A New Algorithm for Assessing Hepatomegaly Through CT Scan of the Abdomen

The importance of the study is in using computed tomography (CT) to measure the size and dimensions of the liver as well as in its discovery of a mathematical technique to attain and increase the accuracy in the calculation of liver's size and dimensions. The study was based on 603 individuals who underwent an abdominal CT scan in medium hospital in Hebron-Palestine. The IntelliSpase Portal 9 (Philips) was used to measure the liver's six dimensions, including transverse, vertical, and anteroposterior dimensions of the right and left lobes. Mathematical equations based on the liver shape were used to calculate the size of the liver. Ultimately, a comparison of the developed and standard formulae’ for the diagnosis of hepatomegaly was carried out. Based on these findings, four hepatic forms were identified and calculations were conducted. The results showed that the Area under Curve (AUC) in the total sample was 0.92, and for the I-IV liver types was 0.87-0.93. The specificity of diagnosing hepatomegaly calculated using general formula was 87%, which practically does not differ from the values of this indicator with a differentiated approach: Type I - 91%, Type II- 84%, Type III- 86%, and Type IV- 90% بي. In conclusion, the standard formula for determining liver can be utilized in clinical practice: V = (HRL+TRL)3/21, (V – volume, HRL – high of right lobe, TRL – thickness of right lobe).


INTRODUCTION
An increase in volume best describes hepatomegaly, defined as an abnormal increase in liver size [1].The liver size volume is a very critical property of the diagnostic value, notably in the diagnosis of hepatomegaly, dynamic medical supervision, and treatment of different illnesses, as well as when planning surgical interventions [2], [3], [4], [5].It has been suggested that the techniques used to estimate the size and volume of the liver typically have poor accuracy owing to the enormous variances in the shapes that the liver may take in humans [6], [7].
Magnetic resonance imaging, ultrasonography, and computed tomography (CT) are superior radiological imaging modalities for determining liver size.In fact, Tomography has become widely used in scientific medical research and industry for its non-destructive and high-resolution means of detecting internal structure.This includes a variety of applications in seismic data, digital rock physics, radar imaging, medical modalities such as computed tomography, magnetic resonance, and others, [8][9][10][11][12].
Radiologists often use landmark-based visual assessments of the hemidiaphragm, stomach displacement, duodenum, hepatic flexure of colon, right kidney, and lower costal cartilage to identify hepatomegaly on imaging studies [13].Nonetheless, landmarkbased estimation of liver volume might be incorrect due to the population's wide variety of typical liver forms.There is a risk of misdiagnosis in the 3-31 percent of the population that exhibits this typical range if volume measurements are not readily available.Furthermore, without regular quantitative assessments of liver size, it is difficult to distinguish between moderate and large hepatomegaly, the latter group of patients potentially benefiting from pharmacological therapies [14].
Radiological scans are often employed, and the height of the liver is measured manually at the mid-hepatic line (MHL).The mediolateral liver distance (MHL) is the axial-plane distance between the spine's midpoint and the liver's outermost point on the right side.Large MHL heights may be seen in livers with Riedel's lobes, indicating that this 2D metric does not adequately capture liver shape [15].Many livers depart from normal lobe sizes [16], [17], [18].As a result, a "saddle-shaped" liver has larger transverse values for the left lobe, while a "triangular-shaped" liver has larger vertical values for the right lobe [19], [20].Considering liver morphologies while calculating volume may lead to erroneous data [21].
To our knowledge, only a few research have published liver study form data, which are not systematized [22].The wide liver, which has longitudinal measurements nearly equal to or slightly greater than transverse measurements, the long liver with a "saddle-shaped shape, " which has a relatively large left shar, the triangular liver with right lobe, which has a tongue-shaped process, and the irregularly shaped liver, which has significant constrictions between the lobes and protrusion or retraction of shares or segments, are the most common liver forms.[23][24].According to the knowledge, liver kinds are not often classified [25], [26].
An organ's complicated geometrical form should affect its linear dimension-volume ratio.The current study conducted a novel investigation to determine whether liver shape influences CT volume measurement.Also, it was conducted to determine how liver shapes affect the accuracy of organ volume and hepatomegaly evaluation on CT and create methods to enhance calculation accuracy for varied liver shapes.

MATERIALS AND METHODS
This research retrospectively investigated 603 abdominal CT scans conducted in the radiology department of a medium-sized hospital in Hebron, Palestine, between January 2020 and December 2021.231 males and 372 females aged 19-94 (mean age 58) participated.
When analyzing CT images, the liver shape was assessed and its six dimensions were measured, including vertically, anteroposterior and transverse dimensions of the right and left lobes of the liver.Next, an advanced visual analysis using multimodal stations where a series of photos from the portal contrast phase were input, and a 3D reconstruction was carried out using specialized software in the IntelliSpase Portal 9.0 [27] (Philips, 603 observations) to calculate the volume of the liver (Figure 1).This made it possible to do mathematical analysis in order to create multiple formulae for determining the volume of the liver based on its shape.These formulas were designed to be as near to the actual volume of the liver as was practically possible.In order to establish equations for calculating liver volume, an approximation of the cubic root of the volume was developed via the use of the least squares approach.Receiver Operating Characteristic (ROC) was used in the production of ROC curves and an assessment of the area under curve (AUC) to evaluate the sensitivity and specificity of diagnosing hepatomegaly based on the produced formulas.This was done in order to determine the sensitivity and specificity of the developed formulae.A comparative analysis of the root-meansquare error, AUC, as well as indicators of sensitivity and specificity was carried out in the process of diagnosing hepatomegaly.This analysis used formulae for liver types I to IV as well as a generic (standard) formula that does not take into consideration the shape of the liver.

RESULT AND DISCUSSION
After analyzing 603 CT scans of the liver, researchers found four primary liver types, each of which is distinguishable from the others based on the ratio of linear parameters of the right and left lobes of the liver.Figure 2 shows that a type I liver will have right and left lobes of the typical size, but a type II liver will have normal right lobes and extended left lobes, a type III liver would have elongated right lobes and normal left lobes, and a type IV liver will have elongated right and left lobes.
The right lobe of the liver's variety (normal, elongated) was determined based on craniocaudal size.When the value of the right lobe is less than 15.5 cm, it is regarded as normal; when it exceeds 15.5 cm, it is called extended.The left lobe of the liver was examined visually.The most prevalent variants were the liver with extended right and normal left lobes (type III) and the liver with normal lobes (type I), accounting for 36.6%(n = 221) and 34% (n = 205), respectively.Elongated right and left lobes were identified in 19.4% (n = 117) of individuals with liver type IV.There were 10% fewer patients (n = 60) with liver type II.To assess the liver's ratio to a specific kind of all employed sizes of the right and left lobes, it is reasonable to evaluate its two sizes, which naturally impact the degree of their elongation: the vertical size for the right lobe and the transverse size for the left lobe.Table 1 displays the values for these dimensions.
Following that, the methods for generating the most exact formulae for determining the volume for each of the four types of hepatic forms were identified.For this aim, the least squares approach was employed in the computations to calculate the approximate volume.This mathematical technique demonstrates a variety of ways for constructing formulae to calculate liver volume.The Least Squares Method estimates liver volume since it fits a mathematical model to experimental data well.Medical imaging data, especially liver volume estimates, may be noisy and inaccurate.The Least Squares Method minimizes the total of the squared differences between the model and data points, making it resilient to noise.The model best fits data variations and mistakes is found.The Least Squares Method works with many mathematical models.Estimating organ volume may employ several mathematical models and alter the procedure to match the facts.This flexibility lets researchers pick  the best model for the situation.Three mathematical methodologies were examined in order to determine the best approach: A function of sum products of dimensions in various combinations using appropriate coefficients: A function that takes into account the sum of cubes of sizes: A function that takes into account the cube of the sum of sizes: Where (S#) is the study number from 1 to 603, (Ls) is the liver size, (a) is the coefficient, and (Ns) is the size number.Approximation graphs that reflect the accuracy of determining the calculated liver volume based on comparison of the true volume obtained as a result of automatic segmentation were constructed in order to evaluate the above mathematical approaches (Figure 3.a, Figure 3.b, and Figure 3.c).The graphs display information on the liver volume values (y-axis) that correspond most closely to the true (solid line) and calculated (broken dotted line) values in each specific observation.According to the actual liver volume, all observations are ordered along the sample number in ascending order.The fluctuations of the estimated curve reflect the inevitable calculation error: the greater the range of fluctuations, the greater the error in the corresponding formula.
The approximation by formula (2) which accounts the sum of the cubes, gives an unacceptably huge systematic error, as shown by the information given in figure 3.b: the plot of the estimated volume (broken dotted line) calculated by this formula does not overlap with the plot of the true volume (solid line).
The approximation graphs produced by formulae ( 1) and ( 3) are quite similar, however, formula (1) requires computations for a large number of indicators and is thus impractical.The researchers attained acceptable accuracy with a modest number of model parameters using formula (3), therefore we'll utilize this unique model based on the cube of the sum of the individual sizes to construct other formulae for estimating liver volume in the future.
As a result, after settling on the best mathematical technique, multiple formulae for each of the four liver forms were created.VPD -the vertical size (height) of the right lobe -and TPD -the anteroposterior size (thickness) of the right lobe -were measured a.) b.) c.)  using the technique described in the article [28].The following step in determining the feasibility of using the formulas developed in the practical work for each of the four types of liver was a comparison of these formulas with a standard (general) formula that does not take the shape of the liver into account, specifically with the formula we previously developed and presented in previous publications [28]: In the comparison, researchers looked at the root-mean-square error and the area under curve, both of which were derived using the formulas for the particular liver type and the whole sample (Table 2, Figure 4).When liver types I through IV are estimated using their own separate formulae, as indicated in Table 2, the root-mean-square error is shown to have a smaller value.This leads one to believe that there may be a hypothesis for a differentiated method of measuring liver volume based on its forms.The ROC analysis showed that the diagnostic accuracy of hepatomegaly did not alter when using the standard formula as opposed to the individual one, despite the higher quantitative scoring error.This was shown to be the case despite the fact that the individual formula produced more accurate results.The area under the curve (AUC) was 0.92 for the overall sample and varied from 0.87 to 0.93 for liver types I through IV.
In addition, researchers examined the sensitivity and specificity of the approach to detect hepatomegaly while estimating organ volume using formulae for liver types I through IV and the standard formula for the full sample (Table 3).With the assistance of ROC-analysis, both the volume threshold that was met for these indications as well as the excess volumes that may be suggestive of hepatomegaly were found.
The findings in table 3 reveal that, as compared to the technique for separating type I liver forms, the sensitivity of the conventional methodology for diagnosing hepatomegaly rose from 76 to 86%, while it remained practically constant for types II-IV liver forms.When the liver volume is calculated using the general method, the specificity for diagnosing hepatomegaly is 87%, which is substantially comparable to the value of this indicator: Type I-91%, Type II-84%, Type III-86%, and Type IV-90%.
The presence of a substantial quantity of material allowed for differential measurement of liver volume and size depending on the form of the liver.According to a comparison of the results of estimating liver volumes using the general formula and the formula devised for specific kinds of liver morphology, using the general formula significantly raised the root-mean-square error of the estimate more in liver types I and II.Despite the increased quantification error, the usual technique has no effect on the accuracy of identifying hepatomegaly.
In addition, the research indicated that when calculating the volume of the liver using the conventional formula, the sensitivity and specificity indicators for predicting whether or not hepatomegaly really existed were 86 and 87%, respectively.This was observed when deciding whether or not hepatomegaly actually existed.They are, in all practical respects, indistinguishable from those who take a differentiated strategy.According to the findings, the fact that  there are considerable disparities in hepatic forms has very little of an effect on the conventional methods that are used in the process of estimating liver volume using CT.
It is significantly more realistic to employ the older methodologies that we established for any liver in practical work without experiencing a significant loss in accuracy while doing so.In a previous study, the cutoff values for hepatomegaly were established to be an excess of either the liver volume that was estimated using the conventional method (1876 ml) or the sum of the vertical and anteroposterior dimensions of the right lobe (34 cm).An increase in either of these values may indicate hepatomegaly [29], [30]: = (VPD + TPD) 3/21 > 1876 (VPD + TPD) > 34

CONCLUSION
Despite the absence of a human categorization, the four liver types may be allocated in practical work: Type I refers to the typical right and left lobe sizes; Type II to the regular right and the elongated left; Type III to the elongated right and the ordinary left; and Type IV to the elongated right and left.CT methods for organ volume and hepatomegaly detection are unaffected by human liver types.Considering the actual work data, it is advised to adopt a single standard formula that takes into consideration the vertical and anteroposterior dimensions of the right lobe and has the following form: = (VPD + TPD) 3/21 .

Figure 1 :
Figure 1: 3D liver image constructions and segments, and determination of liver volume using IntelliSpace Portal 9.0.

Figure 2 :
Figure 2: Liver shapes: a. Type I; b.Type II; c. Type III; and d.Type IV.

Figure 3 :
Figure 3: a.) Graphs of true volume approximation by formula 1. b.) Graphs of true volume approximation by formula 2. c.) Graphs of true volume approximation by formula 3.

Table 1 :
Liver lobes dimensions and volumes of the four types.
type Right lobe vertical size (mm) Left lobe transverse size(mm) Mean liver volume (SD) (mL)

Table 2 :
Differences Between Specific Liver Type Formula and General Formula in Assessing Liver Volume.

Table 3 :
The Sensitivity and Specificity of The Method to Diagnose Hepatomegaly