Progressive disease in glioblastoma: Benefits and limitations of semi-automated volumetry

Preoperative nTMS analysis: a sensitive tool to detect imminent motor deficits in brain tumor patients

BACKGROUND

One of the challenges in surgery of tumors in motor eloquent areas is the individual risk assessment for postoperative motor disorder. Previously a regression model was developed that permits estimation of the risk prior to surgery based on topographical and neurophysiological data derived from investigation with nTMS (navigated Transcranial Magnetic Stimulation). This study aims to analyze the impact of including additional neurophysiological TMS parameters into the established risk stratification model for motor outcome after brain tumor surgery.

METHODS

Biometric and clinical data of 170 patients with glioma in motor eloquent areas were collected prospectively. In addition, the following nTMS parameters were collected bihemispherically prior to surgery: resting motor threshold (RMT), recruitment curve (RC), cortical silent period (CSP) and a nTMS based fibertracking to measure the tumor tract distance (TTD). Motor function was quantified by Medical Research Council Scale (MRCS) preoperatively, seven days and three months postoperatively. Association between nTMS parameters and postoperative motor outcome was investigated in bivariate and multivariable analyses.

RESULTS

The bivariate analysis confirmed the association of RMT ratio with the postoperative motor outcome after seven days with higher rates of worsening in patients with RMT ratio > 1.1 compared to patients with RMT ratio ≤ 1.1 (31.6% vs. 15.1%, p = 0.009). Similarly, an association between a pathological CSP ratio and a higher risk of new postoperative motor deficits after seven days was observed (35.3% vs. 16.7% worsening, p = 0.025). A pathological RC Ratio was associated postoperative deterioration of motor function after three months (42.9% vs. 16.2% worsening, p = 0.004). In multiple regression analysis, none of these associations were statistically robust.

CONCLUSIONS

The current results suggest that the RC ratio, CSP ratio and RMT ratio individually are sensitive markers associated with the motor outcome 7 days and 3 months after tumor resection in a presumed motor eloquent location. They can therefore supply valuable information during preoperative risk-benefit-balancing. However, underlying neurophysiological mechanisms might be too similar to make the parameters meaningful in a combined model.

Prognostic and predictive impact of abnormal signal volume evolution early after chemoradiotherapy in glioblastoma

INTRODUCTION

This study was designed to explore the feasibility of semiautomatic measurement of abnormal signal volume (ASV) in glioblastoma (GBM) patients, and the predictive value of ASV evolution for the survival prognosis after chemoradiotherapy (CRT).

METHODS

This retrospective trial included 110 consecutive patients with GBM. MRI metrics, including the orthogonal diameter (OD) of the abnormal signal lesions, the pre-radiation enhancement volume (PRRCE), the volume change rate of enhancement (rCE), and fluid attenuated inversion recovery (rFLAIR) before and after CRT were analyzed. Semi-automatic measurements of ASV were done through the Slicer software.

RESULTS

In logistic regression analysis, age (HR = 2.185, p = 0.012), PRRCE (HR = 0.373, p < 0.001), post CE volume (HR = 4.261, p = 0.001), rCE_1m (HR = 0.519, p = 0.046) were the significant independent predictors of short overall survival (OS) (< 15.43 months). The areas under the receiver operating characteristic curve (AUCs) for predicting short OS with rFLAIR_3m and rCE_1m were 0.646 and 0.771, respectively. The AUCs of Model 1 (clinical), Model 2 (clinical + conventional MRI), Model 3 (volume parameters), Model 4 (volume parameters + conventional MRI), and Model 5 (clinical + conventional MRI + volume parameters) for predicting short OS were 0.690, 0.723, 0.877, 0.879, 0.898, respectively.

CONCLUSION

Semi-automatic measurement of ASV in GBM patients is feasible. The early evolution of ASV after CRT was beneficial in improving the survival evaluation after CRT. The efficacy of rCE_1m was better than that of rFLAIR_3m in this evaluation.

Ellipsoid calculations versus manual tumor delineations for glioblastoma tumor volume evaluation

In glioblastoma, the response to treatment assessment is essentially based on the 2D tumor size evolution but remains disputable. Volumetric approaches were evaluated for a more accurate estimation of tumor size. This study included 57 patients and compared two volume measurement methods to determine the size of different glioblastoma regions of interest: the contrast-enhancing area, the necrotic area, the gross target volume and the volume of the edema area. The two methods, the ellipsoid formula (the calculated method) and the manual delineation (the measured method) showed a high correlation to determine glioblastoma volume and a high agreement to classify patients assessment response to treatment according to RANO criteria. This study revealed that calculated and measured methods could be used in clinical practice to estimate glioblastoma volume size and to evaluate tumor size evolution.

Intraoperative integration of multimodal imaging to improve neuronavigation: a technical note

BACKGROUND

Brain shift may cause significant error in neuronavigation leading the surgeon to possible mistakes. Intraoperative MRI is the most reliable technique in brain tumor surgery. Unfortunately, it is highly expensive and time consuming and, at the moment, it is available only in few neurosurgical centers.

METHODS

In this case series the surgical workflow for brain tumor surgery is described where neuronavigation of pre-operative MRI, intraoperative CT scan and US as well as rigid and elastic image fusion between preoperative MRI and intraoperative US and CT, respectively, was applied to four brain tumor patients in order to compensate for surgical induced brain shift by using a commercially available software (Elements Image Fusion 4.0 with Virtual iMRI Cranial; Brainlab AG).

RESULTS

Three exemplificative cases demonstrated successful integration of different components of the described intraoperative surgical workflow. The data indicates that intraoperative navigation update is feasible by applying intraoperative 3D US and CT scanning as well as rigid and elastic image fusion applied depending on the degree of observed brain shift.

CONCLUSIONS

Integration of multiple intraoperative imaging techniques combined with rigid and elastic image fusion of preoperative MRI may reduce the risk of incorrect neuronavigation during brain tumor resection. Further studies are needed to confirm the present findings in a larger population.

Modeling Healthy Anatomy with Artificial Intelligence for Unsupervised Anomaly Detection in Brain MRI

PURPOSE

To develop an unsupervised deep learning model on MR images of normal brain anatomy to automatically detect deviations indicative of pathologic states on abnormal MR images.

MATERIALS AND METHODS

In this retrospective study, spatial autoencoders with skip-connections (which can learn to compress and reconstruct data) were leveraged to learn the normal variability of the brain from MR scans of healthy individuals. A total of 100 normal, in-house MR scans were used for training. Subsequently, as the model was unable to reconstruct anomalies well, this characteristic was exploited for detecting and delineating various diseases by computing the difference between the input data and their reconstruction. The unsupervised model was compared with a supervised U-Net- and threshold-based classifier trained on data from 50 patients with multiple sclerosis (in-house dataset) and 50 patients from The Cancer Imaging Archive. Both the unsupervised and supervised U-Net models were tested on five different datasets containing MR images of microangiopathy, glioblastoma, and multiple sclerosis. Precision-recall statistics and derivations thereof (mean area under the precision-recall curve, Dice score) were used to quantify lesion detection and segmentation performance.

RESULTS

The unsupervised approach outperformed the naive thresholding approach in lesion detection (mean F1 scores ranging from 17% to 62% vs 6.4% to 15% across the five different datasets) and performed similarly to the supervised U-Net (20%-64%) across a variety of pathologic conditions. This outperformance was mostly driven by improved precision compared with the thresholding approach (mean precisions, 15%-59% vs 3.4%-10%). The model was also developed to create an anomaly heatmap display.

CONCLUSION

The unsupervised deep learning model was able to automatically detect anomalies on brain MR images with high performance. Supplemental material is available for this article. Keywords: Brain/Brain Stem Computer Aided Diagnosis (CAD), Convolutional Neural Network (CNN), Experimental Investigations, Head/Neck, MR-Imaging, Quantification, Segmentation, Stacked Auto-Encoders, Technology Assessment, Tissue Characterization © RSNA, 2021.

Subtraction Maps Derived from Longitudinal Magnetic Resonance Imaging in Patients with Glioma Facilitate Early Detection of Tumor Progression

Progression of glioma is frequently characterized by increases or enhanced spread of a hyperintensity in fluid attenuated inversion recovery (FLAIR) sequences. However, changes in FLAIR signal over time can be subtle, and conventional (CONV) visual reading is time-consuming. The purpose of this monocentric, retrospective study was to compare CONV reading to reading of subtraction maps (SMs) for serial FLAIR imaging. FLAIR datasets of cranial 3-Tesla magnetic resonance imaging (MRI), acquired at two different time points (mean inter-scan interval: 5.4 ± 1.9 months), were considered per patient in a consecutive series of 100 patients (mean age: 49.0 ± 13.7 years) diagnosed with glioma (19 glioma World Health Organization [WHO] grade I and II, 81 glioma WHO grade III and IV). Two readers (R1 and R2) performed CONV and SM reading by assessing overall image quality and artifacts, alterations in tumor-associated FLAIR signal over time (stable/unchanged or progressive) including diagnostic confidence (1-very high to 5-very low diagnostic confidence), and time needed for reading. Gold-standard (GS) reading, including all available clinical and imaging information, was performed by a senior reader, revealing progressive FLAIR signal in 61 patients (tumor progression or recurrence in 38 patients, pseudoprogression in 10 patients, and unclear in the remaining 13 patients). SM reading used an officially certified and commercially available algorithm performing semi-automatic coregistration, intensity normalization, and color-coding to generate individual SMs. The approach of SM reading revealed FLAIR signal increases in a larger proportion of patients according to evaluations of both readers (R1: 61 patients/R2: 60 patients identified with FLAIR signal increase vs. R1: 45 patients/R2: 44 patients for CONV reading) with significantly higher diagnostic confidence (R1: 1.29 ± 0.48, R2: 1.26 ± 0.44 vs. R1: 1.73 ± 0.80, R2: 1.82 ± 0.85; p < 0.0001). This resulted in increased sensitivity (99.9% vs. 73.3%) with maintained high specificity (98.1% vs. 98.8%) for SM reading when compared to CONV reading. Furthermore, the time needed for SM reading was significantly lower compared to CONV assessments (p < 0.0001). In conclusion, SM reading may improve diagnostic accuracy and sensitivity while reducing reading time, thus potentially enabling earlier detection of disease progression.

How Reliable Are Volumetric Techniques for High-Grade Gliomas? A Comparison Study of Different Available Tools

BACKGROUND

Gliomas are the most common malignant primary brain tumors. Assessment of the tumor volume represents a crucial point in preoperative and postoperative evaluation.

OBJECTIVE

To compare pre- and postoperative tumor volumes obtained with an automated, semi-automatic, and manual segmentation tool. Mean processing time of each segmentation techniques was measured.

METHODS

Manual segmentation was performed on preoperative and postoperative magnetic resonance images with the open-source software Horos (Horos Project). "SmartBrush," a tool of the IPlan Cranial software (Brainlab, Feldkirchen, Germany), was used to carry out the semi-automatic segmentation. The open-source BraTumIA software (NeuroImaging Tools and Resources Collaboratory) was employed for the automated segmentation. Pearson correlation coefficient was used to assess volumetric comparison. Subsequently deviation/range and average discrepancy were determined. The Wilcoxon signed-rank test was used to assess statistical significance.

RESULTS

A total of 58 patients with a newly diagnosed high-grade glioma were enrolled. The comparison of the volumes calculated with Horos and IPlan showed a strong agreement both on preoperative and postoperative images (respectively: "enhancing" ρ = 0.99-0.78, "fluid-attenuated inversion recovery" ρ = 0.97-0.92, and "total tumor volume" ρ = 0.98-0.95). Agreement between BraTumIA and the other 2 techniques appeared to be strong for preoperative images, but showed a higher disagreement on postoperative images. Mean time expenditure for tumor segmentation was 27 min with manual segmentation, 17 min with semi-automated, and 8 min with automated software.

CONCLUSION

The considered segmentation tools showed high agreement in preoperative volumetric assessment. Both manual and semi-automated software appear adequate for the postoperative quantification of residual volume. The evaluated automated software is not yet reliable. Automated software considerably reduces the time expenditure.

Divide and Conquer: Stratifying Training Data by Tumor Grade Improves Deep Learning-Based Brain Tumor Segmentation

It is a general assumption in deep learning that more training data leads to better performance, and that models will learn to generalize well across heterogeneous input data as long as that variety is represented in the training set. Segmentation of brain tumors is a well-investigated topic in medical image computing, owing primarily to the availability of a large publicly-available dataset arising from the long-running yearly Multimodal Brain Tumor Segmentation (BraTS) challenge. Research efforts and publications addressing this dataset focus predominantly on technical improvements of model architectures and less on properties of the underlying data. Using the dataset and the method ranked third in the BraTS 2018 challenge, we performed experiments to examine the impact of tumor type on segmentation performance. We propose to stratify the training dataset into high-grade glioma (HGG) and low-grade glioma (LGG) subjects and train two separate models. Although we observed only minor gains in overall mean dice scores by this stratification, examining case-wise rankings of individual subjects revealed statistically significant improvements. Compared to a baseline model trained on both HGG and LGG cases, two separately trained models led to better performance in 64.9% of cases (p < 0.0001) for the tumor core. An analysis of subjects which did not profit from stratified training revealed that cases were missegmented which had poor image quality, or which presented clinically particularly challenging cases (e.g., underrepresented subtypes such as IDH1-mutant tumors), underlining the importance of such latent variables in the context of tumor segmentation. In summary, we found that segmentation models trained on the BraTS 2018 dataset, stratified according to tumor type, lead to a significant increase in segmentation performance. Furthermore, we demonstrated that this gain in segmentation performance is evident in the case-wise ranking of individual subjects but not in summary statistics. We conclude that it may be useful to consider the segmentation of brain tumors of different types or grades as separate tasks, rather than developing one tool to segment them all. Consequently, making this information available for the test data should be considered, potentially leading to a more clinically relevant BraTS competition.

Comparison of Radiographic Approaches to Assess Treatment Response in Pituitary Adenomas: Is RECIST or RANO Good Enough?

Context

Pituitary adenomas (PA) are often irregularly shaped, particularly posttreatment. There are no standardized radiographic criteria for assessing treatment response, substantially complicating interpretation of prospective outcome data. Existing imaging frameworks for intracranial tumors assume perfectly spherical targets and may be suboptimal.

Objective

To compare a three-dimensional (3D) volumetric approach against accepted surrogate measurements to assess PA posttreatment response (PTR).

Design

Retrospective review of patients with available pre- and postradiotherapy (RT) imaging. A neuroradiologist determined tumor sizes in one dimensional (1D) per Response Evaluation in Solid Tumors (RECIST) criteria, two dimensional (2D) per Response Assessment in Neuro-Oncology (RANO) criteria, and 3D estimates assuming a perfect sphere or perfect ellipsoid. Each tumor was manually segmented for 3D volumetric measurements. The Hakon Wadell method was used to calculate sphericity.

Setting

Tertiary cancer center.

Patients or Other Participants

Patients (n = 34, median age = 50 years; 50% male) with PA and MRI scans before and after sellar RT.

Interventions

Patients received sellar RT for intact or surgically resected lesions.

Main Outcome Measures

Radiographic PTR, defined as percent tumor size change.

Results

Using 3D volumetrics, mean sphericity = 0.63 pre-RT and 0.60 post-RT. With all approaches, most patients had stable disease on post-RT scan. PTR for 1D, 2D, and 3D spherical measurements were moderately well correlated with 3D volumetrics (e.g., for 1D: 0.66, P < 0.0001) and were superior to 3D ellipsoid. Intraclass correlation coefficient demonstrated moderate to good reliability for 1D, 2D, and 3D sphere (P < 0.001); 3D ellipsoid was inferior (P = 0.009). 3D volumetrics identified more potential partially responding and progressive lesions.

Conclusions

Although PAs are irregularly shaped, 1D and 2D approaches are adequately correlated with volumetric assessment.

Brain Tumor-Enhancement Visualization and Morphometric Assessment: A Comparison of MPRAGE, SPACE, and VIBE MRI Techniques

BACKGROUND AND PURPOSE

Postgadolinium MR imaging is crucial for brain tumor diagnosis and morphometric assessment. We compared brain tumor enhancement visualization and the "target" object morphometry obtained with the most commonly used 3D MR imaging technique, MPRAGE, with 2 other routinely available techniques: sampling perfection with application-optimized contrasts by using different flip angle evolutions (SPACE) and volumetric interpolated brain examination (VIBE).

MATERIALS AND METHODS

Fifty-four contrast-enhancing tumors (38 gliomas and 16 metastases) were assessed using MPRAGE, VIBE, and SPACE techniques randomly acquired after gadolinium-based contrast agent administration on a 3T scanner. Enhancement conspicuity was assessed quantitatively by calculating the contrast rate and contrast-to-noise ratio, and qualitatively, by consensus visual comparative ratings. The total enhancing tumor volume and between-sequence discrepancy in the margin delineation were assessed on the corresponding 3D target objects contoured with a computer-assisted software for neuronavigation. The Wilcoxon signed rank and Pearson χ² nonparametric tests were used to investigate between-sequence discrepancies in the contrast rate, contrast-to-noise ratio, visual conspicuity ratings, tumor volume, and margin delineation estimates. Differences were also tested for 1D (Response Evaluation Criteria in Solid Tumors) and 2D (Response Assessment in Neuro-Oncology) measurements.

RESULTS

Compared with MPRAGE, both SPACE and VIBE obtained higher contrast rate, contrast-to-noise ratio, and visual conspicuity ratings in both gliomas and metastases (P range, <.001-.001). The between-sequence 3D target object margin discrepancy ranged between 3% and 19.9% of lesion tumor volume. Larger tumor volumes, 1D and 2D measurements were obtained with SPACE (P range, <.01-.007).

CONCLUSIONS

Superior conspicuity for brain tumor enhancement can be achieved using SPACE and VIBE techniques, compared with MPRAGE. Discrepancies were also detected when assessing target object size and morphology, with SPACE providing more accurate estimates.

Clinical Evaluation of a Multiparametric Deep Learning Model for Glioblastoma Segmentation Using Heterogeneous Magnetic Resonance Imaging Data From Clinical Routine

Objectives

The aims of this study were, first, to evaluate a deep learning–based, automatic glioblastoma (GB) tumor segmentation algorithm on clinical routine data from multiple centers and compare the results to a ground truth, manual expert segmentation, and second, to evaluate the quality of the segmentation results across heterogeneous acquisition protocols of routinely acquired clinical magnetic resonance imaging (MRI) examinations from multiple centers.

Materials and Methods

The data consisted of preoperative MRI scans (T1, T2, FLAIR, and contrast-enhanced [CE] T1) of 64 patients with an initial diagnosis of primary GB, which were acquired in 15 institutions with varying protocols. All images underwent preprocessing (coregistration, skull stripping, resampling to isotropic resolution, normalization) and were fed into an independently trained deep learning model based on DeepMedic, a multilayer, multiscale convolutional neural network for detection and segmentation of tumor compartments. Automatic segmentation results for the whole tumor, necrosis, and CE tumor were compared with manual segmentations.

Results

Whole tumor and CE tumor compartments were correctly detected in 100% of the cases; necrosis was correctly detected in 91% of the cases. A high segmentation accuracy comparable to interrater variability was achieved for the whole tumor (mean dice similarity coefficient [DSC], 0.86 ± 0.09) and CE tumor (DSC, 0.78 ± 0.15). The DSC for tumor necrosis was 0.62 ± 0.30. We have observed robust segmentation quality over heterogeneous image acquisition protocols, for example, there were no correlations between resolution and segmentation accuracy of the single tumor compartments. Furthermore, no relevant correlation was found between quality of automatic segmentation and volume of interest properties (surface-to-volume ratio and volume).

Conclusions

The proposed approach for automatic segmentation of GB proved to be robust on routine clinical data and showed on all tumor compartments a high automatic detection rate and a high accuracy, comparable to interrater variability. Further work on improvements of the segmentation accuracy for the necrosis compartments should be guided by the evaluation of the clinical relevance.

Therefore, we propose this approach as a suitable building block for automatic tumor segmentation to support radiologists or neurosurgeons in the preoperative reading of GB MRI images and characterization of primary GB.

Earliest radiological progression in glioblastoma by multidisciplinary consensus review

BACKGROUND

Detection of glioblastoma progression is important for clinical decision-making on cessation or initiation of therapy, for enrollment in clinical trials, and for response measurement in time and location. The RANO-criteria are considered standard for the timing of progression. To evaluate local treatment, we aim to find the most accurate progression location. We determined the differences in progression free survival (PFS) and in tumor volumes at progression (Vprog) by three definitions of progression.

METHODS

In a consecutive cohort of 73 patients with newly-diagnosed glioblastoma between 1/1/2012 and 31/12/2013, progression was established according to three definitions. We determined (1) earliest radiological progression (ERP) by retrospective multidisciplinary consensus review using all available imaging and follow-up, (2) clinical practice progression (CPP) from multidisciplinary tumor board conclusions, and (3) progression by the RANO-criteria.

RESULTS

ERP was established in 63 (86%), CPP in 64 (88%), RANO progression in 42 (58%). Of the 63 patients who had died, 37 (59%) did with prior RANO-progression, compared to 57 (90%) for both ERP and CPP. The median overall survival was 15.3 months. The median PFS was 8.8 months for ERP, 9.5 months for CPP, and 11.8 months for RANO. The PFS by ERP was shorter than CPP (HR 0.57, 95% CI 0.38-0.84, p = 0.004) and RANO-progression (HR 0.29, 95% CI 0.19-0.43, p < 0.001). The Vprog were significantly smaller for ERP (median 8.8 mL), than for CPP (17 mL) and RANO (22 mL).

CONCLUSION

PFS and Vprog vary considerably between progression definitions. Earliest radiological progression by retrospective consensus review should be considered to accurately localize progression and to address confounding of lead time bias in clinical trial enrollment.

Automated pixel-wise brain tissue segmentation of diffusion-weighted images via machine learning

The diffusion-weighted (DW) MR signal sampled over a wide range of b-values potentially allows for tissue differentiation in terms of cellularity, microstructure, perfusion, and T₂ relaxivity. This study aimed to implement a machine learning algorithm for automatic brain tissue segmentation from DW-MRI datasets, and to determine the optimal sub-set of features for accurate segmentation. DWI was performed at 3 T in eight healthy volunteers using 15 b-values and 20 diffusion-encoding directions. The pixel-wise signal attenuation, as well as the trace and fractional anisotropy (FA) of the diffusion tensor, were used as features to train a support vector machine classifier for gray matter, white matter, and cerebrospinal fluid classes. The datasets of two volunteers were used for validation. For each subject, tissue classification was also performed on 3D T₁ -weighted data sets with a probabilistic framework. Confusion matrices were generated for quantitative assessment of image classification accuracy in comparison with the reference method. DWI-based tissue segmentation resulted in an accuracy of 82.1% on the validation dataset and of 82.2% on the training dataset, excluding relevant model over-fitting. A mean Dice coefficient (DSC) of 0.79 ± 0.08 was found. About 50% of the classification performance was attributable to five features (i.e. signal measured at b-values of 5/10/500/1200 s/mm² and the FA). This reduced set of features led to almost identical performances for the validation (82.2%) and the training (81.4%) datasets (DSC = 0.79 ± 0.08). Machine learning techniques applied to DWI data allow for accurate brain tissue segmentation based on both morphological and functional information.

A prospective case study of high boost, high frequency emphasis and two-way diffusion filters on MR images of glioblastoma multiforme

Glioblastoma multiforme (GBM) appears undifferentiated and non-enhancing on magnetic resonance (MR) imagery. As MRI does not offer adequate image quality to allow visual discrimination of the boundary between GBM focus and perifocal vasogenic edema, surgical and radiotherapy planning become difficult. The presence of noise in MR images influences the computation of radiation dosage and precludes the edge based segmentation schemes in automated software for radiation treatment planning. The performance of techniques meant for simultaneous denoising and sharpening, like high boost filters, high frequency emphasize filters and two-way anisotropic diffusion is sensitive to the selection of their operational parameters. Improper selection may cause overshoot and saturation artefacts or noisy grey level transitions can be left unsuppressed. This paper is a prospective case study of the performance of high boost filters, high frequency emphasize filters and two-way anisotropic diffusion on MR images of GBM, for their ability to suppress noise from homogeneous regions and to selectively sharpen the true morphological edges. An objective method for determining the optimum value of the operational parameters of these techniques is also demonstrated. Saturation Evaluation Index (SEI), Perceptual Sharpness Index (PSI), Edge Model based Blur Metric (EMBM), Sharpness of Ridges (SOR), Structural Similarity Index Metric (SSIM), Peak Signal to Noise Ratio (PSNR) and Noise Suppression Ratio (NSR) are the objective functions used. They account for overshoot and saturation artefacts, sharpness of the image, width of salient edges (haloes), susceptibility of edge quality to noise, feature preservation and degree of noise suppression. Two-way diffusion is found to be superior to others in all these respects. The SEI, PSI, EMBM, SOR, SSIM, PSNR and NSR exhibited by two-way diffusion are 0.0016 ± 0.0012, 0.2049 ± 0.0187, 0.0905 ± 0.0408, 2.64 × 10¹² ± 1.6 × 10¹², 0.9955 ± 0.0024, 38.214 ± 5.2145 and 0.3547 ± 0.0069, respectively.