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1.
Elife ; 122024 Jun 19.
Artigo em Inglês | MEDLINE | ID: mdl-38896568

RESUMO

We present open-source tools for three-dimensional (3D) analysis of photographs of dissected slices of human brains, which are routinely acquired in brain banks but seldom used for quantitative analysis. Our tools can: (1) 3D reconstruct a volume from the photographs and, optionally, a surface scan; and (2) produce a high-resolution 3D segmentation into 11 brain regions per hemisphere (22 in total), independently of the slice thickness. Our tools can be used as a substitute for ex vivo magnetic resonance imaging (MRI), which requires access to an MRI scanner, ex vivo scanning expertise, and considerable financial resources. We tested our tools on synthetic and real data from two NIH Alzheimer's Disease Research Centers. The results show that our methodology yields accurate 3D reconstructions, segmentations, and volumetric measurements that are highly correlated to those from MRI. Our method also detects expected differences between post mortem confirmed Alzheimer's disease cases and controls. The tools are available in our widespread neuroimaging suite 'FreeSurfer' (https://surfer.nmr.mgh.harvard.edu/fswiki/PhotoTools).


Every year, thousands of human brains are donated to science. These brains are used to study normal aging, as well as neurological diseases like Alzheimer's or Parkinson's. Donated brains usually go to 'brain banks', institutions where the brains are dissected to extract tissues relevant to different diseases. During this process, it is routine to take photographs of brain slices for archiving purposes. Often, studies of dead brains rely on qualitative observations, such as 'the hippocampus displays some atrophy', rather than concrete 'numerical' measurements. This is because the gold standard to take three-dimensional measurements of the brain is magnetic resonance imaging (MRI), which is an expensive technique that requires high expertise ­ especially with dead brains. The lack of quantitative data means it is not always straightforward to study certain conditions. To bridge this gap, Gazula et al. have developed an openly available software that can build three-dimensional reconstructions of dead brains based on photographs of brain slices. The software can also use machine learning methods to automatically extract different brain regions from the three-dimensional reconstructions and measure their size. These data can be used to take precise quantitative measurements that can be used to better describe how different conditions lead to changes in the brain, such as atrophy (reduced volume of one or more brain regions). The researchers assessed the accuracy of the method in two ways. First, they digitally sliced MRI-scanned brains and used the software to compute the sizes of different structures based on these synthetic data, comparing the results to the known sizes. Second, they used brains for which both MRI data and dissection photographs existed and compared the measurements taken by the software to the measurements obtained with MRI images. Gazula et al. show that, as long as the photographs satisfy some basic conditions, they can provide good estimates of the sizes of many brain structures. The tools developed by Gazula et al. are publicly available as part of FreeSurfer, a widespread neuroimaging software that can be used by any researcher working at a brain bank. This will allow brain banks to obtain accurate measurements of dead brains, allowing them to cheaply perform quantitative studies of brain structures, which could lead to new findings relating to neurodegenerative diseases.


Assuntos
Doença de Alzheimer , Encéfalo , Imageamento Tridimensional , Aprendizado de Máquina , Humanos , Imageamento Tridimensional/métodos , Doença de Alzheimer/diagnóstico por imagem , Doença de Alzheimer/patologia , Encéfalo/diagnóstico por imagem , Encéfalo/patologia , Fotografação/métodos , Dissecação , Imageamento por Ressonância Magnética/métodos , Neuropatologia/métodos , Neuroimagem/métodos
2.
J Am Heart Assoc ; 12(11): e029242, 2023 06 06.
Artigo em Inglês | MEDLINE | ID: mdl-37218590

RESUMO

Background White matter hyperintensity (WMH) on magnetic resonance imaging (MRI) of the brain is associated with vascular cognitive impairment, cardiovascular disease, and stroke. We hypothesized that portable magnetic resonance imaging (pMRI) could successfully identify WMHs and facilitate doing so in an unconventional setting. Methods and Results In a retrospective cohort of patients with both a conventional 1.5 Tesla MRI and pMRI, we report Cohen's kappa (κ) to measure agreement for detection of moderate to severe WMH (Fazekas ≥2). In a subsequent prospective observational study, we enrolled adult patients with a vascular risk factor being evaluated in the emergency department for a nonstroke complaint and measured WMH using pMRI. In the retrospective cohort, we included 33 patients, identifying 16 (49.5%) with WMH on conventional MRI. Between 2 raters evaluating pMRI, the interrater agreement on WMH was strong (κ=0.81), and between 1 rater for conventional MRI and the 2 raters for pMRI, intermodality agreement was moderate (κ=0.66, 0.60). In the prospective cohort we enrolled 91 individuals (mean age, 62.6 years; 53.9% men; 73.6% with hypertension), of which 58.2% had WMHs on pMRI. Among 37 Black and Hispanic individuals, the Area Deprivation Index was higher (versus White, 51.8±12.9 versus 37.9±11.9; P<0.001). Among 81 individuals who did not have a standard-of-care MRI in the preceding year, we identified WMHs in 43 of 81 (53.1%). Conclusions Portable, low-field imaging could be useful for identifying moderate to severe WMHs. These preliminary results introduce a novel role for pMRI outside of acute care and the potential role for pMRI to reduce disparities in neuroimaging.


Assuntos
Substância Branca , Masculino , Adulto , Humanos , Pessoa de Meia-Idade , Feminino , Substância Branca/diagnóstico por imagem , Substância Branca/patologia , Estudos Prospectivos , Estudos Retrospectivos , Encéfalo/diagnóstico por imagem , Encéfalo/patologia , Imageamento por Ressonância Magnética
3.
Sci Adv ; 9(5): eadd3607, 2023 02 03.
Artigo em Inglês | MEDLINE | ID: mdl-36724222

RESUMO

Every year, millions of brain magnetic resonance imaging (MRI) scans are acquired in hospitals across the world. These have the potential to revolutionize our understanding of many neurological diseases, but their morphometric analysis has not yet been possible due to their anisotropic resolution. We present an artificial intelligence technique, "SynthSR," that takes clinical brain MRI scans with any MR contrast (T1, T2, etc.), orientation (axial/coronal/sagittal), and resolution and turns them into high-resolution T1 scans that are usable by virtually all existing human neuroimaging tools. We present results on segmentation, registration, and atlasing of >10,000 scans of controls and patients with brain tumors, strokes, and Alzheimer's disease. SynthSR yields morphometric results that are very highly correlated with what one would have obtained with high-resolution T1 scans. SynthSR allows sample sizes that have the potential to overcome the power limitations of prospective research studies and shed new light on the healthy and diseased human brain.


Assuntos
Inteligência Artificial , Neuroimagem , Humanos , Estudos Prospectivos , Neuroimagem/métodos , Encéfalo/diagnóstico por imagem , Encéfalo/patologia , Imageamento por Ressonância Magnética/métodos
4.
Proc IEEE Int Symp Biomed Imaging ; 2023: 899-903, 2021 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-38213549

RESUMO

We introduce a strategy for learning image registration without acquired imaging data, producing powerful networks agnostic to magnetic resonance imaging (MRI) contrast. While classical methods accurately estimate the spatial correspondence between images, they solve an optimization problem for every new image pair. Learning methods are fast at test time but limited to images with contrasts and geometric content similar to those seen during training. We propose to remove this dependency using a generative strategy that exposes networks to a wide range of images synthesized from segmentations during training, forcing them to generalize across contrasts. We show that networks trained within this framework generalize to a broad array of unseen MRI contrasts and surpass classical state-of-the-art brain registration accuracy by up to 12.4 Dice points for a variety of tested contrast combinations. Critically, training on arbitrary shapes synthesized from noise distributions results in competitive performance, removing the dependency on acquired data of any kind. Additionally, since anatomical label maps are often available for the anatomy of interest, we show that synthesizing images from these dramatically boosts performance, while still avoiding the need for real intensity images during training.

5.
Front Neurol ; 11: 588883, 2020.
Artigo em Inglês | MEDLINE | ID: mdl-33193055

RESUMO

White matter hyperintensities of presumed vascular origin (WMH) are a prevalent form of cerebral small-vessel disease and an important risk factor for post-stroke cognitive dysfunction. Despite this prevalence, it is not well understood how WMH contributes to post-stroke cognitive dysfunction. Preliminary findings suggest that increasing WMH volume is associated with total hippocampal volume in chronic stroke patients. The hippocampus, however, is a complex structure with distinct subfields that have varying roles in the function of the hippocampal circuitry and unique anatomical projections to different brain regions. For these reasons, an investigation into the relationship between WMH and hippocampal subfield volume may further delineate how WMH predispose to post-stroke cognitive dysfunction. In a prospective study of acute ischemic stroke patients with moderate/severe WMH burden, we assessed the relationship between quantitative WMH burden and hippocampal subfield volumes. Patients underwent a 3T MRI brain within 2-5 days of stroke onset. Total WMH volume was calculated in a semi-automated manner. Mean cortical thickness and hippocampal volumes were measured in the contralesional hemisphere. Total and subfield hippocampal volumes were measured using an automated, high-resolution, ex vivo computational atlas. Linear regression analyses were performed for predictors of total and subfield hippocampal volumes. Forty patients with acute ischemic stroke and moderate/severe white matter hyperintensity burden were included in this analysis. Median WMH volume was 9.0 cm3. Adjusting for intracranial volume and stroke laterality, age (ß = -3.7, P < 0.001), hypertension (ß = -44.7, P = 0.04), WMH volume (ß = -0.89, P = 0.049), and mean cortical thickness (ß = 286.2, P = 0.006) were associated with total hippocampal volume. In multivariable analysis, age (ß = -3.3, P < 0.001) and cortical thickness (ß = 205.2, P = 0.028) remained independently associated with total hippocampal volume. In linear regression for predictors of hippocampal subfield volume, increasing WMH volume was associated with decreased hippocampal-amygdala transition area volume (ß = -0.04, P = 0.001). These finding suggest that in ischemic stroke patients, increased WMH burden is associated with selective hippocampal subfield degeneration in the hippocampal-amygdala transition area.

6.
Proc IEEE Int Symp Biomed Imaging ; 2020: 283-287, 2020 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-32587665

RESUMO

Identification of the specific brain networks that are vulnerable or resilient in neurodegenerative diseases can help to better understand the disease effects and derive new connectomic imaging biomarkers. In this work, we use brain connectivity to find pairs of structural connections that are negatively correlated with each other across Alzheimer's disease (AD) and healthy populations. Such anti-correlated brain connections can be informative for identification of compensatory neuronal pathways and the mechanism of brain networks' resilience to AD. We find significantly anti-correlated connections in a public diffusion-MRI database, and then validate the results on other databases.

7.
Neuroimage ; 210: 116563, 2020 04 15.
Artigo em Inglês | MEDLINE | ID: mdl-31972281

RESUMO

The human hippocampus is vulnerable to a range of degenerative conditions and as such, accurate in vivo measurement of the hippocampus and hippocampal substructures via neuroimaging is of great interest for understanding mechanisms of disease as well as for use as a biomarker in clinical trials of novel therapeutics. Although total hippocampal volume can be measured relatively reliably, it is critical to understand how this reliability is affected by acquisition on different scanners, as multiple scanning platforms would likely be utilized in large-scale clinical trials. This is particularly true for hippocampal subregional measurements, which have only relatively recently been measurable through common image processing platforms such as FreeSurfer. Accurate segmentation of these subregions is challenging due to their small size, magnetic resonance imaging (MRI) signal loss in medial temporal regions of the brain, and lack of contrast for delineation from standard neuroimaging procedures. Here, we assess the test-retest reliability of the FreeSurfer automated hippocampal subfield segmentation procedure using two Siemens model scanners (a Siemens Trio and Prismafit Trio upgrade). T1-weighted images were acquired for 11 generally healthy younger participants (two scans on the Trio and one scan on the Prismafit). Each scan was processed through the standard cross-sectional stream and the recently released longitudinal pipeline in FreeSurfer v6.0 for hippocampal segmentation. Test-retest reliability of the volumetric measures was examined for individual subfields as well as percent volume difference and Dice overlap among scans and intra-class correlation coefficients (ICC). Reliability was high in the molecular layer, dentate gyrus, and whole hippocampus with the inclusion of three time points with mean volume differences among scans less than 3%, overlap greater than 80%, and ICC >0.95. The parasubiculum and hippocampal fissure showed the least improvement in reliability with mean volume difference greater than 5%, overlap less than 70%, and ICC scores ranging from 0.78 to 0.89. Other subregions, including the CA regions, were stable in their mean volume difference and overlap (<5% difference and >75% respectively) and showed improvement in reliability with the inclusion of three scans (ICC â€‹> â€‹0.9). Reliability was generally higher within scanner (Trio-Trio), however, Trio-Prismafit reliability was also high and did not exhibit an obvious bias. These results suggest that the FreeSurfer automated segmentation procedure is a reliable method to measure total as well as hippocampal subregional volumes and may be useful in clinical applications including as an endpoint for future clinical trials of conditions affecting the hippocampus.


Assuntos
Hipocampo/anatomia & histologia , Hipocampo/diagnóstico por imagem , Imageamento por Ressonância Magnética/normas , Neuroimagem/normas , Reconhecimento Automatizado de Padrão/normas , Adulto , Feminino , Humanos , Estudos Longitudinais , Imageamento por Ressonância Magnética/métodos , Masculino , Pessoa de Meia-Idade , Neuroimagem/métodos , Reconhecimento Automatizado de Padrão/métodos , Reprodutibilidade dos Testes , Software , Adulto Jovem
8.
Hum Brain Mapp ; 41(4): 1006-1016, 2020 03.
Artigo em Inglês | MEDLINE | ID: mdl-31696638

RESUMO

Thalamic atrophy is a common feature across all forms of FTD but little is known about specific nuclei involvement. We aimed to investigate in vivo atrophy of the thalamic nuclei across the FTD spectrum. A cohort of 402 FTD patients (age: mean(SD) 64.3(8.2) years; disease duration: 4.8(2.8) years) was compared with 104 age-matched controls (age: 62.5(10.4) years), using an automated segmentation of T1-weighted MRIs to extract volumes of 14 thalamic nuclei. Stratification was performed by clinical diagnosis (180 behavioural variant FTD (bvFTD), 85 semantic variant primary progressive aphasia (svPPA), 114 nonfluent variant PPA (nfvPPA), 15 PPA not otherwise specified (PPA-NOS), and 8 with associated motor neurone disease (FTD-MND), genetic diagnosis (27 MAPT, 28 C9orf72, 18 GRN), and pathological confirmation (37 tauopathy, 38 TDP-43opathy, 4 FUSopathy). The mediodorsal nucleus (MD) was the only nucleus affected in all FTD subgroups (16-33% smaller than controls). The laterodorsal nucleus was also particularly affected in genetic cases (28-38%), TDP-43 type A (47%), tau-CBD (44%), and FTD-MND (53%). The pulvinar was affected only in the C9orf72 group (16%). Both the lateral and medial geniculate nuclei were also affected in the genetic cases (10-20%), particularly the LGN in C9orf72 expansion carriers. Use of individual thalamic nuclei volumes provided higher accuracy in discriminating between FTD groups than the whole thalamic volume. The MD is the only structure affected across all FTD groups. Differential involvement of the thalamic nuclei among FTD forms is seen, with a unique pattern of atrophy in the pulvinar in C9orf72 expansion carriers.


Assuntos
Proteína C9orf72/genética , Demência Frontotemporal/genética , Demência Frontotemporal/patologia , Núcleos Laterais do Tálamo/patologia , Núcleo Mediodorsal do Tálamo/patologia , Pulvinar/patologia , Idoso , Atrofia/patologia , Feminino , Demência Frontotemporal/classificação , Demência Frontotemporal/diagnóstico por imagem , Humanos , Núcleos Laterais do Tálamo/diagnóstico por imagem , Masculino , Núcleo Mediodorsal do Tálamo/diagnóstico por imagem , Pessoa de Meia-Idade , Pulvinar/diagnóstico por imagem
10.
Front Neuroinform ; 12: 13, 2018.
Artigo em Inglês | MEDLINE | ID: mdl-29628885

RESUMO

Imaging the expression patterns of reporter constructs is a powerful tool to dissect the neuronal circuits of perception and behavior in the adult brain of Drosophila, one of the major models for studying brain functions. To date, several Drosophila brain templates and digital atlases have been built to automatically analyze and compare collections of expression pattern images. However, there has been no systematic comparison of performances between alternative atlasing strategies and registration algorithms. Here, we objectively evaluated the performance of different strategies for building adult Drosophila brain templates and atlases. In addition, we used state-of-the-art registration algorithms to generate a new group-wise inter-sex atlas. Our results highlight the benefit of statistical atlases over individual ones and show that the newly proposed inter-sex atlas outperformed existing solutions for automated registration and annotation of expression patterns. Over 3,000 images from the Janelia Farm FlyLight collection were registered using the proposed strategy. These registered expression patterns can be searched and compared with a new version of the BrainBaseWeb system and BrainGazer software. We illustrate the validity of our methodology and brain atlas with registration-based predictions of expression patterns in a subset of clock neurons. The described registration framework should benefit to brain studies in Drosophila and other insect species.

11.
J Gerontol A Biol Sci Med Sci ; 71(9): 1210-5, 2016 09.
Artigo em Inglês | MEDLINE | ID: mdl-26946100

RESUMO

BACKGROUND: Evidence suggests a link between the presence of subjective memory complaints (SMC) and lower volume of the hippocampus, one of the first regions to show neuropathological lesions in Alzheimer's disease. However, it remains unknown whether this pattern of hippocampal atrophy is regionally specific and whether SMC are also paralleled by changes in peripheral levels of amyloid-beta (Aß). METHODS: The volume of hippocampal subregions and plasma Aß levels were cross-sectionally compared between elderly individuals with (SMC(+); N = 47) and without SMC (SMC(-); N = 48). Significant volume differences in hippocampal subregions were further correlated with plasma Aß levels and with objective memory performance. RESULTS: Individuals with SMC exhibited significantly higher Aß1-42 concentrations and lower volumes of CA1, CA4, dentate gyrus, and molecular layer compared with SMC(-) participants. Regression analyses further showed significant associations between lower volume of the dentate gyrus and both poorer memory performance and higher plasma Aß1-42 levels in SMC(+) participants. CONCLUSIONS: The presence of SMC, lower volumes of specific hippocampal regions, and higher plasma Aß1-42 levels could be conditions associated with aging vulnerability. If such associations are confirmed in longitudinal studies, the combination may be markers recommending clinical follow-up in nondemented older adults.


Assuntos
Envelhecimento , Doença de Alzheimer/diagnóstico , Peptídeos beta-Amiloides/sangue , Hipocampo/patologia , Transtornos da Memória/diagnóstico , Idoso , Doença de Alzheimer/sangue , Doença de Alzheimer/epidemiologia , Atrofia , Biomarcadores/sangue , Encéfalo/patologia , Estudos Transversais , Diagnóstico Diferencial , Feminino , Hipocampo/diagnóstico por imagem , Humanos , Imageamento por Ressonância Magnética , Masculino , Transtornos da Memória/sangue , Transtornos da Memória/epidemiologia , Pessoa de Meia-Idade , Testes Neuropsicológicos , Valor Preditivo dos Testes , Sensibilidade e Especificidade
12.
Neuroimage ; 128: 125-137, 2016 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-26747746

RESUMO

The human hippocampal formation can be divided into a set of cytoarchitecturally and functionally distinct subregions, involved in different aspects of memory formation. Neuroanatomical disruptions within these subregions are associated with several debilitating brain disorders including Alzheimer's disease, major depression, schizophrenia, and bipolar disorder. Multi-center brain imaging consortia, such as the Enhancing Neuro Imaging Genetics through Meta-Analysis (ENIGMA) consortium, are interested in studying disease effects on these subregions, and in the genetic factors that affect them. For large-scale studies, automated extraction and subsequent genomic association studies of these hippocampal subregion measures may provide additional insight. Here, we evaluated the test-retest reliability and transplatform reliability (1.5T versus 3T) of the subregion segmentation module in the FreeSurfer software package using three independent cohorts of healthy adults, one young (Queensland Twins Imaging Study, N=39), another elderly (Alzheimer's Disease Neuroimaging Initiative, ADNI-2, N=163) and another mixed cohort of healthy and depressed participants (Max Planck Institute, MPIP, N=598). We also investigated agreement between the most recent version of this algorithm (v6.0) and an older version (v5.3), again using the ADNI-2 and MPIP cohorts in addition to a sample from the Netherlands Study for Depression and Anxiety (NESDA) (N=221). Finally, we estimated the heritability (h(2)) of the segmented subregion volumes using the full sample of young, healthy QTIM twins (N=728). Test-retest reliability was high for all twelve subregions in the 3T ADNI-2 sample (intraclass correlation coefficient (ICC)=0.70-0.97) and moderate-to-high in the 4T QTIM sample (ICC=0.5-0.89). Transplatform reliability was strong for eleven of the twelve subregions (ICC=0.66-0.96); however, the hippocampal fissure was not consistently reconstructed across 1.5T and 3T field strengths (ICC=0.47-0.57). Between-version agreement was moderate for the hippocampal tail, subiculum and presubiculum (ICC=0.78-0.84; Dice Similarity Coefficient (DSC)=0.55-0.70), and poor for all other subregions (ICC=0.34-0.81; DSC=0.28-0.51). All hippocampal subregion volumes were highly heritable (h(2)=0.67-0.91). Our findings indicate that eleven of the twelve human hippocampal subregions segmented using FreeSurfer version 6.0 may serve as reliable and informative quantitative phenotypes for future multi-site imaging genetics initiatives such as those of the ENIGMA consortium.


Assuntos
Hipocampo/anatomia & histologia , Processamento de Imagem Assistida por Computador/métodos , Neuroimagem/métodos , Adulto , Idoso , Idoso de 80 Anos ou mais , Algoritmos , Doença de Alzheimer/genética , Doença de Alzheimer/patologia , Transtornos de Ansiedade/genética , Transtornos de Ansiedade/patologia , Transtorno Depressivo/genética , Transtorno Depressivo/patologia , Feminino , Humanos , Imageamento por Ressonância Magnética , Masculino , Pessoa de Meia-Idade , Fenótipo , Software
13.
Med Image Comput Comput Assist Interv ; 14(Pt 3): 659-66, 2011.
Artigo em Inglês | MEDLINE | ID: mdl-22003756

RESUMO

Skull stripping is the first step in many neuroimaging analyses and its success is critical to all subsequent processing. Methods exist to skull strip brain images without gross deformities, such as those affected by Alzheimer's and Huntington's disease. However, there are no techniques for extracting brains affected by diseases that significantly disturb normal anatomy. Glioblastoma multiforme (GBM) is such a disease, as afflicted individuals develop large tumors that often require surgical resection. In this paper, we extend the ROBEX skull stripping method to extract brains from GBM images. The proposed method uses a shape model trained on healthy brains to be relatively insensitive to lesions inside the brain. The brain boundary is then searched for potential resection cavities using adaptive thresholding and the Random Walker algorithm corrects for leakage into the ventricles. The results show significant improvement over three popular skull stripping algorithms (BET, BSE and HWA) in a dataset of 48 GBM cases.


Assuntos
Mapeamento Encefálico/métodos , Neoplasias Encefálicas/patologia , Encéfalo/patologia , Glioblastoma/patologia , Processamento de Imagem Assistida por Computador/métodos , Imageamento por Ressonância Magnética/métodos , Crânio/patologia , Algoritmos , Neoplasias Encefálicas/diagnóstico , Ventrículos Cerebrais/patologia , Bases de Dados Factuais , Glioblastoma/diagnóstico , Humanos , Reconhecimento Automatizado de Padrão , Software , Técnica de Subtração
14.
Acta Crystallogr A ; 62(Pt 3): 178-94, 2006 May.
Artigo em Inglês | MEDLINE | ID: mdl-16614490

RESUMO

The different close-packed polytypes MX and MX2 have been enumerated for each of the possible space groups by counting the corresponding Zhdanov symbols for each space group and period of stacking, P, by the use of elementary combinatorial techniques. In special cases, simple closed formulae are obtained for these numbers as functions of P. The symmetry properties of the Zhdanov symbol have been investigated with the help of its cyclotomic representation and the two-color symmetry point group thereof. Zhdanov-like rules have been developed for MX2 polytypes. The SiC cases have been generated to P = 18 under the ;1-exclusion' rule and the possible diamond polytypes have been examined.

15.
Acta Crystallogr A ; 62(Pt 3): 195-200, 2006 May.
Artigo em Inglês | MEDLINE | ID: mdl-16614491

RESUMO

The relationship between the space-group symmetry of a close packing of equal balls of repeat period P and the symmetry properties of its representing Zhdanov symbol is analyzed. Proofs are straightforward when some symmetry is assumed for the stacking, and it is investigated how this symmetry is reflected in the structure of the Zhdanov symbol. Most of these proofs are documented in the literature, with variable degrees of rigor. However, the proof is somewhat more involved when working backwards, i.e. when some symmetry properties for the Zhdanov symbol are assumed and the corresponding effect on the symmetry of the polytype structure it represents is investigated, which may explain why these proofs are avoided or shrugged off as ;easily seen', 'obvious' and the like.

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