**3. Results**

Normalization requires a reference element or another parameter which is relatively homogeneous distributed throughout the sample and standard tissue sections. The concentration of a given pixel (*Cpx*) is then calculated according to Eq. (1), whereby is the reference parameter averaged across the calibration standard measurement and *rpx* the reference parameter of the respective pixel, *Ipx* the ion intensity of the isotope (*m/z*) of interest of the respective pixel, and *m* the slope of the calibration line. All these parameters are given as net values after subtraction of the respective glass background.

In the ideal case, when equal conditions apply for the considered pixel and the standard, the normalization factor / becomes one when the normalization reference is one single isotope and *rpx* correspond to the net ion intensity thereof. In case of TIC as normalization reference, *r* is the sum of all ion intensities, in case of EIC the sum of the selected isotopes. When the reference parameter does not enter per pixel, but is averaged throughout the sample, *rpx* becomes constant ().

$$C\_{px} = \frac{\overline{r}\_{Sdd}}{r\_{px}} \frac{I\_{px}}{m} \tag{1}$$

TIC as a reference should also comply with the requirements to homogeneity and constancy in concentration throughout samples of the same type. **Figure 1** shows that after applying a TIC-based normalization strategy, the absolute element concentrations and the background noise are reinforced inversely proportional to the TIC and thus become distorted. The TIC shows a high dependence to the structure of the sample tissue because it is dominated by the intensities of potassium (39K, **Figure 2**) in measurements of liver and brain tissue. Additionally, for potassium despite low dwell times selected, saturation effects of the detector may occur in the ICP-MS. For these reasons, TIC-based normalization does not confer a significant gain of biological information.

occurred in some data sets, but also during prolonged measurement runs, i.e., over 12 h. For calibration, matrix-matched standards were measured at the end of the same run. These were produced from homogenized tissue of a homologous organ spiked with different concentrations of a standard solution [11]. Sample and standard were present at separate slides posi-

402 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

For image generation, the LA-ICP-MS raw data of individual measurements were copied into a standardized Excel summary file, whereupon the user-defined functions (UDF) of ELAI could be accessed. Once the image dimensions (line length) have been found, the absolute element concentrations of each data point were determined from its ion intensity and the slope of a six-point calibration curve. The software tool "ELAI" [8] that we have recently developed is open software offering free customizable semimanual image generation. The complete program, including detailed documentation for installation and disclosure of all program codes is freely available and can be downloaded from the supplementary material of [8].

Normalization requires a reference element or another parameter which is relatively homogeneous distributed throughout the sample and standard tissue sections. The concentration of a given pixel (*Cpx*) is then calculated according to Eq. (1), whereby is the reference parameter averaged across the calibration standard measurement and *rpx* the reference parameter of the respective pixel, *Ipx* the ion intensity of the isotope (*m/z*) of interest of the respective pixel, and *m* the slope of the calibration line. All these parameters are given as net

In the ideal case, when equal conditions apply for the considered pixel and the standard, the normalization factor / becomes one when the normalization reference is one single isotope and *rpx* correspond to the net ion intensity thereof. In case of TIC as normalization reference, *r* is the sum of all ion intensities, in case of EIC the sum of the selected isotopes. When the reference parameter does not enter per pixel, but is averaged throughout the sample,

*Std px*

TIC as a reference should also comply with the requirements to homogeneity and constancy in concentration throughout samples of the same type. **Figure 1** shows that after applying a TIC-based normalization strategy, the absolute element concentrations and the background noise are reinforced inversely proportional to the TIC and thus become distorted. The TIC shows a high dependence to the structure of the sample tissue because it is dominated by the

*r m* <sup>=</sup> (1)

*px*

*r I*

*px*

*C*

values after subtraction of the respective glass background.

tioned side by side into the chamber.

**3. Results**

*rpx* becomes constant ().

**Figure 1.** Normalization of 55Mn in tumorous mouse liver tissue. (A) Depicted is the original liver tissue with normal hepatocytes (*dark tissue*), blood vessels, and tumors (*bright tissue*). The not normalized image of 55Mn (B) shows higher manganese concentrations in regions containing normal tissue architecture than in the tumors and very low manganese concentrations in the blood vessels. (C) The pixelwise TIC divided by the average TIC of the calibration standard that is given in %. The higher signal in the tumor regions is due to the lower water content and therefore a higher amount of dry material in a given area of the slide. Pixelwise division of image (B) by image (C) results in the TICnormalized image of 55Mn that is depicted in (D).

For an EIC-based normalization strategy, a set of the most homogeneously distributed isotopes was chosen. These comprised carbon, magnesium, silicon, and sulfur (**Figure 3**).

**Figure 2.** Percentage contribution of isotope intensities to the TIC in liver and brain tissue and to the background signal of the glass slide. The error bars indicate the standard deviation (SD) throughout all data points of the sample.

**Figure 3.** Homogeneity of the isotope distribution in the liver and brain tissues and the glass slide. The signal-to-noise ratio is logarithmically scaled on the secondary *y*-axis with error bars representing the range of the average signal-tonoise ratio in different measurements.

Silicon originates from the partially ablated glass slide surface subjacent to the sample. In blank background areas, the signal-to-noise ratio was about one. Silicon could therefore be a good candidate as an internal standard. However, the Si signal nonlinearly depends on the geometry of laser spot, focus, and tissue laying over the glass surface. The extreme cases are subtotal ablation of the tissue and no ablation of glass and deep ablation of glass and sparkling of tissue fragments to the side. Furthermore, the most abundant Si isotopes 28Si and 29Si interfere with bi-atomic 14N2 and 14N15N. In liver and brain tissue, carbon and sulfur also show a good homogeneity with moderate signal-to-noise ratios for 13C and 34S. 33S is homogeneously distributed in both sample types, but its signal-to-noise ratio is only slightly above one, making the image of 33S in general very noisy. Although magnesium seems relatively homogeneously distributed in the liver and brain tissue and its signal-to-noise ratio is very high, it is not suitable for normalization because it cannot be assumed to be similar concentrated in samples of the same type. For this reason, all other metals were also omitted, independent from their homogeneities and signal-to-noise ratios. Former measurements also showed biologically and structurally meaningful and heterogeneous distributions of that magnesium, other metals and phosphorus. Therefore, these were considered unsuitable for normalization. In conclusion, taking into account homogeneity, signal-to-noise ratio and constancy of concentration, only silicon, carbon, and sulfur qualified for an extracted ion current.

**Figure 2.** Percentage contribution of isotope intensities to the TIC in liver and brain tissue and to the background signal of the glass slide. The error bars indicate the standard deviation (SD) throughout all data points of the sample.

404 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**Figure 3.** Homogeneity of the isotope distribution in the liver and brain tissues and the glass slide. The signal-to-noise ratio is logarithmically scaled on the secondary *y*-axis with error bars representing the range of the average signal-to-

Silicon originates from the partially ablated glass slide surface subjacent to the sample. In blank background areas, the signal-to-noise ratio was about one. Silicon could therefore be a good candidate as an internal standard. However, the Si signal nonlinearly depends on the geometry of laser spot, focus, and tissue laying over the glass surface. The extreme cases are subtotal ablation of the tissue and no ablation of glass and deep ablation of glass and sparkling of tissue fragments to the side. Furthermore, the most abundant Si isotopes 28Si and 29Si interfere with bi-atomic 14N2 and 14N15N. In liver and brain tissue, carbon and sulfur also show a good

noise ratio in different measurements.

**Figure 4.** Normalization of 55Mn in tumorous mouse liver. (A) Depicted is the non-normalized image of absolute manganese concentrations. Left images present the normalization reference images, right images the normalized manganese concentrations based on the EIC (B), 30Si (C), and 29Si (D).

**Figure 4** shows different normalization methods for 55Mn, again in comparison to the nonnormalized image (**Figure 4A**) generated from absolute concentrations. The EIC image contains the summarized intensities of 13C, 29Si, 30Si, 33S, and 34S relative to the respective sum extracted from the standard measurement. Since the EIC image (**Figure 4B**) shows slightly decreasing intensities (a signal drift) from the top to the bottom, the EIC-normalized image of 55Mn shows too low absolute concentrations in the upper half of the image. However, the lower half of the image looks similar to the not normalized image. The same effect is seen in the image of 30Si and the corresponding normalized image of 55Mn (**Figure 4C**). Since the EIC is dominated by the intensities of 30Si (see below), both methods produce similar results. Additionally, since the normalization factor (/) for 30Si was lower than for the EIC, the overall concentrations in the 30Si-normalized image were lower compared to the EIC and to the non-normalized image. The opposite effect can be seen in 29Si-based normalization (**Figure 4D**), where overcorrection of the vertical drift and overestimation of overall concentrations occurred. Additionally, the image of *m*/*z* = 29 shows slightly increased intensities over sample covered areas pointing to interferences of 29Si and 14N15N [12].

A higher contribution of 13C/16O can be excluded as in this case also at *m*/*z* = 30, a contribution of 12C/18O should be observed. The contribution of five different ion intensities (13C, 29Si, 30Si, 33S, and 34S) to the EIC is resumed in **Figure 5**.

**Figure 5.** Contribution of isotope intensities to the EIC for liver and brain tissue and the glass background. Error bars indicate the standard deviation of all pixels across the area considered.

**Figure 6** presents the results for normalization to other reference isotopes, which are also contained in the set for EIC. In comparison to the not normalized image of 55Mn (**Figure 6A**), the concentrations of the normalized images that are based on 13C (**Figure 6B**), 33S (**Figure 6C**), and 34S (**Figure 6D**) show no distortion and look much more similar than the not normalized image. This is due to the fact that the respective elements (13C, 33S, and 34S) are more homogeneously distributed and only differ in the background height and image noise.

extracted from the standard measurement. Since the EIC image (**Figure 4B**) shows slightly decreasing intensities (a signal drift) from the top to the bottom, the EIC-normalized image of 55Mn shows too low absolute concentrations in the upper half of the image. However, the lower half of the image looks similar to the not normalized image. The same effect is seen in the image of 30Si and the corresponding normalized image of 55Mn (**Figure 4C**). Since the EIC is dominated by the intensities of 30Si (see below), both methods produce similar results. Additionally, since the normalization factor (/) for 30Si was lower than for the EIC, the overall concentrations in the 30Si-normalized image were lower compared to the EIC and to the non-normalized image. The opposite effect can be seen in 29Si-based normalization (**Figure 4D**), where overcorrection of the vertical drift and overestimation of overall concentrations occurred. Additionally, the image of *m*/*z* = 29 shows slightly increased intensities over

406 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

A higher contribution of 13C/16O can be excluded as in this case also at *m*/*z* = 30, a contribution of 12C/18O should be observed. The contribution of five different ion intensities (13C, 29Si, 30Si,

**Figure 5.** Contribution of isotope intensities to the EIC for liver and brain tissue and the glass background. Error bars

**Figure 6** presents the results for normalization to other reference isotopes, which are also contained in the set for EIC. In comparison to the not normalized image of 55Mn (**Figure 6A**), the concentrations of the normalized images that are based on 13C (**Figure 6B**), 33S (**Figure 6C**), and 34S (**Figure 6D**) show no distortion and look much more similar than the not normalized image. This is due to the fact that the respective elements (13C, 33S, and 34S) are more homogeneously distributed and only differ in the background height and image noise.

sample covered areas pointing to interferences of 29Si and 14N15N [12].

33S, and 34S) to the EIC is resumed in **Figure 5**.

indicate the standard deviation of all pixels across the area considered.

**Figure 6.** Normalization of 55Mn in tumorous mouse liver tissue. (A) Depicted is the not normalized image of absolute manganese concentrations. Images on the left present the normalization reference images, the images on the right the normalized manganese concentrations based on 13C (B), 33S (C), and 34S (D) resulting from pixelwise division of image (A) by the respective left hand images.

Consequently, normalization that is based EIC of carbon and sulfur can be a useful method to obtain comparable absolute concentrations for all measurements of one specific sample type. Since 13C and 34S normally provide higher intensities than 33S, with an additionally good signalto-noise ratio (cf. **Figure 3**), normalization with only 13C or 34S is a good and easy to handle option for organic tissue. The final election for 13C or 34S depends on which element is more homogeneous in the analyzed tissue type. However, due to the lower water and therefore higher C and S content in tumor regions, Mn concentrations were underestimated there. This effect is especially obvious in the example depicted in **Figure 6D**.

The principal advantage of pixel per pixel normalization is the attenuation of signal drift and occasionally occurring line artifacts that are caused by sparkling of insufficiently adhering material fragments (**Figure 7A**–**C**) and therefore appearing at all sample related *m*/*z* in parallel or intervention by the user. Of course, drifts and artifacts cannot be overcome by a constant normalization factor (**Figure 7D**). On the other hand, pixelwise normalization introduces and multiplies noise, especially if the divisor image is not graphically smoothed (**Figure 7E**).

**Figure 7.** Image detail containing a line artifact (*dark stripe*) that occurred for all measured isotopes. (A) Depicted is the light microscopic image of the analyzed tissue sample. Exemplarily shown are the images generated for (B) 13C, (C) 24Mg (not normalized), (D) 24Mg (normalized with a constant factor based on 13C), and (E) 24Mg normalized pixel per pixel based on 13C.

In measurements of isotopes with low signal-to-noise ratios (i.e., the averaged ion intensity divided by the standard deviation in areas covered by sample/in glass background areas) or elements that are concentrated just above the detection limit, the normalization could increase the background and therefore make the evaluation of the isotope image more difficult. Here, a correct determination and subtraction of the glass background has special impact. A series of works used image analysis software for hand drawing regions of interest (ROIs) including glass background and read out of average values thereof [10].

In our studies, we used a histogram function within Excel Visual BASIC to identify background pixels and for segmentation of a background and a foreground mask. In typical measurements,

there is a discontinuous histogram showing a bimodal intensity distribution with a clear cut between the sample and background pixel populations. In the "de-spiked data," the scaling was weighted to the mid range. Most data points assigned to the sample were in the range of 50–60% of the maximum percentage ("Max%" in **Figure 8**). Background data points were in the range of 20–30% of the maximum percentage in typical images. The output of the integral of the histogram "cumulative %" allows additional control of plausibility, whether this corresponds to the visual impression of the fraction of background (**Figure 8**). In a second step, the pixels assigned to sample (foreground) by cutting the histogram are further evaluated individually. Therefore, at least one neighbored data point (i.e., left, right, above, and below) must also be greater than the threshold value, otherwise the considered data point is assigned as spike and not added to the final mask.

or intervention by the user. Of course, drifts and artifacts cannot be overcome by a constant normalization factor (**Figure 7D**). On the other hand, pixelwise normalization introduces and multiplies noise, especially if the divisor image is not graphically smoothed (**Figure 7E**).

408 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**Figure 7.** Image detail containing a line artifact (*dark stripe*) that occurred for all measured isotopes. (A) Depicted is the light microscopic image of the analyzed tissue sample. Exemplarily shown are the images generated for (B) 13C, (C) 24Mg (not normalized), (D) 24Mg (normalized with a constant factor based on 13C), and (E) 24Mg normalized pixel per

In measurements of isotopes with low signal-to-noise ratios (i.e., the averaged ion intensity divided by the standard deviation in areas covered by sample/in glass background areas) or elements that are concentrated just above the detection limit, the normalization could increase the background and therefore make the evaluation of the isotope image more difficult. Here, a correct determination and subtraction of the glass background has special impact. A series of works used image analysis software for hand drawing regions of interest (ROIs) including

In our studies, we used a histogram function within Excel Visual BASIC to identify background pixels and for segmentation of a background and a foreground mask. In typical measurements,

glass background and read out of average values thereof [10].

pixel based on 13C.

The mask should edge the sample tissue clearly and ideally exclude cracks and holes in the tissue. If a mask generation is performed based on an image with inhomogeneous distribution, many data points in the sample tissue could be falsely excluded (**Figure 9A**). In contrast to this, the resulting mask may contain many data points that do not belong to the sample tissue, but to the background noise, if the reference image for the mask generation has a low signal-tonoise ratio (**Figure 9B**). Thus, analog to the determination of the normalization factor, best results for the mask can be achieved with a homogeneous reference image and a good signalto-noise ratio (**Figure 9C**). Once the optimum area of interest is found, it is converted into a binary image, in which all background data points are colored black and assigned a value of "0.01" and all sample tissue data points are colored gray and set to "1."


**Figure 8.** Image and histogram of 13C ion intensities in mouse liver weighted to the mid range. Please note the clear separation of pixel populations from background (*blue*, 30% and below) and sample (*green*, 50% and above).

**Figure 9.** Mask generation based on different reference images. Please note the differences in the masks that were prepared with images that are based on (A) the total ion current (TIC), (B) 33S, and (C) 13C.

Thus, all background data points outside of the area of interest are divided by hundred and therefore significantly reduced. On the other hand, all sample tissue data points retain their concentration level, but the achievable contrast between sample tissue and background is much higher.

Of course, there are also some limitations in the generation of images from the measured data sets. Since the length of a formula in Excel 2007 is limited to 1000 characters [13] and a typical data set contains more than 32,000 data points, it is not useful to process every single cell position of all data points that meet the requirements. Therefore, for data compression,

matching data points are combined into blocks whose cell coordinates are stored in a twodimensional matrix. For example, in the third line of an image, data points "cells(3;5)" to "cells(3;12)" fit the conditions, then the cell coordinates are saved as "E3" and "L3" and combined to "E3:L3." One line can include several blocks if the sample tissue contains any gaps. Finally, all blocks are combined in one overall area of interest and stored as cell name reference "total\_mask." The mask is transferred to all previously applied images and stored for each specific image sheet. These masks can be selected in the "name bar" and used for further calculations, for example, the average element concentration in the area of interest. To visualize the mask for verification, sample data points (**Figure 10A**) are colored gray and background is colored black (**Figure 10B**). On this basis, the reference image is recalculated with reduced background (**Figure 10C**). Moreover, background masking is especially useful for reducing background noise in images of low contrast, such as of some trace elements (**Figure 10D**–**F**).

**Figure 10.** Creation of a foreground sample mask from the reference image. The 13C measurement shown in (A) was used to prepare the mask depicted in (B). The reference image was recalculated with reduced background (C). Low concentrated 52Cr (D) shows a higher background (E) after normalization based on (A), but significantly lower background (F) when normalized with (C) as normalization reference.

**Figure 9.** Mask generation based on different reference images. Please note the differences in the masks that were pre-

Thus, all background data points outside of the area of interest are divided by hundred and therefore significantly reduced. On the other hand, all sample tissue data points retain their concentration level, but the achievable contrast between sample tissue and background is

Of course, there are also some limitations in the generation of images from the measured data sets. Since the length of a formula in Excel 2007 is limited to 1000 characters [13] and a typical data set contains more than 32,000 data points, it is not useful to process every single cell position of all data points that meet the requirements. Therefore, for data compression,

pared with images that are based on (A) the total ion current (TIC), (B) 33S, and (C) 13C.

410 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

much higher.

Pixelwise normalization can be used as a powerful tool to minimize deviations of element concentrations due to measurement-related fluctuations. Horizontal brain sections as shown in **Figure 11** are expected to be approximately anatomically symmetrical and thus, signal drifts in the non-normalized images most likely result from insufficient washing and equilibration and also prolonged measurement times (that were here 14 h). This is of course not overcome by background subtraction and normalization with a constant factor. In contrast, pixelwise normalization reduces excessive values and increases too small intensities in relation to the reference isotope which significantly improves the image quality (**Figure 11**).

**Figure 11.** Comparison between images that were normalized using different strategies. Shown are non-normalized images (*left*), congruent to constant factor normalized images (*middle*), and pixelwise normalized images (*right*) of 13C, 23Na, and 64Zn in section derived from mouse brain. The normalization was performed on the basis of the image of 34S (*left*) and the corresponding area of interest (*middle*). The pixelwise normalization of 34S (*right*) shows the theoretical homogeneity obtained by decreasing and increasing signal-drift distorted values.
