PRINCIPAL COMPONENT AND SELF ORGANIZING MAP ANALYSIS OF INHffiITION OF CALCIUM OXALATE CRYSTAL GROWTH BY UROMODUUN Saravanan Dhannaraj, M. Amzad Hossain, Gam Lay Ham and Zhari Ismail School of Pharmacy University Science of Malaysia 11800 Minden email@example.com ABSTRACT This paper reports the use of a modified Schneider's gel slide method to monitor the inhibition of calcium oxalate crystal growth. It is used to monitor the inhibitory effect of uromodulin. The image of crystals in the gel was captured at 24 hours with digital camera arid image analysis was carried out. Nine variables relating to size !l!1d shape parameters were calculated and six were used for further analysis. The principal component analysis (PCA) and the self-organizing map (SOM) were used to visualize the size and shape distribution of the crystals produced. The results indicate that the modified gel slide method with the use of PCA and SOM was capable of producing an intuitive presentation of the differences in the studied crystals. The PCA scores and SOM mapping clearly indicated a decrease in crystal growth for the protein and positive control. INRODUCTION Kidney stones can be one of the most painful conditions known to human kind. The most common stone is calcium oxalate. There are many theories for the formation of kidney stones. One of it, the crystallization precipitation theory implies that super saturation of urine leads to p!'ecipitation of stone crystallites. Clearly other factors seem to playa role as urinary saturation with calcium oxalate is common in the general population (Bihl & Meyers, 2001). Process of aggregation and secondary nucleation leads to formation of large crystals. These critical particles become entrapped and subsequent crystal growth follow and ultimately kidney stones develop. This process is influenced by increased level of super saturation of salts and presence of crystal growth promoters or inhibitors (McDonald & Stoller, 1997; Barbas et aI, 2002). Inhibitors of crystal growth block the growth of crystals and prevent stone formation. Various inhibitors present in urine have been reported by researchers (Chang et aI, 2001; Shirane et aI, 1999, Nakagawa et aI, 1981,1983). Among the various methods by various researchers to measure the inhibitory activity of crystals is by photometry (Schneider et ai, 1983), turbidimetry (Brielmann et ai, 1985), mixed suspension mixed product removal MSMPR (Bretherton & Rodgers, 1998), use of Coulter counter (Grover et ai, 1998; Miyake et ai, 1998; Suzuki et ai, 1999) and spectrophotometry (Hess et ai, 1998). Another way is the use of gel slides for measuring crystal growth (Schneider et ai, 1983; Li et aI, 1987; Ismail et ai, 1997). The crystal is either quantified by densitometry or images captured and crystal size measured. Nowadays, the use of image analysis offers a way to quantify the variations in crystal population. Image analysis can be used as a tool to characterize the size and shape of particles especially crystals subsequent to 7 the visualization of the crystals by light microscopy. However, comparison and analysis of different size and shape characteristics of crystals are very difficult. Several shape and size descriptors are necessary to describe the shape and size of these crystals. Bernard-Michel et at (1999) reported that a simple method for giving rapid insight into the variation of shape and size descriptors is by summarizing all t.he morphological parameters by principal component analysis. Laitinen et at (2002) used self organizing map (SOM) to visualize the size and shape distribution obtained by image analysis and also compared it with principal component analysis (PCA). In this study, a modified Schneider's gel slide method was used to study the inhibition of calcium oxalate crystal (which is the predominant crystal in kidney stone) growth by the protein uromodulin. A positive control was also used to monitor the inhibition. As the image analysis produced a large set of size and shape parameters, multivariate data analysis was carried out with PCA and SOM to visualize the distribution of crystals produced METHODS Purification of uromodulin The purification procedure was according to the report from Grover et al (1998) with slight modification. Sodium chloride was added to the pooled urine at 33.6mg per ml. The urine was stirred and left at 4°C for 1 hr and then the solution-was centrifuged at 10 OOOg for 20min at 4°C. The supernatant liquid was discarded, and the precipitate was redissolved in 0.58M sodium chloride to precipitate the protein. This step was repeated so that the total precipitation step was thrice. The purity of the uromodulin was assessed by SDS- PAGE followed by Coomassie blue staining and human uromodulin migrated as a single band. Gel slide method A solution of 4 ml I % bacteriological agar was used to coat a microscopic slide that was partitioned into three equal areas. Four wells were punched into the agar on each side of the partition. Two wells were made 1.25 cm apart along the longer axis while two wells were made 1.0 cm apart along the perpendicular axis as shown in Fig 1. Solutions of 10 /-ll 0.2 M calcium chloride and ammonium oxalate were pipette into opposite wells along the longer axis. Solutions of 10 /-ll from protein solution or positive control consisting of sodium citrate were pipette into the other two holes. The gel slides were placed in a moist chamber. The crystals formed were monitored at 24 hours under microscope and images were captured with a digital camera mounted onto the microscope. ! blank control sample r A. .A A. , " r "r blank control sam pIe . Ca ions: oxalate ions . . . . . ° .. 00° °0° a °0 0 a t l.Ocm 1.25 em Fig 1. A diagram of the gel slide The optical microscope (Leica MZ6, Leica Microskopie und Systeme, Germany) was connected to image analysis (IA) software (Leica Qwin, Leica Imaging Systems, Cambridge, England), which was used to calculate the size and shape parameters of the calcium oxalate crystals formed. Nine parameters of shape and size were measured of which only six were used for principal component analysis. The IA system measures many very similar kinds of parameters, the ones with high correlation values were omitted to eliminate factors that do not bring any additional information to the analysis of the results. Parameters of length, breadth and perimeter were not used. The six chosen parameters for further analysis were: convex area, aspect ratio, equivalent diameter, . roundness, and fullness ratio, and they are presented in Table 1. . Table I Description of crystal size and shape parameter used in the analysis Parameters Description Area The apparent area ofthe crystals - Convex area The area of the polygon circumscribing the feature formed by tangents to its boundary Aspect ratio The ratio of particle length divided by its breadth Equivalent diameter Equivalent circle diameter-i.e. the diameter of a circle having the same area as the feature Roundness A shape factor which gives a minimum value of unity for a circle (round particles get a value of I, and other particles get values larger than 1) Fullness Ratio A shape factor equal to the square root ofthe ratio of area to circumscribed area Multivariate analysis Multivariate data analysis is capable of giving a perceptive presentation of various data sets. Two common methods, self-organizing map and PCA, enable the lowering of the dimensionality of the multivariate data Principal component analysis The measured image analysis data consisting of mean values of the parameters used was first evaluated using principal component analysis (PCA) employing SPSS program. PCA is a data visualization method that is useful for observing groupings within multivariate data. Data is represented in n dimensional space, where n is the number of variables, and is reduced into a few principal components, which are descriptive dimensions that describe the maximum variation within the data. The principal components can be displayed in a graphical fashion as a "scores" plot.This plot is useful for observing any groupings or trend in the data set (Massart et al., 1988). SOMmapping The use of SOM enables the two dimensional plotting, and compared to PCA it has the advantage that all the information is on the same plot. SOM was used to train and visualize the crystal data. The SOM is available as a Matlab toolbox in a public domain and a Pentium 3 PC was used to train the network. SOM is an unsupervised neural network. It is an elastic net with a map of nodes connected to their neighbors with elastic band. Input data is presented in a random order for training and each observation is projected onto a winning node. The winning node is the one with the shortest distance from the presented vector. The vectors of the winner and its neighboring nodes are modified following the training to represent the input signals more closely. Finally, the SOM net can be brought back to two-dimensions from a n-dimensional space and visualized. Results and discussion Image Analysis measurements The crystal size distribution obtained for the blank, positive control and uromodulin sample at I, 2, 3, 4 and 24 hours are shown in Fig. 2. Blank Control 2.5 ug per ml I I I . . ", areo 0"'0 0 .... Blank Control .5 ug perml ... !! ~ u .. r'I 1\ . l ... 0 ...0 ore. .... Blank Control 10 ug per ml I '"'1, _ i 11 ,lil l i~L.U:Rry. . :C;:>- '-j --,----' 0.00 2OllO.oo 400000 ~oo area area area Blank Control 20 ug perml .. ,I~ J ! -'~ ... , _.. araa area area Fig 2. The histogram Overall, the size distribution shows that the smallest crystals are most numerous for all three; blank, control and sample, at the time period studied. When the blank, control and sample data is compared at 24h it is apparent that mean size distribution is higher for blank compared to control and sample. This is shown by the normal curve that peaks at a higher area value for the curve for blank when compared to control and sample. The normal curve also declines more gradually for the blank when compared to control and sample. Principal component analysis Principal component analysis is a simple method that is capable of summarizing all the morphological variation and then to give a rapid insight into the variations of the size and shape variables. The principal components are determined on the basis of maximum variance criterion. Each subsequent principal component describes a maximum of variance that is not modeled by the former component. According to this m.ost of the variance is contained in the first principal component and then in the second principal component there is more variance than the third. Generally, the first two components are \lsed and they are capable of explaining a high percentage of variance in the data. A measure to quantify, the degree of intercorrelations among the variables and the appropriateness of factor analysis of principal component analysis is the measure of sampling adequacy (MSA). This index ranges from 0 to 1, reaching I when each variable is predicted without error by the other variable. The peA analysis for the crystal data gave a MSA value of 0.666 that justified factor analysis. The Bartlett test of sphericity, a statistical test for the presence of correlations among the variables is another such measure and it also justified factor analysis. There are various criteria for the number of factors to extract. One way is to use the number of factors that give the percentage of explained variance that is greater than 90% and the two factors were required to fulfill this condition (Otto, 1999). Correlations and importance of the size and shape variables can be observed from the principal component loadings as shown in Fig 3. It can be noticed that the size parameters of area, convex area and equivalent diameter are highly correlated among them in the component plot. Shape parameters of roundness and aspect ratio are highly correlated. Both these size and shape parameters load highly on the first component with the shape parameter of convex area having the highest loading. However the size parameters have positive load on the second compartment whereas the shape parameters load negatively. The parameter of full ratio has negative correlation to roundness and aspect ratio and has the highest loading on the second component among the six variables. PCA indicated that the first component explained about 83.6% of the variance in the crystal data and is associated with size para!lleters and shape parameters. The second component explained about 14.4% of the variance and is associated with shape parameters. The two components combined explained 98.1 % variance in the crystal data. The two PCs form a plane in the original image analysis data space and are shown in Figure 4. The crystal data for blank, control and the four protein concentrations at 24 hours shows that the control and protein sample have lower first component loadings when compared to the respective blanks. The blank for the highest protein concentration has much lower first component loading compared to the three other blanks but there is also a corresponding decrease in the control and sample respectively. There seems to be no corresponding pattern in decrease or increase for PC2 when comparing the blank to the respective control and protein sample. Component Plot 1.0 fullratio .5 c eq~rram convell rea 0 0.0 aspectll tio 0 roundnes~ N 0 1: -.5 Ql c: o a. E 8 -1.0 -1.0 -.5 0.0 .5 1.0 Component 1 Fig 3. Plot of component loadings 3~-----------------------, 3 c 2 4 c N 11  C3 a. 12 8 c 9 5 o 7 c 0 1 c 6 c 10 -1  2 c -2 o i - - -........- - - - . . - - - - . . . . - - - - . . . . - - -........----...----l. -2.0 -1.5 -1.0 -.5 0.0 .5 1.0 1.5 peA 1 Fig 4. Principal component scores for the various test samples SOM analysis of crystals The -training data was made toa matrix by combining the image analysis data of the crystals from the measurements. The dimensions of the matrix were 25420 X 6. The matrix includes the data points of the six parameters that describe the 25420 crystals measured from the set of blank, control and protein sample at 24 hours. The size of SOM created for the model particles was 35 X 23. The training of the net for the model particles took 38secs. The results of the trained SOM are visualized in Fi~ 5, which represents the V-matrix for the crystals, and it shows the distances between the nodes or the data clusters in the net. The values of the six different variables of the particles' are also visualized. The color of the node indicates the level of the individual variable on the specific region of the map. The high values are indicated with dark color. It can be noticed that crystals with largest values for size parameters (area, equivalent diameter and convex area) are located at the upper region with the maximum values at the upper right. The crystals with the large values for shape factor roundness and aspect ratio are located in the upper left with the maximum values for aspect ratio being located below slightly compared to the ones for roundness parameter. The crystals with the lowest values for fullness ratio are located at the top right side of the map. The organization of the crystal data on the map for each blank, control, and protein sample at 24 hours is shown in Fig 6. It is observed that for blank, the crystal data is clustered at the lower part of the map. When the blank, control and protein sample data is compared at 24 hours it is apparent that there are less white hexagons at the bottom compared to yellow and red, signaling lesser smaller crystals. It can be observed that there is a corresponding decrease in crystal size for control and sample when compared to blank at 24 hours. Regarding shape parameters there is not much difference in the blank, control and sample at the time period studied as found for size parameters. This is apparent as the crystals in the image were generally of similar type that is mostly calcium oxalate dihydrate. Fig 5 The U matrix and the variable information for the particles The SOM summarizes effectively large sets of particle size and shape parameters. The advantage of SOM as reported is the ability to efficiently visualize the distribution of crystals on the map. Fig 6. The crystal data on the map for each control, blank and sample at 1,2,3,4 and 24 hours Conclusions The modified gel Schneider's method with image analysis methods was capable of monitoring the calcium oxalate crystal growth. 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