Fractal analysis improves tumour size measurement on computed tomography in pancreatic ductal adenocarcinoma: comparison with gross pathology and multi-parametric MRI

A retrospective study was performed after obtaining approval from the institutional review board (IRB number 00012157) and written informed consent was waived. Clinical routine data were analysed and patients with histologically proven PDA either from surgery or biopsy were included if CT and MRI datasets acquired within 1 week at the time of diagnosis were available.

CT imaging was performed in a single-centre, single-scanner (64 rows, Optima CT660, GE Healthcare) setting. Scanning parameters were as follows: helical scan mode with tube voltage of 120 kV and tube current of 140 mAs, 0.8-s gantry rotation time, pitch factor of 1.375, and 64 × 0.675 mm collimation. Images were reconstructed on 512 × 512 pixel image matrices with resolution on the order of 0.7 mm × 0.7 mm × 1.25 mm and 1.25-mm increment using a soft tissue convolution kernel. CT was performed in a non-enhanced phase and after intravenous administration of a non-ionic iodine-based contrast agent (iodine concentration of 300 mg/mL, iopromide, dose of 1.5 mL/kg injected at a rate of 3.5 to 4 mL/s, followed by a 40 mL saline flush at 3 mL/s). The scanning delay for pancreatic parenchymal phase imaging was determined by using a bolus-tracking technique with automated scan-triggering software (SmartPrep; GE Healthcare). Acquisition of the pancreatic parenchymal and hepatic venous phases was started automatically at 17 and 50 s, respectively, after the trigger threshold (100 HU) was reached at the level of the supracoeliac abdominal aorta [22].

All MRI examinations were performed on a single scanner (3 T, Discovery MR 750, GE Healthcare) using body phased array coils. The patients were imaged after an overnight fast. The following pulse sequences were obtained: 2D T2-weighted fat-saturation (FS) fast-recovery fast spin echo (FRFSE); pre-contrast 3D T1-weighted gradient echo (GRE); 3D T1-weighted FS dynamic GRE sequences in the arterial phase (25 s), portal phase (70 s), and delayed phase (3 and 5 min) after gadolinium-based contrast agent injection; and diffusion-weighted imaging (DWI) sequences (three directions, b0 combined with different gradients from the following set 50, 200, 400, 600, and 800 s/mm²). The contrast agent was either gadoteric acid (Dotarem, Guerbet) at a dose of 0.2 mL/kg or gadobutrol (Gadovist, Bayer Schering Pharma) at a dose of 0.1 mL/kg, injected at a flow rate of 2 mL/s and followed by a saline flush (40 mL at 2 mL/s). Apparent diffusion coefficient (ADC) maps were generated using a post-processing console (Advantage Windows) with a monoexponential decay model.

The first author developed the fractal analysis software in Python 3.6, which implements the pre-processing pipeline including image registration and image standardisation as well as fractal analysis and segmentation. The CT imaging data were processed as follows. First, image registration was performed with the SimpleElastix framework, version 4.9 (https://​simpleelastix.​github.​io/​, Kasper Marstal) employing a standard combination of 3D affine and 3D b-spline transformations. Second, images were standardised for voxel size, image noise, and signal intensity. All images were resampled to an isotropic voxel spacing of 0.7 mm as a common denominator. To standardise image noise, a noise-level-adapted denoising scheme was employed consisting of a 3D median filter with a radius set to 2 pixels and a 3D bilateral filter [23], whose distance parameter was set to 1 pixel and range parameter defined according to image noise determined from a region of interest (ROI) placed in the spinal erector muscles. For intensity standardisation, the signal was standardised using the portal-venous signal intensity at each time point as follows. We measured unenhanced portal-venous signal (I₀) and related each voxel’s signal (I_voxel) in the contrast-enhanced phases to the respective portal vein signal intensity (I_pv) to obtain a normalised signal as follows: I = (I_voxel − I₀) / (I_pv − I₀) × 100. This was done to standardise image intensity by a physiological reference, thereby accounting for potential differences in circulation and mitigating the issue of potential variation in timing image acquisition. After pre-processing, four-dimensional, local A fractal analysis was performed to generate maps of the local FD. A previously published method [24] was used and extended to 4D to integrate information from the unenhanced, pancreatic parenchymal and portal-venous phases of perfusion. This method moulds two “blankets” to image texture, one upper blanket and one lower blanket. The blankets are iteratively raised or, respectively, lowered from the original texture to evaluate fractal properties as a function of loss of detail. Fractal analysis yields FD as a quantitative parameter of geometrical complexity, or chaos, and takes fractional values between 4 and 5 in the four-dimensional application. For local fractal analysis, we evaluated each voxel’s immediate vicinity, i.e., its direct neighbours. Local FD maps were calculated for visualisation and segmentation. In addition to local fractal analysis, we performed 4D global fractal analysis by evaluating larger, anatomically coherent regions, i.e., tumour core, tumour rim, and remote pancreas. Unlike its local variant, global fractal analysis does not yield a local FD map, rather it yields a single FD scalar value for the whole ROI. Global FD was interpreted as an explainable measure of the global chaos of the perfusion pattern. Mathematical details of global fractal analysis have been described previously [25].

To characterise the patient cohort, tumour diameter was conventionally measured on CT using the revised RECIST recommendations [26], which reflects pre-operative size measurement in clinical practice. For further analysis, the tumours were volumetrically segmented by the first author (experience in abdominal CT: 6 years) using a freehand drawing tool and subjected to a consensus reading (senior authors, experience in abdominal CT: > 20 years) on CT, FD maps, and MRI. On CT, the visible tumour portion (usually the hypoperfused tumour core) was segmented using the phase with the best visual conspicuity, incorporating information from both contrast-enhanced phases. We performed image fusion of FD maps and CT images to ensure correct anatomical positioning when using local FD maps for size measurement. Segmentation was performed using FD discrepancies between tumour and adjacent pancreatic tissue. In MRI, we used DWI at the highest b-value (i.e., 800 s/mm² in our study) and T2-weighted images for volumetric tumour segmentation and T1-weighted fat-saturated contrast-enhanced images to visually assess conspicuity [9]. Voxel spacing on DWI ranged between 1 and 1.6 mm in-plane and 5 mm in z-direction, which yields a precision of at least 1.6 mm × 1.6 mm × 5 mm = 12.8 mm³ = 0.128 mL. From tumour segmentations, volume and maximum diameter were calculated [27]. The maximum diameter, which was subjected to statistical analysis, is given in terms of Feret’s diameter, which represents the maximum tumour extent independently of spatial alignment or axis orientation. As such, it is a robust and objective method of diameter quantification, suffering less from inter-observer variability than conventional diameter measurement according to RECIST recommendations [27‐30]. The largest tumour diameter on gross pathology examination served as the reference standard, where available, and was analysed in an initial discovery cohort. The findings in the discovery cohort were independently validated in the remaining patients as a separate cohort with intermodal size estimation comparisons.

In the discovery cohort with gross pathology reference, diameter measurements were tested for linear correlation of CT, mpMRI, and fractal analysis with pathology ground truth. Differences in size estimation between each method and the reference standard were evaluated using the pairwise Wilcoxon rank sum test for paired samples and Bonferroni correction for multiple testing. In the validation cohort with mpMRI as reference, CT and fractal analysis measurements of tumour volume and diameter were evaluated for linear correlation with mpMRI as reference. Furthermore, the t-test was used to assess measurement differences per method. Bland-Altman statistics were calculated to evaluate systematic size measurement differences for each method, and the f-test was performed to evaluate variances of the differences. In a subpopulation of 20 cases, we assessed inter-reader agreement (two readers with 6 and > 15 years of experience in abdominal imaging) in terms of relative size measurement discrepancy (in %) and Spearman’s ρ. To test whether fractal analysis is capable of identifying the tumour rim, local chaos per anatomical region (i.e., tumour core, tumour rim, and adjacent non-tumourous pancreas) was analysed using descriptive statistics as well as the Kruskal-Wallis test and pairwise group comparisons using the Mann-Whitney U-test with Bonferroni correction to test for perfusion chaos differences between those anatomical sites. A level of p ≤ 0.05 (after Bonferroni correction where appropriate) was considered statistically significant. Statistical analysis was performed with R (v3.4.1; R Foundation for Statistical Computing).

A total of 46 patients were retrospectively included. The median diameter of all included tumours was 40 mm (range: 18–82 mm). Tumour characteristics and imaging findings are summarised in Table 1. Image processing and fractal analysis were successful in all patients and took about 20 min per patient including registration (5 min), image processing including local and global fractal dimension calculation (1 min), and manual multimodal segmentation with volumetry and diameter measurement (CT: 5 min, FD map: 3 min, mpMRI: 5–10 min).

Our initial discovery cohort consisted of 10 patients, in which diameter measurements on gross pathology were available as reference standard. Both mpMRI and FD size estimates correlated well with gross pathology measurements (mpMRI: R² = 0.96; FD: R² = 0.92) and did not show significant diameter differences (mpMRI: Δdiameter = 0.9 mm, p = 0.32; FD: Δdiameter = −0.6 mm, p = 1.0). Moreover, measurements on FD maps correlated excellently to mpMRI (R² = 0.88) without significant differences between those methods (p = 0.63). In contrast, CT measurements systematically underestimated tumour diameter in comparison to gross pathology (Δdiameter = 5.7 mm, p = 0.03). A representative example with correlation to gross pathology is depicted in Figure 1 alongside a boxplot to summarise diameter differences measured on each modality to pathological reference. Detailed statistics for the discovery cohort are summarised in Table 2.

Since pathological reference was not available in our validation cohort (n = 36), we used mpMRI as surrogate due to its excellent correlation with gross pathology measurements as demonstrated in the initial discovery cohort. Tumour volume on FD maps correlated well with mpMRI volumetry (Δvolume = −0.6 mL, p = 0.86) and showed no size-dependent variation (p = 0.77). In contrast, tumour volume was consistently underestimated on CT in comparison to mpMRI (Δvolume = 10.2 mL, p < 0.001) with the amount of underestimation increasing with absolute tumour size (p = 0.01).

For diameter measurements, FD-derived maximum tumour diameters agreed well with MRI reference (Δdiameter = 1.5 mm, p = 0.63), while maximum tumour diameters were consistently underestimated on CT (Δdiameter = 10.6 mm, p < 0.001). None of the diameter measurement methods showed an evident dependence on the actual tumour diameter (FD: p = 0.84, CT: p = 0.95). In a subgroup of 20 PDA lesions, inter-reader agreement was excellent both for diameter measurement (mpMRI—median diameter discrepancy: 3.9%, interquartile range [IQR]: 10.8%, Spearman’s ρ = 0.99; FD—median diameter discrepancy: 0.1%, IQR: 10.8%, ρ = 0.96; CT—median diameter discrepancy: 4.8%, IQR: 12.4%, ρ = 0.92) and for volume measurement (mpMRI—median volume discrepancy: 1.1%, IQR: 9.1%, ρ = 0.99; FD—median volume discrepancy: 4.5%, IQR: 6.5%, ρ = 0.99; CT—median volume discrepancy: 4.4%, IQR: 27.3%, ρ = 0.98). Detailed statistics on correlation and bias of the methods, including Bland-Altman plots, can be found in Figure 2 and Table 3. Two representative cases are presented in Figures 3 and 4.

To test the pathophysiological hypothesis of high perfusion chaos in the tumour rim, we performed an additional global fractal analysis of the tumour rim, the tumour core, and adjacent pancreatic tissue (Figure 5). In contrast to the local FD maps as reported above, the global FD yields a scalar value, which quantitatively summarises the overall chaos in a ROI. The global FD was significantly (p ≤ 0.003) higher in the tumour rim (global FD_rim = 4.43, [quartiles: 4.38–4.49]) than in the tumour core (global FD_core = 4.37 [quartiles: 4.33–4.43]), and both were higher than the FD in remote pancreas tissue (global FD_pancreas = 4.28 [quartiles: 4.19–4.35]); i.e., perfusion was highly chaotic in the tumour rim, less chaotic in the tumour core, and least chaotic in remote pancreas tissue (Figure 5). Interestingly, CT was hardly, if ever, capable of depicting the tumour rim visually, which is evident from measured tumour volumes and diameters.