Diffusion Coefficient
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2022 ◽  
Vol 11 ◽  
Haolin Yin ◽  
Yu Jiang ◽  
Zihan Xu ◽  
Wenjun Huang ◽  
Tianwu Chen ◽  

Background and PurposeBreast ductal carcinoma in situ (DCIS) has no metastatic potential, and has better clinical outcomes compared with invasive breast cancer (IBC). Convolutional neural networks (CNNs) can adaptively extract features and may achieve higher efficiency in apparent diffusion coefficient (ADC)-based tumor invasion assessment. This study aimed to determine the feasibility of constructing an ADC-based CNN model to discriminate DCIS from IBC.MethodsThe study retrospectively enrolled 700 patients with primary breast cancer between March 2006 and June 2019 from our hospital, and randomly selected 560 patients as the training and validation sets (ratio of 3 to 1), and 140 patients as the internal test set. An independent external test set of 102 patients during July 2019 and May 2021 from a different scanner of our hospital was selected as the primary cohort using the same criteria. In each set, the status of tumor invasion was confirmed by pathologic examination. The CNN model was constructed to discriminate DCIS from IBC using the training and validation sets. The CNN model was evaluated using the internal and external tests, and compared with the discriminating performance using the mean ADC. The area under the curve (AUC), sensitivity, specificity, and accuracy were calculated to evaluate the performance of the previous model.ResultsThe AUCs of the ADC-based CNN model using the internal and external test sets were larger than those of the mean ADC (AUC: 0.977 vs. 0.866, P = 0.001; and 0.926 vs. 0.845, P = 0.096, respectively). Regarding the internal test set and external test set, the ADC-based CNN model yielded sensitivities of 0.893 and 0.873, specificities of 0.929 and 0.894, and accuracies of 0.907 and 0.902, respectively. Regarding the two test sets, the mean ADC showed sensitivities of 0.845 and 0.818, specificities of 0.821 and 0.829, and accuracies of 0.836 and 0.824, respectively. Using the ADC-based CNN model, the prediction only takes approximately one second for a single lesion.ConclusionThe ADC-based CNN model can improve the differentiation of IBC from DCIS with higher accuracy and less time.

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 124
Juan Cesar Flores

For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5.

Chen Chen ◽  
Yuhui Qin ◽  
Haotian Chen ◽  
Junying Cheng ◽  
Bo He ◽  

Abstract Objective We used radiomics feature–based machine learning classifiers of apparent diffusion coefficient (ADC) maps to differentiate small round cell malignant tumors (SRCMTs) and non-SRCMTs of the nasal and paranasal sinuses. Materials A total of 267 features were extracted from each region of interest (ROI). Datasets were randomized into two sets, a training set (∼70%) and a test set (∼30%). We performed dimensional reductions using the Pearson correlation coefficient and feature selection analyses (analysis of variance [ANOVA], relief, recursive feature elimination [RFE]) and classifications using 10 machine learning classifiers. Results were evaluated with a leave-one-out cross-validation analysis. Results We compared the AUC for all the pipelines in the validation dataset using FeAture Explorer (FAE) software. The pipeline using RFE feature selection and Gaussian process classifier yielded the highest AUCs with ten features. When the “one-standard error” rule was used, FAE produced a simpler model with eight features, including Perc.01%, Perc.10%, Perc.90%, Perc.99%, S(1,0) SumAverg, S(5,5) AngScMom, S(5,5) Correlat, and WavEnLH_s-2. The AUCs of the training, validation, and test datasets achieved 0.995, 0.902, and 0.710, respectively. For ANOVA, the pipeline with the auto-encoder classifier yielded the highest AUC using only one feature, Perc.10% (training/validation/test datasets: 0.886/0.895/0.809, respectively). For the relief, the AUCs of the training, validation, and test datasets that used the LRLasso classifier using five features (Perc.01%, Perc.10%, S(4,4) Correlat, S(5,0) SumAverg, S(5,0) Contrast) were 0.892, 0.886, and 0.787, respectively. Compared with the RFE and relief, the results of all algorithms of ANOVA feature selection were more stable with the AUC values higher than 0.800. Conclusions We demonstrated the feasibility of combining artificial intelligence with the radiomics from ADC values in the differential diagnosis of SRCMTs and non-SRCMTs and the potential of this non-invasive approach for clinical applications. Key Points • The parameter with the best diagnostic performance in differentiating SRCMTs from non-SRCMTs was the Perc.10% ADC value. • Results of all the algorithms of ANOVA feature selection were more stable and the AUCs were higher than 0.800, as compared with RFE and relief. • The pipeline using RFE feature selection and Gaussian process classifier yielded the highest AUC.

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 33
Valerie Hietsch ◽  
Phil Ligrani ◽  
Mengying Su

We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.

Axel Målqvist ◽  
Barbara Verfürth

In this paper, we propose an offline-online strategy based on the Localized Orthogonal Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed diffusion coefficient. We consider a periodic deterministic coefficient with local defects that occur with probability $p$. The offline phase pre-computes entries to global LOD stiffness matrices on a single reference element (exploiting the periodicity) for a selection of defect configurations. Given a sample of the perturbed diffusion the corresponding LOD stiffness matrix is then computed by taking linear combinations of the pre-computed entries, in the online phase. Our computable error estimates show that this yields a good approximation of the solution for small $p$, which is illustrated by extensive numerical experiments.  This makes the proposed technique attractive already for moderate sample sizes in a Monte Carlo simulation.

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 555
Mourad Keddam ◽  
Peter Jurči

In the work of this contribution, two kinetics models have been employed to assess the boron diffusivities in nickel borides in case of Inconel 718 alloy. The first approach, named the alternative diffusion model (ADM), used the modified version of mass conservation equations for a three-phase system whilst the second one employed the mean diffusion coefficient (MDC) method. The boron diffusivities in nickel borides were firstly evaluated in the interval of 1123 to 1223 K for an upper boron concentration of 11.654 wt% in Ni4B3. The boron activation energies in the three phases (Ni4B3, Ni2B and Ni3B) were secondly deduced by fitting the values of boron diffusivities with Arrhenius relations. Finally, these values of energy were compared with the results from the literature for their experimental validation.

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