isbe-astrazeneca strategic alliance project # 42 modelling dce-mri arterial input functions in rats...

ISBE-AstraZeneca Strategic Alliance Project # 42

Modelling DCE-MRI Arterial Input Functions in rats

Deirdre McGrath,Strategic Alliance meeting 1st July 2005


Project Aim

• Identify a suitable model function of the population of Arterial Input Functions (AIFs) acquired in DCE-MRI studies of rats at Alderley Park

• Develop an approach to parameterise this function on new data


Initial data set


Example AIFs


Signals from tumours


Solve for DCE-MRI Kinetic Parameters • Using extended Kety Model:

t

e

trans

AIFtrans

AIFptissue duutV

KuCKtCVtC0

).(exp).()(.)(

Where:•Ctissue is the concentration of contrast agent in the tissue •CAIF that in the artery•Vp fractional blood plasma volume•Ktrans volume transfer constant•Ve fractional extravascular, extracellular space (EES) volume


Possible Approaches

• Approach 1: Develop analytical model to fit populationCandidates:

– Exponential– Linear peak followed by exponential– Gamma-variate, the log normal function or the lagged

normal density curve– Sum of 2 Gaussians + exponential modulated by sigmoid:(Parker et al, ISMRM, 2005)

2

12

2

)))(exp(1()exp(

2)(

exp2

)(n n

n

n

nb ts

tTtAtC


Possible Approaches contd.

• Approach 2: generate a model based on Principal Component Analysis (PCA):

» Generate a Point Distribution Model (PDM) (Bookstein, 1991)

» Using the Minimum Description Length (MDL) correspondence points (Davies et al, IEEE Trans Med Img, 2002)

» Limit modes of variation to remove effects of noise ->Either new data sets are projected onto first N axes of PDM to

get noise reduced AIF ->Or calculate Maximum Likelihood mode coefficients

-> Output noise reduced (and possibly higher resolution) AIF

-> Could potentially correlate physiology with PDM modes to generate simulated AIFs


Approach 1: Fit Analytical Model• Sum of 2 Gaussians + exponential modulated by sigmoid


Reproducibility of extended Kety model parameters

meanmsdwCV

2

AIF input wCV Vp wCV Ktrans wCV Ve Raw AIF data 0.8434 0.7569 0.9972 Analytical fit of overall mean AIF 0.5816 0.6202 0.8805 Analytical fit of individual AIFs 0.8727 0.8435 1.1176

Calculated the within-subject coefficient of variation, wCV (Galbraith et al, NMR Biomed, 2002)

nd

msd 2

Where msd is the mean squared difference and mean the overall mean for the parameter

And d is the difference in parameters between scans and n the number of subjects


Approach 2: Generate PDM• Generate a Point Distribution Model (PDM) using raw data as training set. • Out of 27 modes, 20 have a significant influence


Remove noise using Analytical Fit

• Performing a pre-fit of the data to remove noise• Reduces no. of significant modes to 8


Future direction

• Optimisation of automatically generated MDL

• Manually registered MDLs

• Correlation of physiological factors with PDM modes

• Use Factor Analysis as opposed to PCA – can better handle noisy input

• Reproducibility study incorporating all AIF models, including simpler models (exponential etc.)

isbe-astrazeneca strategic alliance project # 42 modelling dce-mri arterial input functions in rats...

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