sj-docx-1-ijj-10.1177_03064190231203692 - Supplemental material for Pattern recognition as a learning strategy in the study of engineering dynamics

Supplemental material, sj-docx-1-ijj-10.1177_03064190231203692 for Pattern recognition as a learning strategy in the study of engineering dynamics by Simon Li, Kashif Raza, Ahmad Ghasemloonia and Catherine Chua in International Journal of Mechanical Engineering Education</p

Bridging Structure, Magnetism, and Disorder in Iron-Intercalated Niobium Diselenide, Fe_<i>x</i>NbSe₂, below <i>x</i> = 0.25

Transition-metal dichalcogenides (TMDs) intercalated with magnetic ions serve as a promising materials platform for developing next-generation, spin-based electronic technologies. In these materials, one can access a rich magnetic phase space depending on the choice of intercalant, host lattice, and relative stoichiometry. The distribution of these intercalant ions across given crystals, however, is less well definedparticularly away from ideal packing stoichiometriesand a convenient probe to assess potential longer-range ordering of intercalants is lacking. Here, we demonstrate that confocal Raman spectroscopy is a powerful tool for mapping the onset of intercalant superlattice formation in Fe-intercalated NbSe2 (FexNbSe2) for 0.14 ≤ x < 0.25. We use single-crystal X-ray diffraction to confirm the presence of longer-range intercalant superstructure and employ polarization-, temperature-, and magnetic field-dependent Raman measurements to examine both the symmetry of emergent phonon modes in the intercalated material and potential magnetoelastic coupling. Magnetometry measurements further indicate a correlation between the onset of magnetic ordering and the relative degree of intercalant superlattice formation. These results show Raman spectroscopy to be an expedient, local probe for mapping intercalant ordering in this class of magnetic materials

Quantification of the Heterogeneity of Prognostic Cellular Biomarkers in Ewing Sarcoma Using Automated Image and Random Survival Forest Analysis

<div><p>Driven by genomic somatic variation, tumour tissues are typically heterogeneous, yet unbiased quantitative methods are rarely used to analyse heterogeneity at the protein level. Motivated by this problem, we developed automated image segmentation of images of multiple biomarkers in Ewing sarcoma to generate distributions of biomarkers between and within tumour cells. We further integrate high dimensional data with patient clinical outcomes utilising random survival forest (RSF) machine learning. Using material from cohorts of genetically diagnosed Ewing sarcoma with EWSR1 chromosomal translocations, confocal images of tissue microarrays were segmented with level sets and watershed algorithms. Each cell nucleus and cytoplasm were identified in relation to DAPI and CD99, respectively, and protein biomarkers (e.g. Ki67, pS6, Foxo3a, EGR1, MAPK) localised relative to nuclear and cytoplasmic regions of each cell in order to generate image feature distributions. The image distribution features were analysed with RSF in relation to known overall patient survival from three separate cohorts (185 informative cases). Variation in pre-analytical processing resulted in elimination of a high number of non-informative images that had poor DAPI localisation or biomarker preservation (67 cases, 36%). The distribution of image features for biomarkers in the remaining high quality material (118 cases, 10⁴ features per case) were analysed by RSF with feature selection, and performance assessed using internal cross-validation, rather than a separate validation cohort. A prognostic classifier for Ewing sarcoma with low cross-validation error rates (0.36) was comprised of multiple features, including the Ki67 proliferative marker and a sub-population of cells with low cytoplasmic/nuclear ratio of CD99. Through elimination of bias, the evaluation of high-dimensionality biomarker distribution within cell populations of a tumour using random forest analysis in quality controlled tumour material could be achieved. Such an automated and integrated methodology has potential application in the identification of prognostic classifiers based on tumour cell heterogeneity.</p></div

Random survival forest analysis of biomarker image feature distributions.

<p>An overview of the imaging, the RSF survival analysis algorithm and validation approach. Single cell features are combined into patient features by estimating the probability distribution (PDF) for each feature, and taking measurements of each distribution at 100 points. Each RSF is used to analyse all patients, with prognostic features identified. The use of bagging in each RSF means error rate estimates should be unbiased, and this is verified using randomised cross-validation. This procedure also allows the variability in performance of the algorithm to be simulated without requiring an additional dataset.</p

Image thresholds bias significance of tissue biomarker results.

<p><b>a</b>. Thresholds for CD99 and Ki67 were split into centiles of the log₂ (nuclear/cytoplasmic ratio) distribution. The heat map shows the Cox regression <i>p</i> value (log₁₀) for each pair of centiles with respect to survival outcome of the whole imaged cohort. The square marker shows the optimal threshold with respect to the <i>p</i> value (CD99; −0.18 [62%tile], Ki67; 0.31 [22%tile]. <b>b</b>. Using this pair of thresholds, the Ki67 index and the log-rank test is calculated for all possible dichotomised splits of patient groups. <b>c</b>. Optimal threshold values defined in <b>a</b>. and <b>b</b>. lead to the Kaplan-Meier plot of overall survival outcome for good (low Ki67 index, blue) and poor prognosis (high Ki67 index, red) cases (dotted lines; 95% confidence intervals). Cox regression (b = 1.6, z = 4.8, p = 1.6×10⁻⁶, log-rank p = 2.6×10⁻⁷). <b>d</b>. A single observer (CB) scored the same images for Ki67 labelling by eye based on a binary low (blue) or high (red) score, resulting in the Kaplan Meier plot (Cox regression  = 1.3, z = 3.7, p = 2.5×10⁻⁴, log-rank p = 1×10⁻⁴).</p

Clinical features of patients with informative images from cohorts utilised in combined random forest analyses.

<p>*ND cohort a  =  outside bone</p>#<p>Non EWS-FLI1  =  EWS-ERG; EWS-NFATC2 or EWSR1-re-arranged (no FLI or ERG partner).</p><p>Note: all patients treated in Europe with standard chemotherapeutic, radiotherapy and surgical trial protocol (EICESS92/EE99 CESS81).</p><p>ND: data not available.</p><p>Clinical features of patients with informative images from cohorts utilised in combined random forest analyses.</p

Random survival forest classifier error rates, distribution features and mortality.

<p><b>a</b>. Error rates for nine RSF analyses trained with the variable hunting algorithm, shown as box plots (median line, inter-quartile range box, minimum and maximum). SiBio refers to combined analysis of signalling biomarkers Egr1, Foxo3a, pS6 with and without pMAPK*. Errors were lower for Ki-67 marker. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0107105#pone-0107105-t002" target="_blank">Table 2</a>. <b>b</b>. As each iteration of variable hunting is independent, so the frequency of selection of each feature and its overall ranking can be shown following 100 re-samplings. <b>c</b>. Selected features plotted (vertical lines) against the original distribution. Red and black lines indicate deceased and censored patients, with insert showing magnified plots. <b>d</b>. Based on 100 iterations of variable hunting RSF, an overall mortality plot can be generated as a function of the RSF and each feature. The top six (*) separate features are shown for the CD99 negative Ki-67 RSF, with the RSF integrating all ranked features<b>^‡</b> within one classifier. Red crosses and black dots, deceased and censored patients, respectively.</p

Development of a single cell segmentation algorithm for tumour tissues.

<p>Confocal images of agar pellets of EWS-FLI1 positive Ewing sarcoma cell lines were used to optimise image segmentation. <b>a</b>. Multi-channel and single channel images (with segmentation lines) of the CHP-100 cell line in cores labelled with DAPI, CD99 and EGR1 biomarkers indicating nucleus and cytoplasm localisation, respectively (see high magnification insert). In <b>b</b>., >500 cells were manually segmented and compared to the image segmentation algorithm (see Fig. S1 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0107105#pone.0107105.s004" target="_blank">File S1</a>) using Bland-Altman and Hausdorff distance. Also, example distributions are shown for nuclear DNA content and nuclear and cytoplasmic localisation of EGR1. Image segmentation was applied to tissue microarrays of <b>c</b>. Ewing sarcoma core biopsies on a tissue microarray (TMA), and <b>d</b>., multi-channel confocal images captured for DAPI, CD99 and Ki67 proliferation marker. In <b>e</b>. >500 cells from TMA cores were manually segmented and compared to the image segmentation algorithm using Bland-Altman and Hausdorff distance, with distributions for DNA and Ki67. Bars: 20 µm (<b>a</b>. and <b>d</b>.), and in <b>c</b>, 200, 100 and 50 µm, respectively.</p

Cross-validation of the full RSF algorithm.

<p>The imaging dataset was randomly partitioned into a training set (e.g. two-thirds of patients  = 79) and a testing set (one-third of patients  = 39), with 50 repeats. Example results from 4 of the 50 cross-validation repeats for the CD99- Ki67 RSF, encompassing the full range of error rates (0.22–0.53) shown in black). Patients in the test set were divided into two approximately equal groups using the RSF predicted mortality (low, high) and survival curves plotted using the known survival data (solid lines), with a low error rate corresponding to a difference in survival of the groups. In addition to predicting mortality the RSF could also predict an individual time dependent survival curve for each patient (dashed lines). Plots are truncated at 2500 days, in some cases predicted survival times do not reach this far since they are limited by the last event in the randomly selected training set. (see also Figure S12 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0107105#pone.0107105.s004" target="_blank">File S1</a>).</p

Image feature distributions utilised in nine independent random survival forest analyses.

1<p>DAPI: Nuclear DAPI (totals and means) in all cells.</p>2<p>CD99-DAPI: Nuclear DAPI in CD99- cells.</p>3<p>CD99+DAPI: Nuclear DAPI in CD99+ cells.</p>4<p>Ki67: Ki67 nuclear: cytoplasm ratios (totals and means) in all cells.</p>5<p>CD99-Ki67: Ki67 in CD99- cells.</p>6<p>CD99+Ki67: Ki67 in CD99+ cells</p>7, 8, 9<p>CD99+ Multiple markers in CD99+ and CD99- cells.</p><p>N: number of patients. Some patients did not have a full set of labelled images, so the number of samples used for each RSF varies depending on the combination of markers used. One patient did not have any cells labelled with Ki67. All features: the out-of-bag error rate calculated on a classifier containing all features from the indicated marker distributions. Variable hunting: the internal test set error rate using a RSF trained using variable hunting feature selection, and are the mean and standard deviations of the error rates are shown.</p><p>VH Rand-CV: the mean and the standard deviation of the cross-validation error rate using a RSF trained using variable hunting feature selection, with 50 rounds of two-thirds train: one-third test sets.</p><p>Image feature distributions utilised in nine independent random survival forest analyses.</p