomography (CT), ultrasonography and magnetic resonance imaging (MRI). Among them, CT is the most widely used. The deviation in the estimation of the volume of irregular organs by three-dimensional CT reconstruction is reported to be within 5%, so CT is considered to be an effective means for the measurement of the volume of irregular organs. However, this involves calculating the surface area of each layer, which is very laborious and which may diminish its clinical utility [10,11] . Therefore, an accurate formula to calculate the volume of the liver and spleen is still a valuable tool, especially for patients with cirrhosis.
Liver and spleen sizes vary depending on the race, gender and body size [12] . Many researchers have reported formulas which can be used to calculate the liver volume in different ethnic groups. Among them, Urata's [13] formula is the most widely used, and Poovathumkadavil's [14] formula shows the lowest percentage error. Feng et al. [15] and Fu et al. [16] also reported formulas which can be used in the Chinese population and which have shown a higher degree of accuracy and less error.
Until now, there have been few reports on formulas to calculate the spleen volume [17,18] and this has been attributed to differences in methodology. Yet, an easy to use formula to calculate the splenic volume would be very useful for cirrhotic patients, since the liver volume formula alone is not enough to evaluate the severity of esophageal varices and the bleeding risk.
Due to increased blood flow in the portal and splenic veins, the PVD(portal venous diameter), PVCSA(portal venous cross-sectional area) and the SVD(spleen venous diameter) increase significantly in cirrhotic patients [19,20] , so these indices can be used to determine if there is portal hypertension. However, these indices vary depending on the race, age and gender. Therefore, the aim of this study was to develop new formulas to calculate the volumes of the liver and spleen, using as input the morphological index values found in Chinese people, to apply them clinically in cirrhotic patients.

Patients
The data were obtained from patients who underwent upper abdominal CT scans between October 2016 and December 2018 at The Second Affiliated hospital of Xi'an Jiaotong University, (Xi'an, China) and who met the following eligibility criteria: (1) age > 18 years old, (2) normal liver function and no history of liver or hematologic diseases, (3) no history of cancer and 4) of either gender. The exclusion criteria were as follows: (1) history of viral hepatitis, alcoholic liver disease, non-alcoholic fatty liver disease, autoimmune liver disease or other forms of hepatitis; (2) history of liver cirrhosis or other liver diseases; (3) suspected of having liver cancer; (4) past liver or spleen resection; (5) history of diseases affecting the volume of the liver or spleen, such as cysts, hematologic diseases, or other benign lesions of the liver or spleen (more than one lesion, or if only one, having a diameter > 1 cm); (6) conditions having a hemodynamic effect on the PV or SV, such as thrombosis, embolism, or sponge-like appearance of the parenchyma. The study protocol was reviewed and approved by the Institutional Ethics Committee of the second affiliated hospital of Xi'an Jiaotong University. As the study is a retrospective research, the Ethics Committee exempted the informed consent.

Assessment of TLV and TSV by CT
Upper abdominal CT scans were performed using a multi-slice spiral CT scanner (GE 128slice spiral CT scanner; Inux Medical System, United States of America) with a collimated reconstruction thickness of 5 mm and an interval of 5 mm. The CT procedures were conducted by professional technicians in accordance with standard operating procedures.
To improve the quality of examinations, patients were placed in the supine position and trained to hold their breath to prevent movement artifacts during scanning.

Liver volume calculated using previous formulas
In the validation group, the liver volume formulas were applied from four other researchers and then these results were compared with their formula.

Statistical analysis
Statistical analyses were performed with SPSS (IBM SPSS, Chicago, IL, United States). Data are expressed as the mean ± SD. The correlations between CTLV, CTSV and age, BW, BH, BSA, and BMI were analyzed by using Pearson correlation analysis.
Step-wise multiple linear regression analysis was performed to evaluate the impact of each parameter and to develop the new formula for liver and spleen volumes. The CTLV was compared with the SLV (calculated through formulas) by means of the t-test, with the absolute volume and percentage error, as follows: (SLV -CTLV)/CTLV × 100. ± 10% and ± 15% were used as acceptable ranges for differences between the estimated SLV and CTLV. The proportion of the estimates within these acceptable ranges was determined for each SLV formula to assess its level of accuracy. All statistical analyses were two-tailed, and p values less than 0.05 were considered statistically significant.  Table 1.

Characteristics of Chinese adults
Variables which correlate with CTLV and CTSV Five variables were selected to conduct the Pearson correlation analysis for CTLV and CTSV, including age, BH, BW, BSA and BMI. Among these variables, age showed a negative correlation with CTLV and CTSV, whereas BH, BW, BSA and BMI showed a positive correlation. The correlation coefficients between CTLV and age, BH, BW, BSA and BMI were: -0.328, 0.438, 0.574, 0.592 and 0.390, respectively. The correlation coefficients between CTSV and age, BH, BW, BSA and BMI were: -0.182, 0.258, 0.353, 0.361 and 0.246, respectively (Table 2). Of these variables, BSA showed the strongest correlation.
Next, a step-wise multiple linear regression analysis was conducted. The results showed that age and BSA were independent variables for CTLV. Because the partial regression coefficient for age was small (r = -0.937/year), and the effect on CTLV was negligible, therefore it was removed. BSA was the only independent factor for CTSV. Next, this factor was used to calculate the new formulas, as follows: SLV = 858.186*BSA-393.349 (R 2 = 0.350), SSV = 188.813*BSA-140.981(R 2 = 0.126). The scatter plots are shown in Figure 1 and Figure 2.
Comparison of the new formula for liver volume with existing formulas In the past, many researchers have proposed different formulas to calculate the liver volume. Among these, Urata's formula is the most frequently used. Thus, the level of agreement was assessed between this formula and their formula ( Figure 3). The liver volume calculated by using our formula showed perfect agreement with the volume determined with Urata's formula (R 2 = 100%, p<0.001). On the other hand, Poovathumkadavil's formula has been shown to yield the lowest percentage error with respect to the actual liver volume. Chinese researchers have also proposed formulas to calculate the liver volume, such as the highly accurate Fu formula and Feng formula, which incorporates the body weight index and BSA index respectively. Therefore, these four formulas were chosen for comparison with their liver volume formula in another group of 98 participants, and the results are shown in Table 3. Of all the formulas analyzed, only Fu's formula and their formula yielded a mean percentage error below 5%. The mean percentage error using their formula was only 1.83%. 15% and 10% were chosen as the acceptable percentage errors to calculate the accuracy of their formula for liver and spleen volumes, and the results are shown in Table 4. The proportion of SLV and SSV estimated with their formula with percentage errors within ±10% and ±15 when compared with the CTLV and CTSV were 40.8% and 72.4%, and 21.4% and 25.6%, respectively.
Hence, their liver formula showed the highest accuracy and lowest percentage error.

Discussion
In China, the number of patients newly diagnosed with liver cirrhosis is about 300,000 per year, and the number of deaths due to cirrhosis is as high as 110,000 per year [21][22][23] .
Among the causes of death, bleeding due to esophageal varices is the most common [24,25] .
Currently, the diagnosis of esophageal varices and evaluation of its severity is mainly performed by gastroscopy. However, gastroscopy is an invasive procedure, so it is important to explore alternative, non-invasive detection methods. In this regard, it has been shown that the ratio of liver volume to spleen volume is an effective non-invasive index. CT is the most commonly used method to calculate liver and spleen volumes, but it is a time-consuming and laborious procedure. Thus, many researchers have developed formulas to calculate the liver volume. In contrast, very little has been published regarding spleen volume formulas.
In this study, multiple morphological indexes were evaluated, including PVD, SVD, PVCSA, CTLV and CTSV, providing a reference range of these indexes for the Chinese population.
Based on Pearson's correlation and step-wise multiple linear regression analysis, it was found that gender, BH, BW, BSA and BMI correlated with CTLV and CTSV, with BSA showing a very strong correlation. Hence, BSA was chosen to establish an accurate formula for determining the liver volume and this new formula was compared with four other existing liver volume formulas. In addition, the proportion of values was calculated with percentage errors falling within an acceptable range when compared with CTLV and CTSV.
According to the literature, the liver in Asians is smaller than in Europeans [2] . The liver size in Chinese individuals reportedly ranges from 1099.1 to 1220.1 cm 3 . Their results agree with these values, since the mean total liver volume of the 207 subjects in this study was 1043.18 ±244.60 cm 3 . On the other hand, there are very few reports investigating the spleen volume. However, the mean total spleen volume was 175.07 ± 88.15 cm 3 .
It has been reported that the liver volume correlates with many different factors, including gender, BH, BW, BSA and BMI. Of these, BSA is considered to be one of the strongest factors influencing the liver volume, so many researchers have developed liver volume formulas based on this parameter. Like the liver, the spleen is an irregular organ, but it is unknown how these indices correlate with its volume. Five indices mentioned above were chosen to establish their formulas. Many different formulas can be used to calculate the BSA. However, Mosteller's formula is more accurate in the Chinese population [26] . Therefore, this formula is chosen to calculate the BSA. In this study, it is proved that BSA showed a strong correlation with CTLV and CTSV.
Age is an important factor to consider when assessing the liver volume [27,28] . In this study, it is found that age influenced the liver volume, as shown by Pearson's correlation and step-wise multiple linear regression analysis. Therefore, BSA and age were initially incorporated to develop their new liver volume formula: SLV = 786.151*BSA-2.837*age-107.538(R 2 = 0.370). However, when the mean error was calculated between SLV and CTLV, its mean error was 3.19%, which was higher than when the formula included only the BSA value (mean error = 1.83). In addition, the proportion of SLV values with percentage errors falling within an acceptable range (10% and 15%) were 36.8% and 60.2%, respectively, which were also not better than when the formula included only the BSA value. Furthermore, the correlation coefficient for age was only -2.837 in the stepwise multiple linear regression analysis. Therefore, it is concluded that the effect on liver volume was small and it was eliminated. On the other hand, when the effect of age on the SLV was analyzed, it is found that age cannot be used as a factor to establish the spleen volume.
Although BH, BW and BMI were thought to affect the liver volume [29,30] , and Pearson's correlation analysis showed that BH and BW correlated with CTLV, the correlation coefficients were 0.438,0.574 and 0.390, respectively. After the step-wise multiple linear regression analysis, both the factors were eliminated to establish the formula. A similar outcome was observed for the analysis of spleen volume.
Many formulas are currently available to calculate the liver volume. Urata's formula is the most widely used. Poovathumkadavil's formula has been shown to yield the lowest percentage error when compared with the actual liver volume. Fu's formula incorporates the BW and shows good agreement and low percentage error. Feng compared her formula with seven other proposed formulas and found it worked better than the others. In this study, these four formulas were chosen to compare with new formula, and ±10% and ±15% are acceptable percentage errors. In addition, the SLV-CTLV mean error was calculated. It was found that the formula showed the highest percentage of agreement (within ±10% and ±15), and the lowest SLV-CTLV mean error (only 1.83%). Importantly, the formula showed perfect agreement with Urata's formula, and the mean error was significant lower (1.73% vs 17.3%). Thus, the formula may be a better choice to calculate the liver volume in the Chinese population.
Many researchers have tried to develop spleen volume formulas, with limited success.
There are few reports on this topic, a situation that is attributed to the use of different methodologies. In this study, a spleen volume formula was determined: SSV = 188.813*BSA-140.981 (R 2 = 0.126). It is found that the proportion of estimated SSV values with percentage errors within ±10% and ±15 of the CTSV values were only 21.4% and 25.6%, and the mean error was 6.98%. Because the acceptable percent error values were not sufficiently high, the applicability of the spleen volume formula must be demonstrated through additional research.
In cirrhotic patients, due to the presence of portal hypertension and increased blood flow, the PVD, SVD and PVCSA values increase. A PVD > 13 mm is an important index to predict portal hypertension [31] . The mean PVD, SVD and PVCSA values in normal Chinese subjects in this study were 8.84 ± 1.55 mm, 5.53 ± 1.28 mm, 98.33 ± 33.08 mm 3 , respectively.
In the past, even though there were some formulas about the liver and spleen volume, their clinical application is not clear. In our latter research, we combine the actual volume of liver and spleen with the volume calculated by our formulas, and we we have The CTLV and CTSV is actual liver and spleen volume calculate by CT, and SLV and SSV is standard liver and spleen volume calculated by the formula. The area under the Roc curve is 87.3%, the specificity and sensitivity is 89.7% and 65.3%, respectively. The cutoff value is 0.85. If the P is higher than the cutoff value, we can think the presence of the esophageal varices. So the foundation of the formulas is very important for latter work.
The foundation of the formulas is very meaningful.
Although the new accurate liver and spleen volume formulas were developed, there are still many limitations. The thickness of the CT slices was 5 mm, which may be a factor influencing the accuracy of the calculation of the actual liver and spleen volumes. In addition, normal study subjects were selected based on biochemical and imaging tests.
Biopsies or bone marrow punctures was not performed. Therefore, certain occult liver or blood diseases may have gone undetected in their study. Also, their goal was to calculate the liver and spleen volumes of cirrhotic patients with these formulas, but the subjects in their study were all normal people. In cirrhotic patients, the BSA may be influenced by the ascites. Therefore, it is unclear whether the formulas would still be accurate and show low percentage error in cirrhotic patients. In the future, it is planned to use these formulas in patients with cirrhosis, and apply the SLV and SSV ratio to establish a formula, which can be used to evaluate esophageal varices and the risk of bleeding after esophageal variceal ligation.
In conclusion, new liver and spleen volume formulas were established using the BSA which showed more accuracy and lower error than existing formulas. It is believed that these new formulas may be a better choice to predict the liver and spleen volumes in the Chinese population.

Declarations
Ethics approval and consent to participate The study protocol was reviewed and approved by the Institutional Ethics Committee of the second affiliated hospital of Xi'an Jiaotong University. As the study is a retrospective research, the Ethics Committee exempted the informed consent.

Consent for publication
Not applicable.

Availability of data and material
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.    Figure 3 Correlation between liver volume calculated by our formula and Urata's formula.

Supplementary Files
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