# Simultaneous assessment of lung morphology and respiratory motion in retrospectively gated in-vivo microCT of free breathing anesthetized mice

Cinematic X-ray imaging has already successfully been used to quantify breathing motion. The breathing changes the expansion state and the air content of the lung, which in turn modulates the X-ray attenuation and can therefore be detected as a change in the intensity of the lung region over time12.

### Principle

To enable quantification of the respiratory motion this information needs to be extracted from the acquired projection images. To this end the average brightness in a user-defined rectangular region over the lung-diaphragm interface is analyzed as indicated in red in Fig. 1D. Breathing modulates the position of the diaphragm and the expansion state of the chest both resulting in a change in the average X-ray transmission over time $$U(\alpha )$$ (blue-curve, Fig. 1A). However, the angular projection of the mouse anatomy as well as the modulation of the X-ray tube intensity caused by the electronics contribute more strongly to the obtained X-ray attenuation function than the breathing as evidenced by the large baseline of obtained function (blue) in both the polar and linear plot Fig. 1A,B. To remove this unwanted effects we exploited the facts that the data should be periodic in 360$$^\circ$$ and that the anatomy of the mouse is mostly reflected in the first K frequencies of the Fourier transformation of the signal. However, the insert in Fig. 1A shows that the modulation of the intensity of the X-ray tube yielded in a non-2pi-periodic function. We therefore extended the function by adding its mirrored version, which then always results in a periodic function in 4pi. Thus, we reconstructed the background signal by inverse Fourier transformation of the first K frequencies and subtracted the results from the original data, resulting in the red trace Fig. 1A, which is also shown in a linear plot in Fig. 1B. (Note: for the demonstrated example $$K = 20$$ was used). It can be seen in Fig. 1A,B (red curves) that the breathing peaks are now well defined. To further suppress potential imprecision in the background correction at the beginning and end of the acquisition, the angular ranges from 0–90$$^\circ$$ to 630–720$$^\circ$$ are discarded as indicated by the black dashed vertical lines in Fig. 1B. The amplitude of the remaining angular range was scaled between 0 and 1 and a level of 0.3 was used to detect breathing events (horizontal black line in Fig. 1. Example projection images are illustrated in Fig. 1C at angles of 0, 90, 180 and 270$$^\circ$$. The normalized power spectra shown in Fig. 1D demonstrate that once the strong contributions of shape of the mouse (blue, beginning of the spectrum) is removed the breathing events and their harmonics (asterisks) can clearly be observed. Moreover, in the filtered spectrum (red) a peak at approximately 470 bpm is visible Fig. 1D (§) depicting the heart rate of the mouse Fig. 1D. This trace is used for both deriving functional parameter and sorting the projection images to perform RG CT reconstruction.

### X-ray dose measurements

A commercial X-ray dose measurement system was used to measure the dose length product for several acquisition protocols as summarized in Table 3. Wrapping the probe with a 1 cm layer of pork to mimic scattering processes in the mouse did not affect the readings substantially. Note, that the standard CT acquisition protocol of 17 s, includes ramping up the tube voltage for 2 s resulting in a total exposure time of 19 s. Therefore, our acquisition protocol for rgXLF using a tube voltage of 90 kV, a current of 100 $$\upmu$$A, a field-of-view (FOV) of 20x20 $$\hbox {mm}^2$$ and an acquisition time of 34 s results in a dose of approximately 37 mGy. Whereas the planar XLF measurement performed with the same parameters apart from the tube current of 40 $$\upmu$$A and a total acquisition time of 30 s, results in a total X-ray dose of approximately 13 mGy.

### Parametrization of the breathing pattern

In order to parameterize the obtained breathing pattern we applied the same strategy described by Khan et al.11. In short, a level function at 30% of the relative X-ray attenuation signal was used to identify single breathing events. The start of the inspiration phase was defined as point with the highest curvature prior each breathing peak. The expiration phase is defined as as descending part of the curve from the peak till the start of the next breathing event is reached. Although, several parameters can be calculated for each individual event11 in this study we focused on the parameter k of a function $$f(t) = I_{0}\exp (-k \times t^{2})+c$$ fitted to the expiration phase and of the heart rate measured in Fourier space. Since, the underlying lung motion is more complex the used function presents a simplification. The magnitude of the movement of the lung tissue increases towards the position of the diaphragm, thus size and placement of the region affects the calculated k-value as shown in Supplemental Fig. 1A. Therefore, similar regions should be used for comparison of the bulk motion of the lung between different subjects. To increase the robustness fit and to account for the noise and limited temporal resolution of the data, the data of all measured expiration phases are overlaid (Supplemental Fig. 1B).

### Validation of the RG based respiratory motion measurements in the mdx mouse model

To evaluate the accuracy of rgXLF we compared it to the established planar XLF method performed subsequently in the same mdx mice and wild type controls (wt) applying the same analysis pipeline described above. Figure 2A,B demonstrates that in both methods the k-value of the expiration phase as well as the heart rate showed similar results (Pearson correlation coefficient of 0.92 for the k-value and heart rate). Moreover, both methods allowed to successfully discriminate mdx from wt mice (Mann-Whitney U = 0 for both k-value and heart rate) and revealed an elevated k-value and heart rate in mdx. Note, that XLF and rgXLF have been performed subsequently. Due to the variations of the breathing rates of 15% on average between the measurements a perfect correlation can not be expected.

### Retrospectively gated CT reconstruction

The data derived breathing curves (exemplary shown in Fig. 1B) were used to sort the angular projections acquired over 720$$^\circ$$ rotation into two bins: (i) inspiration and (ii) expiration. Since the inspiration phases are very short, only a few projections are recorded. Thus, only predominately the expiration phase was 3D reconstructed. To this end we used the following scheme. Since, each projection angle between 0 and 360$$^\circ$$ has been acquired twice we generate a new data set over 360$$^\circ$$ taking either the corresponding projection from the first or from the second rotation depending on which showed the lowest value in the calculated breathing curve. If both projections in the first and second rotation had a value below 0.1 the average of both frames was used. In addition, the amount of angles at which no frame was found to have a value of less then 0.3 was reported as a measure of the reliability of the approach. Since we applied a standard filtered back projection algorithm for 3D reconstruction, which requires a set of equally distributed angular projections, only in cases in which the breathing events do not largely overlap between the 1st and 2nd rotation, we achieved reconstructions with a sharper delineation of the lung and the absence of motion artifacts as shown in Fig. 3B in contrast to the reconstruction demonstrated in Fig. 3A obtained without applying RG. Averaging the two frames at the same angle, if both belong to the expiration phase, reduced the noise level and therefore further improved the image quality. This is helpful if the lung needs to be segmented for subsequent analysis as demonstrated in Fig. 3C.

### Combined functional and anatomical characterization of the mdx mouse model

The use of our improved RG approach allows to simultaneously quantify anatomical and functional differences in the mdx mice compared to their wild type controls. In Fig. 4 representative cross-sections, lungs segmented in 3D and parts of the isolated breathing events are shown for one wild type control Fig. 4A,B and a mdx mouse Fig. 4C,D. For segmenting the lung envelope a simple threshold based segmentation followed by manual removal of the air outside the mouse was used. As threshold the arithmetic average between the mean grey values of the lung region and soft-tissue was employed. Already the cross-sections Fig. 4A,C demonstrate that the shape and position of the diaphragm is dramatically different between the mdx and the control mouse. This is further demonstrated in the 3D renderings of the segmented lungs. In mdx post-caval lung lobe appears enlarged and elongated towards the abdomen. Additionally, the lumen of the airways is increased in the mdx animal (Fig. 4B,D). Figure 4E show the traces of the breathing events extracted from the raw-data sets of the CT acquisitions according to the principle described above. Clearly, a more rapid decay (larger k-value) was evidenced in mdx mice (red) compared to healthy controls (blue). In addition, the high frequency modulations of the traces represent the heart beat.