A Hierarchical Mixed Effect Model for the Analysis of Model for the - PowerPoint PPT Presentation

A Hierarchical Mixed Effect Model for the Analysis of Model for the Analysis of Longitudinal DCE-MRI Studies Volker J. Schmid Department of Statistics Ludwig-Maximilians-University Munich L d i M i ili U i i M i h joint work with j Brandon Whitcher Clinical Imaging Centre GlaxoSmithKline, London, UK

Outline Outline • I t • Introduction d ti • Quantitative analysis of DCE-MRI • Standard analysis for longitudinal studies S d d l i f l i di l di • LoMIS model • Breast cancer study B d • Head and neck cancer study • Extensions Luebeck, 3.12.2009 # 2 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model DCE-MRI DCE MRI Breast cancer study Head&neck cancer study • Dynamic Contrast-Enhanced Magnetic Resonance Imaging • D i C t t E h d M ti R I i • Usually a contrast agent (Gd-DTPA) is injected to enhance perfusion i e the blood flow in tissue perfusion, i.e. , the blood flow in tissue • After injection several MR scans are acquired every 5-10 seconds seconds • In each voxel contrast concentration over time can be computed from the signal p g • Quantitative analysis is achieved by fitting pharmacokinetic models to the concentration curves Luebeck, 3.12.2009 # 3 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model DCE-MRI in oncology DCE MRI in oncology Breast cancer study Head&neck cancer study • Cancerous tissue typically has increased perfusion • C ti t i ll h i d f i • Growth of vessels can be initiated from the tumor (angiogenesis) (angiogenesis) • DCE-MRI allows to detect tumors, measure volume, diagnose cancer type evaluate status of tumor diagnose cancer type, evaluate status of tumor • Cancer treatment often targets angiogenesis ( inter alia ) • Hence success of treatment can be evaluated via DCE-MRI Hence, success of treatment can be evaluated via DCE MRI • Longitudinal drug studies, reduction is perfusion as target • Typically early phase 1 low patient numbers • Typically early phase 1, low patient numbers Luebeck, 3.12.2009 # 4 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model Data example Data example Breast cancer study Head&neck cancer study Luebeck, 3.12.2009 # 5 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies [image removed]

Introduction Standard analysis LoMIS model Data example Data example Breast cancer study Head&neck cancer study Luebeck, 3.12.2009 # 6 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies [image removed]

Introduction Standard analysis LoMIS model Compartment model Compartment model Breast cancer study Head&neck cancer study        trans C C t t v v C C t t C C t t K K k k t t ( ( ) ) ( ( ) ) ( ( ) ) exp( exp( ) ) t p p p ep Luebeck, 3.12.2009 # 7 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies [image removed]

Introduction Standard analysis LoMIS model Kinetic model & parameters Kinetic model & parameters Breast cancer study Head&neck cancer study        trans C C t t v v C C t t C C t t K K k k t t ( ( ) ) ( ( ) ) ( ( ) ) exp( exp( ) ) t p p p ep K trans : transfer rate between plasma space and EES, main target parameter k ep : rate constant for transfer between EES and space v e = K trans / k ep : volume of EES v p : volume of plasma space C p : Arterial input function (AIF), can be measured from large vessels in the field of view or given by literature Luebeck, 3.12.2009 # 8 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model Non linear regression Non-linear regression Breast cancer study Head&neck cancer study        trans C C t t v v C C t t C C t t K K k k t t ( ( ) ) ( ( ) ) ( ( ) ) exp( exp( ) ) t p p p ep • Given a functional form of the AIF, we can use non-linear , regression • Least squares algorithms like Levenberg-Marquardt suffer from a couple of problems: • Convergence is not guaranteed g g • Choice of starting values is crucial • Estimates can be biological unrealistic (K trans > 10) Luebeck, 3.12.2009 # 9 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model Bayesian non linear regression Bayesian non-linear regression Breast cancer study Head&neck cancer study        trans C C t t v v C C t t C C t t K K k k t t ( ( ) ) ( ( ) ) ( ( ) ) exp( exp( ) ) t p p p ep • As alternative we use a Bayesian approach: y pp log(K trans ) ~ N(0,1) log(k ep ) ~ N(0,1) g( ep ) ( , ) v p ~ Beta(1,19) • Estimation via MCMC • Estimates are more robust biological realistic Estimates are more robust, biological realistic Luebeck, 3.12.2009 # 10 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis K trans parameter maps LoMIS model K parameter maps Breast cancer study Head&neck cancer study Schmid, Whitcher, Padhani, Taylor, Yang, IEEE TMI (2006), 25:12, 1627-1636 Luebeck, 3.12.2009 # 11 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies [image removed]

Introduction Breast cancer study Standard analysis LoMIS model Data Data Breast cancer study Head&neck cancer study • E l • Early phase 1 study of breast cancer patients h 1 t d f b t ti t • 12 patients were scanned before treatment and two weeks after first treatment after first treatment • After the treatment six of these patients were identified as pathological responders the others were nonresponders pathological responders, the others were nonresponders • Regions of interest (ROIs) were drawn manually by an expert radiologist on a scan-by-scan basis g y Luebeck, 3.12.2009 # 12 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Breast cancer study Standard analysis LoMIS model Standard analysis Standard analysis Breast cancer study Head&neck cancer study Patien Patien Pre Pre Post Post  For each scan, an average time curve  F h ti t in the ROI was computed 1 0.208 0.161  A kinetic model was fitted to the  A kinetic model was fitted to the 2 2 0.355 0 3 0 120 0.120 averaged concentration 3 0.255 0.031  Change of K trans values between pre Change of K values between pre 4 4 0 230 0.230 0 245 0.245 treatment and post treatment scans is 5 0.199 0.208 tested via Wald test 6 0.154 0.173 7 0.264 0.327 8 0.198 0.223 p = 0.055 p 9 9 0.305 0 305 0 122 0.122 10 0.267 0.221 11 11 0 432 0.432 0.111 0 111 12 0.174 0.113 Luebeck, 3.12.2009 # 13 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model LoMIS model LoMIS model Breast cancer study Head&neck cancer study Id Idea of Longitudinal Medical Imaging Studies (LoMIS) model f L it di l M di l I i St di (L MIS) d l Model all curves in all tumor voxels of all scans • simultaneously simultaneously Incorporate information about patients and scans (pre/post) • similar to a mixed effect model , i e decompose kinetic similar to a mixed effect model , i.e. , decompose kinetic parameters in baseline, treatment, patient, interaction and voxel effect Hence, incorporate information about uncertainty in kinetic • parameters Use posterior of treatment effect to test for success of • treatment Use posterior of other effects to gain further insight • Luebeck, 3.12.2009 # 14 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Standard analysis LoMIS model Breast cancer study Head&neck cancer study Schmid, Whitcher, Padhani, Taylor, Yang, MRM (2009), 61, 163-174 Luebeck, 3.12.2009 # 15 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies [image removed]

Introduction Breast cancer study Standard analysis LoMIS model LoMIS model LoMIS model Breast cancer study Head&neck cancer study      trans C t v C t K C t tk e ( ) ( ) ( ) exp( ) t is p is p is p ep is tis , , ,           trans t T T K z x x log( ) is s i i s is ~ ~ ~ ~ ~                     T k k z z x x x x log( log( ) ) ep s i i s is      v v e e 2 2 2 ~ Beta eta ( ( 1 , , 19 9 ), ), ~ N N ( ( 0 0 , , ), ), ~ IG G ( ( 1 , , 10 0 ) ) p p tis tis s s s s     p p ( ) ( ) const.    γ 5 , ~ IG ( 1 , 1 ), ~ IG ( 1 , 10 ) i i is Luebeck, 3.12.2009 # 16 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

Introduction Breast cancer study Standard analysis LoMIS model Treatment effect Treatment effect Breast cancer study Head&neck cancer study p = 0.001 0 001 Luebeck, 3.12.2009 # 17 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies [image removed]