the broad range of medical images and image processing technologies , representing the integration of computer technology in presurgical planning and surgical procedures are often applied in urology . such systems can be seen as a combination of several procedures and tools developed in order to overcome the drawbacks of invasive surgery and helps the surgeon 's orientation inside the three dimensional ( 3d ) anatomy during surgery . partial nephrectomy ( pn ) has gained more importance in the treatment of patients with small renal masses [ 2 , 3 , 4 ] and it can be performed for selected tumors with a maximum diameter of 7 cm [ 510 ] . moreover , the benefits of pn are well established and include , above all , a decreased risk of long  term renal insufficiency and consequently a positive impact on the quality of life [ 11 , 12 , 13 ] . the knowledge about kidney arteries branching is very important for safe performance of varies urological procedures . an invasive arteriography allows obtaining precise but two  dimensional image ( and ) angio  ct can follow the renal arteries only up to their second branches . there is lack of strategies which enable imaging of the whole renal arterial pathway in presurgical planning . therefore we proposed the novel self  developed approach for analyzing and improving the understanding of anatomical relationships between kidney endocasts of intrarenal arteries . examples of such structures are the blood  vessel system , the airway tree of a lung , bronchial tree , nerve tissues , a lymphatic system , and the retinal vascular network , for example [ 1417 ] . simulation studies have been frequently used to gain a better understanding of both diagnostic and therapeutic aspects of blood flow . by applying the strategy proposed in this work it is possible to generate an optimized arterial tree model tree in three dimensions . additionally , these computerized image analysis techniques can then be applied to compute the desired features of the arterial system that are usually associated with function or pathology , and can be used in presurgical planning . the work presents the methodology of renal arterial trees analysis that consists of the following steps . then , the endocast is processed ( transformed ) to a numeric form using high  resolution computed tomography . to perform this type of analysis , a pre  processing step is usually required : the arteries are traced and extracted from the image , using manual or automated procedures . additionally , the series of intersections is analyzed using our self  developed image processing procedures in a matlab environment to find the contours in the ct scans , which defined the boundary of each artery . first , the structure outline needs to be traced and segmented from the rest of the tissue or background in the image . the arterial network is modeled as a branching tree of nonintersecting , rigid cylindrical tubes . starting at the main renal artery ( root segment ) , the tree successively bifurcates down to the last level , where the model tree is truncated in the form of terminal segments . the geometry of the tree is characterized by the cartesian coordinates of the endpoint of each segment together with its actual ( outer ) radius . the three  dimensional model of arterial systems is converted for further analysis to a graph tree constituting typical and convenient data structure . in particular , we focus on structures modeled by directed rooted trees , defined as directed acyclic graphs in which there exists only one path between any two nodes . each node has one or no parents , while the node at the top of the tree that has no parents is identified as the root of the tree . when the nodes of the tree are assigned labels , then the tree is referred to as a labeled rooted tree . in this paper we consider tree  like structures that represent the renal arterial system . in the proposed tree finally , the full information about parameters of the renal arterial system is evaluated and preserved , i.e. diameters and lengths of individual branches and coordinates of the nodes . further , a statistical analysis of the renal arterial tree was realized by a matlab software specifically designed for three  dimensional quantitative evaluation of arterial pathways . our experimental results demonstrate the effectiveness of the proposed method in automatically characterizing tree  like structures in kidney images . these methods can potentially provide insight to the relationship between branching topology and function or pathology . in the work we applied the elaborated methodology and tools in evaluation of the selected , typical renal arterial system . the created data structure in the tree form was studied using software tools of descriptive statistics . the analyses mainly relied on exploration of the branch lengths , diameters , and volume distributions throughout the tree , and its location in the space . first the endocast was imaged using a high  resolution ct and processed by various specialized procedures to form the 3d connected tubes ( figure 1 ) . further such image was converted to the form of tree data structure ( figure 2 ) , in which the information about coordinates ( x , y and z ) of the nodes and also branch lengths and diameters was stored . the volume of the convex hull circumscribed on the analyzed arterial tree was about 53.5 cm , while the number of analyzed branches in the presented endocast was 181 with 14 bifurcation levels . the mean diameter of the artery in the tree root amounted to 4.58 mm , while the length the number of branches was highest ( n = 32 ) at the 9th bifurcation level ( figure 3 ) . plot , the detailed descriptive statistic of the branch lengths and areas at respective bifurcation levels ( the smallest observation , lower quartile , arithmetic mean , median , upper quartile , largest observation ) . it may be noticed that the mean length of the arterial branch on each bifurcation level was constant and amounted to approx . this conclusion did not regard the second or third level , in which the length was even 18 mm . there was also noticed a relevant dispersion of the branched areas ( rsd up to 80% at the 6 and 7 levels of the arterial tree ) . arterial system after high  resolution ct and image volume rendering processing ( the subtrees were marked with different colours ) . distribution of arterial branches ( n = 181 ) at respective bifurcation levels . averaged segment length at respective bifurcation levels . solid squares indicate the mean length of all vessel segments at a certain bifurcation level ; vertical bars minimum and maximum values ; rectangles  lower and upper quartiles ; horizontal line  median . averaged segment area at respective bifurcation levels . it was observed ( figure 6 ) that the sum of areas of each level increased to the 67 bifurcation and further decreased ( the number of branches of each level was lower ) . the reason of such situation may be explained by the decreasing blood pressure and flow speed . the highest sum of areas and volumes of the arteries was observed on the 6 level ( 55 mm , 320 mm ) . summary evaluation of the arteries at respective bifurcation levels : a ) sum of the artery areas and b ) sum of the artery volumes . the number of terminal branches increases up to 9 level where there are 19 terminal branches . the mean length of terminal arteries was 7.17 mm ( changing in the range from 1 mm to 15 mm ) with standard deviation 3.67 mm . the mean radius was 0.46 mm ( area was changing in the range from 0.5 \to 1.5 , only one 2.3 mm ) with standard deviation 0.09 mm . also , a detailed analysis of the four main sub  trees ( renal arterial segments ) was done ( figure 1 ) . localization of the nodes in the renal space at the 6 and 7 bifurcation levels is presented in figure 8 . for each sub  tree the following parameters were evaluated and relationships between them were observed . these were : number of branches , volume of convex hull circumscribed on each sub  tree , diameter and area of the artery in the sub the calculated values of these parameters are presented in table 1 . in the presented endocast each sub  tree consisted of 37 ( 21% ) , 78 ( 44% ) , 36 ( 20% ) , and 27 ( 15% ) branches with volume of convex hull circumscribed on each segment of 4.28 , 24.47 , 3.07 and 2.68 cm , respectively . localization of the nodes ( only x and y coordinates from ct image ) including bifurcation for the main four sub  trees : a ) 6th level and b ) 7th level . statistics of the main four sub  trees of the arterial system we found a statistically significant correlation between all pairs of considered parameters . the value of the correlation coefficient in each case was greater than 0.89 and often was close to 0.99 . it is very important that the main sub  tree artery diameter is correlated with the number of branches ( r = 0.89 ) , volume of convex hull circumscribed on each sub  tree ( r = 0.95 ) , the total length ( r = 0.93 ) , the volume of the arteries in each sub  tree ( r = 0.95 ) , and the number of terminal segments ( r = 0.91 ) . additionally , after conducting calculations and analyses with novel software tools , it may be concluded that the individual artery segments occupy a separate space in the kidney volume . a similar correlation is observed when the tree was divided into more sub  trees . the anatomical relationship between the intrarenal arteries and kidney parenchyma was studied in xix century with the beginning of kidney surgery . analyzing kidney vessel endocasts , hyrtl first discovered that the renal arterial system was divided into anterior and posterior part by the renal collecting system . in 1901 , broedel described the branching of the renal artery in a tree  like pattern . in the same study , the avascular plane between the sub  tree of the renal artery was discovered . in xx century , graves , analyzing kidney endocasts , introduced a constant pattern of intrarenal artery arrangement , which divides the kidney cortex into specific anatomical segments . the same anatomical segments are described in our study with the application of modern statistical tools . the 3d statistical analyses provide data that can verify the previous descriptions of renal artery trees for practical implications during kidney surgery and can be applied in the preoperative planing . our observations confirmed that the kidney can be divided into segments with a separate arterial vascularization . the presented description of the methodology and the statistical analyses results , which enabled evaluation of the arterial system of the selected kidney , are a part of the project in which the greater set of objects will be tested . the verification of previous observations will contribute to our knowledge of the renal arterial system with in critical in precise nephrong sparing surgery procedure .