AutoCorNN: An Unsupervised Physics-Aware Deep Learning Model for Geometric Distortion Correction of Brain MRI Images Towards MR-Only Stereotactic Radiosurgery.

Geometric distortions in brain MRI images arising from susceptibility artifacts at air-tissue interfaces pose a significant challenge for high-precision radiation therapy modalities like stereotactic radiosurgery, necessitating sub-millimeter accuracy. To achieve this goal, we developed AutoCorNN, an unsupervised physics-aware deep-learning model for correcting geometric distortions. Two publicly available datasets, the MPI-Leipzig Mind-Brain-Body with 318 subjects, and the Vestibular Schwannoma-SEG dataset, encompassing 242 patients were utilized. AutoCorNN integrates two 2D convolutional encoder-decoder neural networks with the forward physical model of MRI signal generation to predict undistorted MR and field map images from distorted MR input. The network is trained in an unsupervised manner by minimizing the mean absolute error between the measured and estimated k-space data, without requiring ground truth images during training or deployment. The model was evaluated on vestibular schwannoma cases. AutoCorNN achieved a peak signal-to-noise ratio (PSNR) of 41.35 ± 0.02 dB, a root mean square error (RMSE) of 0.02 ± 0.003, and a structural similarity index (SSIM) of 0.99 ± 0.02 outperforming uncorrected and B0-mapping correction methods. Geometric distortions of about 1.6 mm were observed at the air-tissue interfaces at the air canal and nasal cavity borders. Geometrically, distortion correction increased the target volume from 3.12 ± 0.52 cc to 3.84 ± 0.54 cc. Dosimetrically, AutoCorNN improved target coverage (0.96 ± 0.01 to 0.97 ± 0.02), conformity index (0.92 ± 0.03 to 0.94 ± 0.03), and reduced dose gradients outside the target. AutoCorNN achieves accurate geometric distortion correction comparable to conventional iterative methods while offering substantial computational acceleration, enabling precise target delineation and conformal dose delivery for improved radiation therapy outcomes.

Fast MRI Reconstruction Using Deep Learning-based Compressed Sensing: A Systematic Review.

Magnetic resonance imaging (MRI) has revolutionized medical imaging, providing a non-invasive and highly detailed look into the human body. However, the long acquisition times of MRI present challenges, causing patient discomfort, motion artifacts, and limiting real-time applications. To address these challenges, researchers are exploring various techniques to reduce acquisition time and improve the overall efficiency of MRI. One such technique is compressed sensing (CS), which reduces data acquisition by leveraging image sparsity in transformed spaces. In recent years, deep learning (DL) has been integrated with CS-MRI, leading to a new framework that has seen remarkable growth. DL-based CS-MRI approaches are proving to be highly effective in accelerating MR imaging without compromising image quality. This review comprehensively examines DL-based CS-MRI techniques, focusing on their role in increasing MR imaging speed. We provide a detailed analysis of each category of DL-based CS-MRI including end-to-end, unroll optimization, self-supervised, and federated learning. Our systematic review highlights significant contributions and underscores the exciting potential of DL in CS-MRI. Additionally, our systematic review efficiently summarizes key results and trends in DL-based CS-MRI including quantitative metrics, the dataset used, acceleration factors, and the progress of and research interest in DL techniques over time. Finally, we discuss potential future directions and the importance of DL-based CS-MRI in the advancement of medical imaging. To facilitate further research in this area, we provide a GitHub repository that includes up-to-date DL-based CS-MRI publications and publicly available datasets - https://github.com/mosaf/Awesome-DL-based-CS-MRI.

Unsupervised MRI motion artifact disentanglement: introducing MAUDGAN.

Objective.This study developed an unsupervised motion artifact reduction method for magnetic resonance imaging (MRI) images of patients with brain tumors. The proposed novel design uses multi-parametric multicenter contrast-enhanced T1W (ceT1W) and T2-FLAIR MRI images.Approach.The proposed framework included two generators, two discriminators, and two feature extractor networks. A 3-fold cross-validation was used to train and fine-tune the hyperparameters of the proposed model using 230 brain MRI images with tumors, which were then tested on 148 patients'in-vivodatasets. An ablation was performed to evaluate the model's compartments. Our model was compared with Pix2pix and CycleGAN. Six evaluation metrics were reported, including normalized mean squared error (NMSE), structural similarity index (SSIM), multi-scale-SSIM (MS-SSIM), peak signal-to-noise ratio (PSNR), visual information fidelity (VIF), and multi-scale gradient magnitude similarity deviation (MS-GMSD). Artifact reduction and consistency of tumor regions, image contrast, and sharpness were evaluated by three evaluators using Likert scales and compared with ANOVA and Tukey's HSD tests.Main results.On average, our method outperforms comparative models to remove heavy motion artifacts with the lowest NMSE (18.34±5.07%) and MS-GMSD (0.07 ± 0.03) for heavy motion artifact level. Additionally, our method creates motion-free images with the highest SSIM (0.93 ± 0.04), PSNR (30.63 ± 4.96), and VIF (0.45 ± 0.05) values, along with comparable MS-SSIM (0.96 ± 0.31). Similarly, our method outperformed comparative models in removingin-vivomotion artifacts for different distortion levels except for MS- SSIM and VIF, which have comparable performance with CycleGAN. Moreover, our method had a consistent performance for different artifact levels. For the heavy level of motion artifacts, our method got the highest Likert scores of 2.82 ± 0.52, 1.88 ± 0.71, and 1.02 ± 0.14 (p-values≪0.0001) for our method, CycleGAN, and Pix2pix respectively. Similar trends were also found for other motion artifact levels.Significance.Our proposed unsupervised method was demonstrated to reduce motion artifacts from the ceT1W brain images under a multi-parametric framework.

High-resolution 3T to 7T ADC map synthesis with a hybrid CNN-transformer model.

BACKGROUND: 7 Tesla (7T) apparent diffusion coefficient (ADC) maps derived from diffusion-weighted imaging (DWI) demonstrate improved image quality and spatial resolution over 3 Tesla (3T) ADC maps. However, 7T magnetic resonance imaging (MRI) currently suffers from limited clinical unavailability, higher cost, and increased susceptibility to artifacts. PURPOSE: To address these issues, we propose a hybrid CNN-transformer model to synthesize high-resolution 7T ADC maps from multimodal 3T MRI. METHODS: The Vision CNN-Transformer (VCT), composed of both Vision Transformer (ViT) blocks and convolutional layers, is proposed to produce high-resolution synthetic 7T ADC maps from 3T ADC maps and 3T T1-weighted (T1w) MRI. ViT blocks enabled global image context while convolutional layers efficiently captured fine detail. The VCT model was validated on the publicly available Human Connectome Project Young Adult dataset, comprising 3T T1w, 3T DWI, and 7T DWI brain scans. The Diffusion Imaging in Python library was used to compute ADC maps from the DWI scans. A total of 171 patient cases were randomly divided into 130 training cases, 20 validation cases, and 21 test cases. The synthetic ADC maps were evaluated by comparing their similarity to the ground truth volumes with the following metrics: peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and mean squared error (MSE). In addition, RESULTS: The results are as follows: PSNR: 27.0 ± 0.9 dB, SSIM: 0.945 ± 0.010, and MSE: 2.0E-3 ± 0.4E-3. Both qualitative and quantitative results demonstrate that VCT performs favorably against other state-of-the-art methods. We have introduced various efficiency improvements, including the implementation of flash attention and training on 176×208 resolution images. These enhancements have resulted in the reduction of parameters and training time per epoch by 50% in comparison to ResViT. Specifically, the training time per epoch has been shortened from 7.67 min to 3.86 min. CONCLUSION: We propose a novel method to predict high-resolution 7T ADC maps from low-resolution 3T ADC maps and T1w MRI. Our predicted images demonstrate better spatial resolution and contrast compared to 3T MRI and prediction results made by ResViT and pix2pix. These high-quality synthetic 7T MR images could be beneficial for disease diagnosis and intervention, producing higher resolution and conformal contours, and as an intermediate step in generating synthetic CT for radiation therapy, especially when 7T MRI scanners are unavailable.

High-resolution MRI synthesis using a data-driven framework with denoising diffusion probabilistic modeling.

Objective. High-resolution magnetic resonance imaging (MRI) can enhance lesion diagnosis, prognosis, and delineation. However, gradient power and hardware limitations prohibit recording thin slices or sub-1 mm resolution. Furthermore, long scan time is not clinically acceptable. Conventional high-resolution images generated using statistical or analytical methods include the limitation of capturing complex, high-dimensional image data with intricate patterns and structures. This study aims to harness cutting-edge diffusion probabilistic deep learning techniques to create a framework for generating high-resolution MRI from low-resolution counterparts, improving the uncertainty of denoising diffusion probabilistic models (DDPM).Approach. DDPM includes two processes. The forward process employs a Markov chain to systematically introduce Gaussian noise to low-resolution MRI images. In the reverse process, a U-Net model is trained to denoise the forward process images and produce high-resolution images conditioned on the features of their low-resolution counterparts. The proposed framework was demonstrated using T2-weighted MRI images from institutional prostate patients and brain patients collected in the Brain Tumor Segmentation Challenge 2020 (BraTS2020).Main results. For the prostate dataset, the bicubic interpolation model (Bicubic), conditional generative-adversarial network (CGAN), and our proposed DDPM framework improved the noise quality measure from low-resolution images by 4.4%, 5.7%, and 12.8%, respectively. Our method enhanced the signal-to-noise ratios by 11.7%, surpassing Bicubic (9.8%) and CGAN (8.1%). In the BraTS2020 dataset, the proposed framework and Bicubic enhanced peak signal-to-noise ratio from resolution-degraded images by 9.1% and 5.8%. The multi-scale structural similarity indexes were 0.970 ± 0.019, 0.968 ± 0.022, and 0.967 ± 0.023 for the proposed method, CGAN, and Bicubic, respectively.Significance. This study explores a deep learning-based diffusion probabilistic framework for improving MR image resolution. Such a framework can be used to improve clinical workflow by obtaining high-resolution images without penalty of the long scan time. Future investigation will likely focus on prospectively testing the efficacy of this framework with different clinical indications.

MRI motion artifact reduction using a conditional diffusion probabilistic model (MAR-CDPM).

BACKGROUND: High-resolution magnetic resonance imaging (MRI) with excellent soft-tissue contrast is a valuable tool utilized for diagnosis and prognosis. However, MRI sequences with long acquisition time are susceptible to motion artifacts, which can adversely affect the accuracy of post-processing algorithms. PURPOSE: This study proposes a novel retrospective motion correction method named "motion artifact reduction using conditional diffusion probabilistic model" (MAR-CDPM). The MAR-CDPM aimed to remove motion artifacts from multicenter three-dimensional contrast-enhanced T1 magnetization-prepared rapid acquisition gradient echo (3D ceT1 MPRAGE) brain dataset with different brain tumor types. MATERIALS AND METHODS: This study employed two publicly accessible MRI datasets: one containing 3D ceT1 MPRAGE and 2D T2-fluid attenuated inversion recovery (FLAIR) images from 230 patients with diverse brain tumors, and the other comprising 3D T1-weighted (T1W) MRI images of 148 healthy volunteers, which included real motion artifacts. The former was used to train and evaluate the model using the in silico data, and the latter was used to evaluate the model performance to remove real motion artifacts. A motion simulation was performed in k-space domain to generate an in silico dataset with minor, moderate, and heavy distortion levels. The diffusion process of the MAR-CDPM was then implemented in k-space to convert structure data into Gaussian noise by gradually increasing motion artifact levels. A conditional network with a Unet backbone was trained to reverse the diffusion process to convert the distorted images to structured data. The MAR-CDPM was trained in two scenarios: one conditioning on the time step t $t$ of the diffusion process, and the other conditioning on both t $t$ and T2-FLAIR images. The MAR-CDPM was quantitatively and qualitatively compared with supervised Unet, Unet conditioned on T2-FLAIR, CycleGAN, Pix2pix, and Pix2pix conditioned on T2-FLAIR models. To quantify the spatial distortions and the level of remaining motion artifacts after applying the models, quantitative metrics were reported including normalized mean squared error (NMSE), structural similarity index (SSIM), multiscale structural similarity index (MS-SSIM), peak signal-to-noise ratio (PSNR), visual information fidelity (VIF), and multiscale gradient magnitude similarity deviation (MS-GMSD). Tukey's Honestly Significant Difference multiple comparison test was employed to quantify the difference between the models where p-value  < 0.05 $ < 0.05$ was considered statistically significant. RESULTS: Qualitatively, MAR-CDPM outperformed these methods in preserving soft-tissue contrast and different brain regions. It also successfully preserved tumor boundaries for heavy motion artifacts, like the supervised method. Our MAR-CDPM recovered motion-free in silico images with the highest PSNR and VIF for all distortion levels where the differences were statistically significant (p-values < 0.05 $< 0.05$ ). In addition, our method conditioned on t and T2-FLAIR outperformed (p-values < 0.05 $< 0.05$ ) other methods to remove motion artifacts from the in silico dataset in terms of NMSE, MS-SSIM, SSIM, and MS-GMSD. Moreover, our method conditioned on only t outperformed generative models (p-values < 0.05 $< 0.05$ ) and had comparable performances compared with the supervised model (p-values > 0.05 $> 0.05$ ) to remove real motion artifacts. CONCLUSIONS: The MAR-CDPM could successfully remove motion artifacts from 3D ceT1 MPRAGE. It is particularly beneficial for elderly who may experience involuntary movements during high-resolution MRI imaging with long acquisition times.

MedFusionGAN: multimodal medical image fusion using an unsupervised deep generative adversarial network.

PURPOSE: This study proposed an end-to-end unsupervised medical fusion generative adversarial network, MedFusionGAN, to fuse computed tomography (CT) and high-resolution isotropic 3D T1-Gd Magnetic resonance imaging (MRI) image sequences to generate an image with CT bone structure and MRI soft tissue contrast to improve target delineation and to reduce the radiotherapy planning time. METHODS: We used a publicly available multicenter medical dataset (GLIS-RT, 230 patients) from the Cancer Imaging Archive. To improve the models generalization, we consider different imaging protocols and patients with various brain tumor types, including metastases. The proposed MedFusionGAN consisted of one generator network and one discriminator network trained in an adversarial scenario. Content, style, and L1 losses were used for training the generator to preserve the texture and structure information of the MRI and CT images. RESULTS: The MedFusionGAN successfully generates fused images with MRI soft-tissue and CT bone contrast. The results of the MedFusionGAN were quantitatively and qualitatively compared with seven traditional and eight deep learning (DL) state-of-the-art methods. Qualitatively, our method fused the source images with the highest spatial resolution without adding the image artifacts. We reported nine quantitative metrics to quantify the preservation of structural similarity, contrast, distortion level, and image edges in fused images. Our method outperformed both traditional and DL methods on six out of nine metrics. And it got the second performance rank for three and two quantitative metrics when compared with traditional and DL methods, respectively. To compare soft-tissue contrast, intensity profile along tumor and tumor contours of the fusion methods were evaluated. MedFusionGAN provides a more consistent, better intensity profile, and a better segmentation performance. CONCLUSIONS: The proposed end-to-end unsupervised method successfully fused MRI and CT images. The fused image could improve targets and OARs delineation, which is an important aspect of radiotherapy treatment planning.

Patient-specific geometrical distortion corrections of MRI images improve dosimetric planning accuracy of vestibular schwannoma treated with gamma knife stereotactic radiosurgery.

PURPOSE: To investigate the impact of MRI patient-specific geometrical distortion (PSD) on the quality of Gamma Knife stereotactic radiosurgery (GK-SRS) plans of the vestibular schwannoma (VS) tumors. METHODS AND MATERIALS: Three open access datasets including the MPI-Leipzig Mind-Brain-Body (318 patients), the slow event-related fMRI designs dataset (62 patients), and the VS dataset (242 patients) were used. We used first two datasets to train a 3D convolution network to predict the distortion map of third dataset that were then used to calculate and correct the PSD. GK-SRS plans of VS dataset were used to evaluate dose distribution of PSD-corrected MRI images. GK-SRS prescription dose of VS cases was 12 Gy. Geometric and dosimetric discrepancies were assessed between the dose distributions and contours before and after the PSD corrections. Geometry indices were center of the contours, Dice coefficient (DC), Hausdorff distance (HD), and dosimetric indices were D µ ${D_\mu }$ , D m a x ${D_{max}}$ , D m i n ${D_{min}}$ , and D 95 % ${D_{95{\mathrm{\% }}}}$ doses, target coverage (TC), Paddick's conformity index (PCI), Paddick's gradient index (GI), and homogeneity index (HI). RESULTS: Geometric distortions of about 1.2 mm were observed at the air-tissue interfaces at the air canal and nasal cavity borders. Average center of the targets was significantly distorted along the frequency encoding direction after the PSD-correction. Average DC and HD metrics were 0.90 and 2.13 mm. Average D µ ${D_\mu }$ , D 95 % , ${D_{95{\mathrm{\% ,}}}}$ and D m i n ${D_{min}}$ in Gy significantly increased after PSD correction from 16.85 to 17.25, 12.30 to 12.77, and from 8.98 to 9.92. D m a x ${D_{max}}$ did not significantly change after the correction. Average TC and PCI significantly increased from 0.97 to 0.98, and 0.94 to 0.96. Average GI decreased significantly from 2.24 to 2.15 after PSD correction. However, HI did not significantly change after the correction. CONCLUSION: The proposed method could predict and correct the PSD that indicates the importance of PSD correction before GK-SRS plans of the VS patients.

Shuffle-ResNet: Deep learning for predicting LGG IDH1 mutation from multicenter anatomical MRI sequences.

Background and Purpose.The world health organization recommended to incorporate gene information such as isocitrate dehydrogenase 1 (IDH1) mutation status to improve prognosis, diagnosis, and treatment of the central nervous system tumors. We proposed our Shuffle Residual Network (Shuffle-ResNet) to predict IDH1 gene mutation status of the low grade glioma (LGG) tumors from multicenter anatomical magnetic resonance imaging (MRI) sequences including T2-w, T2-FLAIR, T1-w, and T1-Gd.Methods and Materials.We used 105 patient's dataset available in The Cancer Genome Atlas LGG project where we split them into training and testing datasets. We implemented a random image patch extractor to leverage tumor heterogeneity where about half a million image patches were extracted. RGB dataset were created from image concatenation. We used random channel-shuffle layer in the ResNet architecture to improve the generalization, and, also, a 3-fold cross validation to generalize the network's performance. The early stopping algorithm and learning rate scheduler were employed to automatically halt the training.Results.The early stopping algorithm terminated the training after 131, 106, and 96 epochs in fold 1, 2, and 3. The accuracy and area under the curve (AUC) of the validation dataset were 81.29% (95% CI (79.87, 82.72)) and 0.96 (95% CI (0.92, 0.98)) when we concatenated T2-FLAIR, T1-Gd, and T2-w to produce an RGB dataset. The accuracy and AUC values of the test dataset were 85.7% and 0.943.Conclusions.Our Shuffle-ResNet could predict IDH1 gene mutation status using multicenter MRI. However, its clinical application requires more investigation.

Findings of DTI-p maps in comparison with T2/T2-FLAIR to assess postoperative hyper-signal abnormal regions in patients with glioblastoma.

PURPOSE: The aim of this study was to compare diffusion tensor imaging (DTI) isotropic map (p-map) with current radiographically (T2/T2-FLAIR) methods based on abnormal hyper-signal size and location of glioblastoma tumor using a semi-automatic approach. MATERIALS AND METHODS: Twenty-five patients with biopsy-proved diagnosis of glioblastoma participated in this study. T2, T2-FLAIR images and diffusion tensor imaging (DTI) were acquired 1 week before radiotherapy. Hyper-signal regions on T2, T2-FLAIR and DTI p-map were segmented by means of semi-automated segmentation. Manual segmentation was used as ground truth. Dice Scores (DS) were calculated for validation of semiautomatic method. Discordance Index (DI) and area difference percentage between the three above regions from the three modalities were calculated for each patient. RESULTS: Area of abnormality in the p-map was smaller than the corresponding areas in the T2 and T2-FLAIR images in 17 patients; with mean difference percentage of 30 ± 0.15 and 35 ± 0.15, respectively. Abnormal region in the p-map was larger than the corresponding areas in the T2-FLAIR and T2 images in 4 patients; with mean difference percentage of 26 ± 0.17 and 29 ± 0.28, respectively. This region in the p-map was larger than the one in the T2 image and smaller than the one in the T2-FLAIR image in 3 patients; with mean difference percentage of 34 ± 0.08 and 27 ± 0.06, respectively. Lack of concordance was observed ranged from 0.214-0.772 for T2-FLAIR/p-map (average: 0.462 ± 0.18), 0.266-0.794 for T2 /p-map (average: 0.468 ± 0.13) and 0.123-0.776 for T2/ T2-FLAIR (average: 0.423 ± 0.2). These regions on three modalities were segmented using a semi-automatic segmentation method with over 86% sensitivity, 90% specificity and 89% dice score for three modalities. CONCLUSION: It is noted that T2, T2-FLAIR and DTI p-maps represent different but complementary information for delineation of glioblastoma tumor margins. Therefore, this study suggests DTI p-map modality as a candidate to improve target volume delineation based on conventional modalities, which needs further investigations with follow-up data to be confirmed.

Heterogeneity analysis of diffusion-weighted MRI for prediction and assessment of microstructural changes early after one cycle of induction chemotherapy in nasopharyngeal cancer patients.

PURPOSE: To evaluate whether the pretreatment apparent diffusion coefficient (ADC) heterogeneity parameters and their alterations, after one cycle of induction chemotherapy, can be used as reliable markers of treatment response to induction chemotherapy in patients with nasopharyngeal cancer. MATERIALS AND METHODS: Ten patients were recruited and received induction chemotherapy (IC). Diffusion-weighted imaging was performed prior to, during, and after IC. The first-order ADC histogram parameters at the intra-treatment time-point were compared to the baseline time-point in the metastatic lymph nodes (LNs). Some ADC pretreatment parameters were combined with each other, employing discriminant analysis to achieve a feasible model to separate the complete response (CR) from the partial response (PR) groups. RESULTS: For ten patients, significant rise in Mean and Txt1Mean (p = 0.048 and 0.015, respectively) was observed in the metastatic nodes following one cycle of IC. Txt5Energy significantly decreased (p = 0.002). Discriminant analysis on pretreatment parameters illustrated that Txt5Energypre was the best parameter to use to correctly classify CR and PR patients. This was followed by Txt9Percentile75pre, Txt1Meanpre, and Txt2Standard Deviationpre. CONCLUSIONS: Our results suggest that heterogeneity metrics extracted from ADC-maps in metastatic lymph nodes, before and after IC, can be used as supplementary IC response indicators.

Biological removal of phenol from saline wastewater using a moving bed biofilm reactor containing acclimated mixed consortia.

In this study, the performance of an aerobic moving bed biofilm reactor (MBBR) was assessed for the removal of phenol as the sole substrate from saline wastewater. The effect of several parameters namely inlet phenol concentration (200-1200 mg/L), hydraulic retention time (8-24 h), inlet salt content (10-70 g/L), phenol shock loading, hydraulic shock loading and salt shock loading on the performance of the 10 L MBBR inoculated with a mixed culture of active biomass gradually acclimated to phenol and salt were evaluated in terms of phenol and chemical oxygen demand (COD) removal efficiencies. The results indicated that phenol and COD removal efficiencies are affected by HRT, phenol and salt concentration in the bioreactor saline feed. The MBBR could remove up to 99% of phenol and COD from the feed saline wastewater at inlet phenol concentrations up to 800 mg/L, HRT of 18 h and inlet salt contents up to 40 g/L. The reactor could also resist strong shock loads. Furthermore, measuring biological quantitative parameters indicated that the biofilm plays a main role in phenol removal. Overall, the results of this investigation revealed that the developed MBBR system with high concentration of the active mixed biomass can play a prominent role in order to treat saline wastewaters containing phenol in industrial applications as a very efficient and flexible technology.

Synthesis of iron-doped TiO2 for degradation of reactive Orange16.

In this study the optimum conditions for preparing the iron-doped TiO2 nanoparticles were investigated. Samples were synthesized by sol-gel impregnation method. Three effective parameters were optimized using Taguchi method, consisted of: (i) atomic ratios of Fe to Ti; (ii) sintering temperature; (iii) sintering time. The characterization of samples was determined using X-ray diffraction, BET- specific surface area, UV- Vis reflectance spectra (DRS) and scanning electron microscope (SEM). The XRD patterns of the samples indicated the existence of anatase crystal phase in structure. UV- Vis reflectance spectra showed an enhancement in light absorbance in the visible region (wavelength > 400 nm) for iron-doped samples. The photocatalytic activity of samples was investigated by the degradation of RO 16 (RO 16) dye under UV irradiation. The results illustrated that the photocatalytic activity of iron-doped TiO2 was more than pure TiO2, because of the smaller crystal size, grater BET surface area and higher light absorption ability.

Response surface analysis of photocatalytic degradation of methyl tert-butyl ether by core/shell Fe3O4/ZnO nanoparticles.

The degradation of methyl tert-butyl ether (MTBE) was investigated in the aqueous solution of coated ZnO onto magnetite nanoparticale based on an advanced photocatalytic oxidation process. The photocatalysts were synthesized by coating of ZnO onto magnetite using precipitation method. The sample was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and vibration sample magnetometer (VSM). Besides, specific surface area was also determined by BET method. The four effective factors including pH of the reaction mixture, Fe3O4/ZnO magnetic nanoparticles concentration, initial MTBE concentration and molar ratio of [H2O2]/ [MTBE] were optimized using response surface modeling (RSM). Using the four-factor-three-level Box-Behnken design, 29 runs were designed considering the effective ranges of the influential factors. The optimized values for the operational parameters under the respective constraints were obtained at PH of 7.2, Fe3O4/ZnO concentration of 1.78 g/L, initial MTBE concentration of 89.14 mg/L and [H2O2]/ [MTBE] molar ratio of 2.33. Moreover, kinetics of MTBE degradation was determined under optimum condition. The study about core/shell magnetic nanoparticles (MNPs) recycling were also carried out and after about four times, the percentage of the photocatalytic degradation was about 70%.