MRI Diffusion Model Identifies High-Proliferation Rectal Carcinoma in 84 Patients

A diffusion-weighted MRI model combining two measurements from different mathematical approaches classified rectal carcinomas by Ki-67 proliferation status with an area under the receiver operating characteristic curve of 0.924 in a retrospective diagnostic-accuracy study of 84 patients. The model combined D1, derived from the varying diffusion curvature model, with ADCslow, derived from the intravoxel incoherent motion model. Logistic regression identified both measurements as independent predictors of high Ki-67 expression. At the study’s reported cutoff, the combined model had a sensitivity of 70.83% and a specificity of 97.22% for identifying the high-proliferation group. The researchers developed and internally validated the model in a single-center cohort, so its performance in other populations remains unknown.

The study population comprised 48 patients whose tumors were classified as high proliferation and 36 whose tumors were classified as low proliferation. The classification was based on postoperative immunohistochemical staining for Ki-67, with two senior pathologists blinded to the imaging results evaluating the specimens. At 400× magnification, they selected five hotspot fields for each tumor, counted positive tumor-cell nuclei and total tumor cells, and calculated the Ki-67 labeling index as the percentage of positively stained cells. Tumors with Ki-67 above 50% were placed in the high-proliferation group, while weak or moderate expression, with Ki-67 below or equal to 50%, formed the low-proliferation group. The two groups did not differ significantly in age, sex, body mass index, maximum tumor diameter or serum carcinoembryonic antigen level.

Several diffusion parameters differed between the proliferation groups. Relative to low-proliferation tumors, high-proliferation tumors had significantly higher D1 and perfusion fraction f values and significantly lower D0, conventional apparent diffusion coefficient and ADCslow values, with all reported P values below 0.05. In the multivariable logistic regression, which included baseline clinical variables and all six quantitative imaging parameters, D1 and ADCslow were the only independent imaging predictors of high Ki-67 category. The odds ratio was 9.347 per one-standard-deviation increase in D1, with a 95% confidence interval of 2.576 to 33.915 and P<0.001, and 0.228 for ADCslow, with a 95% confidence interval of 0.064 to 0.808 and P=0.022. These are associations within the analyzed cohort rather than evidence that either measurement causes tumor proliferation.

All examinations were performed on a 3.0-tesla whole-body MRI system using a 16-channel phased-array body coil. The pelvic protocol included axial two-dimensional fast spin-echo T2-weighted imaging and single-shot echo-planar diffusion-weighted imaging. The diffusion sequence sampled b-values of 0, 25, 50, 100, 150, 200, 400, 600, 800, 1,000, 1,500 and 2,000 seconds per square millimeter. Its repetition time was 4,400 milliseconds, echo time was 89.2 milliseconds, field of view was 34×34 centimeters, matrix was 128×128, slice thickness was 3 millimeters and total acquisition time was 277 seconds. The diffusion series covered the same slices as the T2-weighted images, with matching positions, thickness and gaps to reduce spatial inconsistency between the anatomical and functional acquisitions.

The investigators generated all quantitative maps from one set of multi-b-value diffusion data. Before fitting, they corrected B0-field inhomogeneity, gradient nonlinearity and eddy-current distortion. The conventional monoexponential model used a two-point calculation at b=0 and b=800 seconds per square millimeter to estimate ADC as a general measure of water mobility. The bi-exponential intravoxel incoherent motion model was fitted with ten b-values extending from 0 to 1,000 seconds per square millimeter. Its ADCslow parameter represents slow tissue-water diffusion, ADCfast represents fast pseudo-diffusion attributed to microcirculatory perfusion, and f represents the perfusion fraction. The varying diffusion curvature model was fitted with eight b-values extending to 2,000 seconds per square millimeter. D0 represents overall diffusion and is associated with cellular density, while D1 describes the rate at which apparent diffusion falls as b-value increases and is interpreted as reflecting microstructural complexity.

Voxelwise nonlinear fitting for intravoxel incoherent motion and varying diffusion curvature used a Levenberg–Marquardt optimizer, equal weighting for the included b-values, physiologically constrained initial values and parameter bounds. Convergence required a relative change in the sum of squared residuals below 1×10^-6, with a maximum of 1,000 iterations. Voxels were excluded if a parameter exceeded its bounds, optimization did not converge or the residual sum of squares was more than three times the noise variance. Failed fits represented less than 2% of tumor voxels for every parameter. The b=0 image served as the reference for rigid registration to axial T2-weighted imaging. Completed three-dimensional regions of interest were then transferred to the ADC, ADCslow, ADCfast, f, D0 and D1 maps, and mean values across each tumor volume were extracted automatically.

Two radiologists, with six and nine years of abdominal MRI experience, independently delineated the whole solid tumor in successive slices while blinded to clinical and pathological information. They excluded intratumoral cystic degeneration, coagulative necrosis, hemorrhage and dystrophic calcification, as well as adjacent normal rectal mucosa, muscularis propria, luminal gas, fecal contents and perirectal adipose tissue. Interobserver agreement was excellent for all six parameters. Intraclass correlation coefficients were 0.936 for ADC, 0.925 for ADCslow, 0.851 for ADCfast, 0.895 for f, 0.933 for D0 and 0.914 for D1. The study defined an ICC above 0.75 as excellent reliability. Mean measurements from the two readers were used in subsequent analyses, showing consistency between the assessors in this cohort but not establishing reproducibility across scanners or institutions.

Receiver operating characteristic analysis showed that D1 had an AUC of 0.857, with a 95% confidence interval of 0.764 to 0.924, for identifying high-proliferation tumors. ADCslow had an AUC of 0.832, f had an AUC of 0.802, ADC had an AUC of 0.780 and D0 had an AUC of 0.696. ADCfast produced an AUC of 0.569 and did not differ significantly between the groups, with P=0.205. The combined D1-plus-ADCslow model had an AUC of 0.924, with a 95% confidence interval of 0.845 to 0.971. DeLong comparisons found that its AUC was significantly higher than those of ADC, ADCslow, f, D0 and D1 individually, with all reported P values below 0.05. The combined model’s reported cutoff was 0.793, accompanied by 70.83% sensitivity and 97.22% specificity.

Internal validation with 1,000 bootstrap resamples produced an AUC of 0.917, with a 95% confidence interval of 0.904 to 0.923, and calibration analysis showed agreement between predicted and observed probabilities. The authors described these results as supporting the stability and reliability of the model within the available data. The conventional ADC result was consistent with restricted water movement in high-proliferation tumors, whose densely packed cells and reduced extracellular space can limit diffusion. ADCslow showed a stronger discriminatory result in this cohort, consistent with its design to estimate tissue diffusion while reducing the influence of microvascular perfusion. The higher f value among high-proliferation tumors was interpreted as potentially reflecting greater microvascular perfusion, whereas ADCfast did not distinguish the groups. The investigators noted that ADCfast can be less stable because of respiratory motion and intestinal-gas artifacts in pelvic imaging, although that limitation was not directly measured as a source of error in this analysis.

The interpretation of D1 remains less established. In the varying diffusion curvature framework, D1 characterizes the curvature of apparent diffusion across b-values rather than a single diffusion coefficient. The high-proliferation group’s higher D1 and lower D0 pattern was associated by the authors with denser cellular arrangement and more complex tumor microstructure, but the exact biological meaning of these parameters in rectal carcinoma requires further pathological and molecular study. The study has several constraints: it was retrospective, single-center and limited to 84 analyzed patients from 137 initially screened; the high-proliferation group was larger; and all diffusion data were acquired with single-shot echo-planar imaging, which may introduce distortion for some lesions. Varying diffusion curvature also has a shorter clinical evidence history than conventional DWI. These results therefore establish a promising within-cohort diagnostic signal, not a clinical benefit, and the model requires evaluation in larger independent multicenter cohorts before its performance and practical application can be determined.

Subject of Research: Diffusion MRI models for assessing Ki-67-defined proliferation in rectal carcinoma

Article Title: Varying diffusion curvature, intravoxel incoherent motion, and conventional monoexponential diffusion models for evaluating Ki-67 expression in rectal carcinoma

Article References: Cui, Y., Yin, H., Wang, Y., Liu, Y., Wu, Y., Bai, Y., Li, H., Jiang, B., Meng, N., & Yu, X. (2026). Varying diffusion curvature, intravoxel incoherent motion, and conventional monoexponential diffusion models for evaluating Ki-67 expression in rectal carcinoma. Frontiers in Oncology, 16, Article 1935475. https://doi.org/10.3389/fonc.2026.1935475

Image Credits: AI Generated

DOI: 10.3389/fonc.2026.1935475

Keywords: rectal carcinoma, Ki-67, diffusion MRI, varying diffusion curvature, intravoxel incoherent motion, DWI, tumor proliferation, diagnostic accuracy, Varying, diffusion, curvature, intravoxel