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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

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SLIDE 1

A Hierarchical Mixed Effect Model for the Analysis of Model for the Analysis of Longitudinal DCE-MRI Studies

Volker J. Schmid

Department of Statistics L d i M i ili U i i M i h Ludwig-Maximilians-University Munich joint work with j

Brandon Whitcher

Clinical Imaging Centre GlaxoSmithKline, London, UK

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SLIDE 2

Outline Outline

  • I t

d ti

  • Introduction
  • Quantitative analysis of DCE-MRI

S d d l i f l i di l di

  • Standard analysis for longitudinal studies
  • LoMIS model

B d

  • Breast cancer study
  • Head and neck cancer study
  • Extensions

# 2 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 3

DCE-MRI

Introduction Standard analysis LoMIS model Breast cancer study

DCE MRI

  • D

i C t t E h d M ti R I i

Head&neck cancer study

  • Dynamic Contrast-Enhanced Magnetic Resonance Imaging
  • 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

# 3 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 4

DCE-MRI in oncology

Introduction Standard analysis LoMIS model Breast cancer study

DCE MRI in oncology

  • C

ti t i ll h i d f i

Head&neck cancer study

  • Cancerous tissue typically has increased perfusion
  • 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

# 4 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 5

Data example

Introduction Standard analysis LoMIS model Breast cancer study

Data example

Head&neck cancer study

# 5 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 6

Data example

Introduction Standard analysis LoMIS model Breast cancer study

Data example

Head&neck cancer study

# 6 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 7

Compartment model

Introduction Standard analysis LoMIS model Breast cancer study

Compartment model

Head&neck cancer study

) exp( ) ( ) ( ) ( t k K t C t C v t C

trans

  

# 7 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

) exp( ) ( ) ( ) ( t k K t C t C v t C

ep p p p t

   

[image removed]

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SLIDE 8

Kinetic model & parameters

Introduction Standard analysis LoMIS model Breast cancer study

Kinetic model & parameters

) exp( ) ( ) ( ) ( t k K t C t C v t C

trans

   

Head&neck cancer study

Ktrans: transfer rate between plasma space and EES, main target

) exp( ) ( ) ( ) ( t k K t C t C v t C

ep p p p t

  

parameter kep: rate constant for transfer between EES and space ve = Ktrans / kep: volume of EES vp: volume of plasma space Cp: Arterial input function (AIF), can be measured from large vessels in the field of view or given by literature

# 8 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 9

Non-linear regression

Introduction Standard analysis LoMIS model Breast cancer study

Non linear regression

) exp( ) ( ) ( ) ( t k K t C t C v t C

trans

   

Head&neck cancer study

  • Given a functional form of the AIF, we can use non-linear

) exp( ) ( ) ( ) ( t k K t C t C v t C

ep p p p t

  

, 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 (Ktrans > 10)

# 9 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 10

Bayesian non-linear regression

Introduction Standard analysis LoMIS model Breast cancer study

Bayesian non linear regression

) exp( ) ( ) ( ) ( t k K t C t C v t C

trans

   

Head&neck cancer study

  • As alternative we use a Bayesian approach:

) exp( ) ( ) ( ) ( t k K t C t C v t C

ep p p p t

  

y pp log(Ktrans) ~ N(0,1) log(kep) ~ N(0,1) g( ep) ( , ) vp ~ Beta(1,19)

  • Estimation via MCMC
  • Estimates are more robust biological realistic

Estimates are more robust, biological realistic

# 10 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 11

Ktrans parameter maps

Introduction Standard analysis LoMIS model Breast cancer study

K parameter maps

Head&neck cancer study

# 11 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies Schmid, Whitcher, Padhani, Taylor, Yang, IEEE TMI (2006), 25:12, 1627-1636

[image removed]

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SLIDE 12

Breast cancer study Data

Introduction Standard analysis LoMIS model Breast cancer study

Data

  • E l

h 1 t d f b t ti t

Head&neck cancer study

  • Early phase 1 study of breast cancer patients
  • 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

# 12 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 13

Breast cancer study Standard analysis

Introduction Standard analysis LoMIS model Breast cancer study

Standard analysis

  • F

h ti

Patien Pre Post

Head&neck cancer study

  • For each scan, an average time curve

in the ROI was computed

  • A kinetic model was fitted to the

Patien t Pre Post 1 0.208 0.161 2 0 3 0 120

  • A kinetic model was fitted to the

averaged concentration

  • Change of Ktrans values between pre

2 0.355 0.120 3 0.255 0.031 4 0 230 0 245

Change of K values between pre treatment and post treatment scans is tested via Wald test

4 0.230 0.245 5 0.199 0.208 6 0.154 0.173

p = 0.055

7 0.264 0.327 8 0.198 0.223 9 0 305 0 122

p

9 0.305 0.122 10 0.267 0.221 11 0 432 0 111

# 13 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

11 0.432 0.111 12 0.174 0.113

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SLIDE 14

LoMIS model

Introduction Standard analysis LoMIS model Breast cancer study

LoMIS model Id f L it di l M di l I i St di (L MIS) d l

Head&neck cancer study

Idea of Longitudinal Medical Imaging Studies (LoMIS) model

  • 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

# 14 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

  • Use posterior of other effects to gain further insight
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SLIDE 15

Introduction Standard analysis LoMIS model Breast cancer study Head&neck cancer study

# 15 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies Schmid, Whitcher, Padhani, Taylor, Yang, MRM (2009), 61, 163-174

[image removed]

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SLIDE 16

Breast cancer study LoMIS model

Introduction Standard analysis LoMIS model Breast cancer study

LoMIS model

Head&neck cancer study

) exp( ) ( ) ( ) (

, , ,

    

T t tis is ep p trans is p is p is t

e tk t C K t C v t C ~ ~ ~ ~ ~ ) log( ) log(          

T is s i i s T trans is

x x z k x x z K           ) 10 , 1 ( IG ~ ), , ( N ~ ), 19 , 1 ( Beta ~ ) log(

2 2 2 

    

s s tis p is s i i s ep

e v x x z k        const. ) ( ) ( ) , ( G ), , ( N ), 9 , ( eta  

s s tis p

p p e v     ) 10 , 1 ( IG ~ ), 1 , 1 ( IG ~ ,

5  is i i

γ  

# 16 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 17

Breast cancer study Treatment effect

Introduction Standard analysis LoMIS model Breast cancer study

Treatment effect

Head&neck cancer study

0 001

# 17 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

p = 0.001

[image removed]

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SLIDE 18

Breast cancer study Patient/interaction effect

Introduction Standard analysis LoMIS model Breast cancer study

Patient/interaction effect

Head&neck cancer study

# 18 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 19

Breast cancer study Ktrans per voxel

Introduction Standard analysis LoMIS model Breast cancer study

K per voxel

Head&neck cancer study

# 19 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 20

Head and neck cancer study

Introduction Standard analysis LoMIS model Breast cancer study

Head and neck cancer study

  • Ni

ti t ith t i h d k

Head&neck cancer study

  • Nine patients with tumor in head or neck area
  • Two sites (Royal Marsden Hospital, London, Vall d’Hebron

University Hospital Barcelona) with different scanners University Hospital, Barcelona) with different scanners

  • Placebo (n=6) and treatment (n=3) group
  • Vessels were present in images and a population AIF was
  • Vessels were present in images and a population AIF was

computed

  • Regions of interest were drawn by an expert radiologist

Regions of interest were drawn by an expert radiologist

# 20 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 21

Head and Neck cancer study Ktrans map

Introduction Standard analysis LoMIS model Breast cancer study

K map

Head&neck cancer study

# 21 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 22

Head and Neck Cancer study LoMIS results 1

Introduction Standard analysis LoMIS model Breast cancer study

LoMIS results 1

Head&neck cancer study

p = 0 30 p = 0.30

# 22 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies Whitcher, Schmid, Collins, Orton, Koh et al., MRI 2010 (accepted)

[image removed]

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SLIDE 23

Head and Neck Cancer study LoMIS results 2

Introduction Standard analysis LoMIS model Breast cancer study

LoMIS results 2

Head&neck cancer study

# 23 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 24

Head and Neck Cancer study LoMIS results 3

Introduction Standard analysis LoMIS model Breast cancer study

LoMIS results 3

Head&neck cancer study

# 24 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 25

Head and Neck Cancer study LoMIS results 4

Introduction Standard analysis LoMIS model Breast cancer study

LoMIS results 4

Head&neck cancer study

# 25 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

[image removed]

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SLIDE 26

MCMC

Introduction Standard analysis LoMIS model Breast cancer study

MCMC

  • U d t

f i d ff t i ( lti i t G i )

Head&neck cancer study

  • Update of mixed effects is easy (multivariate Gaussian)
  • Update of voxel effects is ugly, similar to update of log(Ktrans)

and log(k ) and log(kep)

 

) exp( ) exp( exp .) | (

5 4 2 3 2 2 1

    c c c c c p    

  • Lot of data:

 

  • 1000 – 10000 voxel per scan
  • 40 – 50 time points per scan

p p

  • ~ 1 – 2 million data points

# 26 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 27

Extensions

Introduction Standard analysis LoMIS model Breast cancer study

Extensions

  • T

t t t (t i ll d t l t li bilit )

Head&neck cancer study

  • Two pre treatment scans (typically used to evaluate reliability)
  • Two or more post treatment scans, gain time line for

treatment effect treatment effect

  • Use clinical covariates or genetic expression
  • Extensions can easily be included into the mixed effect model
  • Extensions can easily be included into the mixed effect model
  • U

m d l n th r im in m d liti

  • Use model on other imaging modalities

# 27 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 28

Conclusions

Introduction Standard analysis LoMIS model Breast cancer study

Conclusions

  • DCE MRI

b d t l t t t t

Head&neck cancer study

  • DCE-MRI can be used to evaluate treatment success
  • Scans are expensive, patient numbers are small

S d d l i l i f i i l l l

  • Standard analysis neglects information given on voxel level
  • Mixed effect models can be used to evaluate treatment effect

W d l ll i i ll l f

  • We propose to model all concentration curves in all voxels of

all scans simultaneously

  • Tr

tm nt ff t n b t t d fr m p t ri r p r f t t

  • Treatment effect can be tested from posterior – power of test

is higher

  • We gain further insight in patient/treatment interaction and
  • We gain further insight in patient/treatment interaction and

can account for covariates

# 28 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 29

Acknowledgments Acknowledgments

  • B

d Whit h Cli i l I i C t GSK

  • Brandon Whitcher, Clinical Imaging Centre, GSK
  • Guang-Zhong Yang, Institute of Biomedical Engineering,

Imperial College London UK Imperial College London, UK

  • Anwar Padhani, Jane Taylor, Mt Vernon Hospital,

Northwood UK Northwood, UK

  • David Collins, Matt Orton, Dow-Mu Koh, Institute of

Cancer Research UK

  • Teams at Royal Marsden Hospital and Vall d’Hebron

University Hospital y p

  • BioMed-S: Analysis and modelling of complex systems in

biology and medicine (part of the LMUinnovativ initiative)

# 29 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies

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SLIDE 30

References References

  • Schmid V J et al : Bayesian methods for pharmacokinetic models in
  • Schmid, V.J. et al.: Bayesian methods for pharmacokinetic models in

dynamic contrast-enhanced magnetic resonance imaging. IEEE Transactions on Medical Imaging 25 (2006) 1627-1636

  • Schmid, V.J., et al.: A Bayesian Hierarchical Model for the Analysis of a

Longitudinal Dynamic Contrast-Enhanced MRI Cancer Study. Magnetic Resonance in Medicine 61 (2009) 163-174 ( )

  • Whitcher, B., et al.: A Bayesian Hierarchical Model for Dynamic Contrast-

Enhanced MRI in a Phase II Study in Advanced Squamous Cell Carcinoma of the Head and Neck Submitted to Magnetic Resonance Imaging Carcinoma of the Head and Neck. Submitted to Magnetic Resonance Imaging

Thank you for your attention! Thank you for your attention!

# 30 Luebeck, 3.12.2009 V.J. Schmid: Hierachical MEM for longitudinal DCE-MRI studies