Bayesian estimation of templates in computational anatomy: Difference between revisions
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== The Bayes model of computational anatomy ==
The central statistical model of [[computational anatomy]] in the context of [[medical imaging]] is the source-channel model of [[Shannon theory]];<ref>{{Cite journal|title = Statistical methods in computational anatomy|journal = Statistical Methods in Medical Research|date = 1997-06-01|issn = 0962-2802|pmid = 9339500|pages = 267–299|volume = 6|issue = 3|doi = 10.1177/096228029700600305|language = en|first1 = Michael|last1 = Miller|first2 = Ayananshu|last2 = Banerjee|first3 = Gary|last3 = Christensen|first4 = Sarang|last4 = Joshi|first5 = Navin|last5 = Khaneja|first6 = Ulf|last6 = Grenander|first7 = Larissa|last7 = Matejic|s2cid = 35247542}}</ref><ref>{{Cite book|title = Pattern Theory: From Representation to Inference|author = U. Grenander and M. I. Miller |publisher = Oxford University Press|date = 2007-02-08|isbn = {{Format ISBN|9780199297061}}|language = English}}</ref><ref>{{Cite book|title = Bayesian Multiple Atlas Deformable Templates|author = M. I. Miller and S. Mori and X. Tang and D. Tward and Y. Zhang | series = Brain Mapping: An Encyclopedic Reference|url = https://books.google.com/books?id=ysucBAAAQBAJ|publisher = Academic Press|date = 2015-02-14|isbn = {{Format ISBN|9780123973160}}|language = en}}</ref> the source is the deformable template of images <math> I \in \mathcal {I} </math>, the channel outputs are the imaging sensors with observables <math> I^D \in {\mathcal I}^{\mathcal D} </math> . The variation in the anatomical configurations are modelled separately from the Medical imaging modalities [[Computed axial tomography|Computed Axial Tomography]] machine, [[Magnetic resonance imaging|MRI]] machine, [[Positron emission tomography|PET]] machine, and others. The [[Bayes' theorem|Bayes theory]] models the prior on the source of images <math> \pi_{\mathcal{I}} (\cdot) </math> on <math>I \in \mathcal{I} </math>, and the conditional density on the observable imagery <math> p(\cdot |I) \ \text{on} \ I^D \in {\mathcal I}^{\mathcal D} </math>, conditioned on <math> I \in \mathcal{I} </math>. For images with [[Computational anatomy#Groups and group actions|diffeomorphism group action]] <math>I \doteq \phi \cdot I_\mathrm{temp}, \phi \in Diff_V</math>, then the prior on the group <math>\pi_{Diff_V} (\cdot)</math> induces the prior on images <math>\pi_{\mathcal{I}} (\cdot)</math>, written as densities the log-posterior takes the form
:<math>
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== Surface templates for computational neuroanatomy and subcortical structures ==
The study of sub-cortical neuroanatomy has been the focus of many studies. Since the original publications by Csernansky and colleagues of hippocampal change in Schizophrenia,<ref>{{Cite journal|last1=Csernansky|first1=John G.|last2=Joshi|first2=Sarang|last3=Wang|first3=Lei|last4=Haller|first4=John W.|last5=Gado|first5=Mokhtar|last6=Miller|first6=J. Philip|last7=Grenander|first7=Ulf|last8=Miller|first8=Michael I.|date=1998-09-15|title=Hippocampal morphometry in schizophrenia by high dimensional brain mapping|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=95|issue=19|pages=11406–11411|issn=0027-8424|pmc=21655|pmid=9736749|doi=10.1073/pnas.95.19.11406|bibcode=1998PNAS...9511406C|doi-access=free}}</ref><ref>{{Cite journal|last1=Csernansky|first1=John G.|last2=Wang|first2=Lei|last3=Jones|first3=Donald|last4=Rastogi-Cruz|first4=Devna|last5=Posener|first5=Joel A.|last6=Heydebrand|first6=Gitry|last7=Miller|first7=J. Philip|last8=Miller|first8=Michael I.|s2cid=14924093|date=2002-12-01|title=Hippocampal deformities in schizophrenia characterized by high dimensional brain mapping|journal=The American Journal of Psychiatry|volume=159|issue=12|pages=2000–2006|doi=10.1176/appi.ajp.159.12.2000|issn=0002-953X|pmid=12450948}}</ref><ref>{{Cite journal|last1=Wang|first1=L.|last2=Joshi|first2=S. C.|last3=Miller|first3=M. I.|last4=Csernansky|first4=J. G.|s2cid=16573767|date=2001-09-01|title=Statistical analysis of hippocampal asymmetry in schizophrenia|journal=NeuroImage|volume=14|issue=3|pages=531–545|doi=10.1006/nimg.2001.0830|issn=1053-8119|pmid=11506528}}</ref><ref>{{Cite journal|last1=Csernansky|first1=John G.|last2=Schindler|first2=Mathew K.|last3=Splinter|first3=N. Reagan|last4=Wang|first4=Lei|last5=Gado|first5=Mohktar|last6=Selemon|first6=Lynn D.|last7=Rastogi-Cruz|first7=Devna|last8=Posener|first8=Joel A.|last9=Thompson|first9=Paul A.|date=2004-05-01|title=Abnormalities of thalamic volume and shape in schizophrenia|journal=The American Journal of Psychiatry|volume=161|issue=5|pages=896–902|doi=10.1176/appi.ajp.161.5.896|issn=0002-953X|pmid=15121656}}</ref> Alzheimer's disease,<ref>{{Cite journal|last1=Csernansky|first1=J. G.|last2=Wang|first2=L.|last3=Swank|first3=J.|last4=Miller|first4=J. P.|last5=Gado|first5=M.|last6=McKeel|first6=D.|last7=Miller|first7=M. I.|last8=Morris|first8=J. C.|date=2005-04-15|title=Preclinical detection of Alzheimer's disease: hippocampal shape and volume predict dementia onset in the elderly|journal=NeuroImage|volume=25|issue=3|pages=783–792|doi=10.1016/j.neuroimage.2004.12.036|issn=1053-8119|pmid=15808979|s2cid=207164390}}</ref><ref>{{Cite journal|last1=Wang|first1=Lei|last2=Miller|first2=J. Philp|last3=Gado|first3=Mokhtar H.|last4=McKeel|first4=Daniel W.|last5=Rothermich|first5=Marcus|last6=Miller|first6=Michael I.|last7=Morris|first7=John C.|last8=Csernansky|first8=John G.|date=2006-03-01|title=Abnormalities of hippocampal surface structure in very mild dementia of the Alzheimer type|journal=NeuroImage|volume=30|issue=1|pages=52–60|doi=10.1016/j.neuroimage.2005.09.017|issn=1053-8119|pmc=2853193|pmid=16243546}}</ref><ref>{{Cite journal|last1=Wang|first1=Lei|last2=Swank|first2=Jeffrey S.|last3=Glick|first3=Irena E.|last4=Gado|first4=Mokhtar H.|last5=Miller|first5=Michael I.|last6=Morris|first6=John C.|last7=Csernansky|first7=John G.|date=2003-10-01|title=Changes in hippocampal volume and shape across time distinguish dementia of the Alzheimer type from healthy aging|journal=NeuroImage|volume=20|issue=2|pages=667–682|doi=10.1016/S1053-8119(03)00361-6|issn=1053-8119|pmid=14568443|s2cid=21246081}}</ref> and Depression,<ref>{{Cite journal|last1=Posener|first1=Joel A.|last2=Wang|first2=Lei|last3=Price|first3=Joseph L.|last4=Gado|first4=Mokhtar H.|last5=Province|first5=Michael A.|last6=Miller|first6=Michael I.|last7=Babb|first7=Casey M.|last8=Csernansky|first8=John G.|s2cid=12131077|date=2003-01-01|title=High-dimensional mapping of the hippocampus in depression|journal=The American Journal of Psychiatry|volume=160|issue=1|pages=83–89|doi=10.1176/appi.ajp.160.1.83|issn=0002-953X|pmid=12505805}}</ref><ref>{{Cite journal|last1=Munn|first1=Melissa A.|last2=Alexopoulos|first2=Jim|last3=Nishino|first3=Tomoyuki|last4=Babb|first4=Casey M.|last5=Flake|first5=Lisa A.|last6=Singer|first6=Tisha|last7=Ratnanather|first7=J. Tilak|last8=Huang|first8=Hongyan|last9=Todd|first9=Richard D.|date=2007-09-01|title=Amygdala Volume Analysis in Female Twins with Major Depression|journal=Biological Psychiatry|volume=62|issue=5|pages=415–422|doi=10.1016/j.biopsych.2006.11.031|issn=0006-3223|pmc=2904677|pmid=17511971}}</ref> many neuroanatomical shape statistical studies have now been completed using templates built from all of the subcortical structures for depression,<ref>{{Cite web|url=https://www.researchgate.net/publication/271515359|title=Amygdala and Hippocampal in ADHD: Volumetric and Morphometric Analysis and Relation to Mood Symptoms.|website=ResearchGate|access-date=2016-03-22}}</ref> Alzheimer's,<ref name="Tang 599–611"/><ref name="Tang 2093–2117"/><ref>{{Cite journal|last1=Qiu|first1=Anqi|last2=Fennema-Notestine|first2=Christine|last3=Dale|first3=Anders M.|last4=Miller|first4=Michael I.|date=2009-04-15|title=Regional shape abnormalities in mild cognitive impairment and Alzheimer's disease|journal=NeuroImage|volume=45|issue=3|pages=656–661|issn=1053-8119|pmc=2847795|pmid=19280688|doi=10.1016/j.neuroimage.2009.01.013}}</ref><ref>{{Cite journal|last1=Qiu|first1=Anqi|last2=Younes|first2=Laurent|last3=Miller|first3=Michael I.|last4=Csernansky|first4=John G.|date=2008-03-01|title=Parallel Transport in Diffeomorphisms Distinguishes the Time-Dependent Pattern of Hippocampal Surface Deformation due to Healthy Aging and the Dementia of the Alzheimer's Type|journal=NeuroImage|volume=40|issue=1|pages=68–76|doi=10.1016/j.neuroimage.2007.11.041|issn=1053-8119|pmc=3517912|pmid=18249009}}</ref><ref>{{Cite journal|last1=Miller|first1=Michael I.|last2=Younes|first2=Laurent|last3=Ratnanather|first3=J. Tilak|last4=Brown|first4=Timothy|last5=Reigel|first5=Tommy|last6=Trinh|first6=Huong|last7=Tang|first7=Xiaoying|last8=Barker|first8=Peter|last9=Mori|first9=Susumu|date=2012-10-01|title=Amygdala Atrophy in MCI/Alzheimer's Disease in the BIOCARD cohort based on Diffeomorphic Morphometry|journal=Medical Image Computing and Computer-assisted Intervention|volume=2012|pages=155–166|pmc=4063307|pmid=24955432}}</ref><ref>{{Cite journal|last1=Miller|first1=Michael I.|last2=Ratnanather|first2=J. Tilak|last3=Tward|first3=Daniel J.|last4=Brown|first4=Timothy|last5=Lee|first5=David S.|last6=Ketcha|first6=Michael|last7=Mori|first7=Kanami|last8=Wang|first8=Mei-Cheng|author8-link= Mei-Cheng Wang |last9=Mori|first9=Susumu|date=2015-01-01|title=Network neurodegeneration in Alzheimer's disease via MRI based shape diffeomorphometry and high-field atlasing|journal= Frontiers in Bioengineering and Biotechnology|
Shown in the accompanying Figure is an example of subcortical structure templates generated from T1-weighted [[Magnetic resonance imaging|magnetic resonance imagery]] by Tang et al.<ref name="Tang 599–611"/><ref name="Tang 2093–2117"/><ref name="Tang 645–660"/> for the study of Alzheimer's disease in the ADNI population of subjects.
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