1. Microstructure Imaging Sequence Simulation Toolbox
MISST
Microstructure Imaging Sequence Simulation Toolbox
Ianuş, D. C. Alexander, I. Drobnjak
Centre for Medical Image Computing, University College London, London, UK
SASHIMI workshop, MICCAI, 21 Oct 2016 1

2. (cell size & shape, volume fraction)
Microstructure Imaging
Map of microscopic features from non-invasive imaging modalities, e.g. MRI
Diffusion MRI
Tissue models
Microscopic features
(cell size & shape, volume fraction)
ActiveAx – axon diameter index, CC
Alexander et al NeuroImage 2010
Potential biomarkers for diagnosing and monitoring various pathologies 2

3. Motivation
SDE
Standard diffusion acquisition – single diffusion encoding (SDE)
→ indices of axon diameter or cell radius, techniques such as AxCaliber, ActiveAx, VERDICT, etc
Recent work → advanced sequences improve sensitivity to various tissue features
Oscillating gradients
Double diffusion encoding
Q-space trajectory imaging
ActiveAx –
axon diameter index, CC
VERDICT –
cell radius map, prostate cancer
Alexander et al NeuroImage 2010
Panagiotaki et al Inv Radiology 2015

4. Why simulations?
Wide range of computational techniques to synthesize diffusion signal
Computational time
Complexity
Accuracy
Analytical models
Algebraic models
Numerical models

5. … … Previous work Example of algebraic methods:
Examples of numerical methods: …
Monte Carlo Simulations
Numerical solution to the
Diffusion PDE …

6. Limitations of available simulators
Limited options for the diffusion sequences
Limited choice of substrates
Long computational time
Source code is not always available
Why MISST?
Algebraic method
→ Signal is fast to compute
Fully flexible, user defined 3D gradient waveforms
Large variety of substrates, with modular construction a)
Implemented in Matlab for fast prototyping
Open source

7. Theoretical background
Diffusion contrast – achieved by applying magnetic field gradients
The phase acquired by each spin is:
The diffusion signal decay is given by the ensemble average:
Free diffusion
Gradient with fixed orientation
Gradient with varying orientation – requires a tensor form

8. Theoretical background
Restricted diffusion
3D extension of matrix method (Callaghan 1995, Drobnjak 2011),
based on a multi-propagator approach
Gradient waveform is discretized and approximated as:
infinitesimal gradient impulses that change the phase of the spins
“empty” time intervals during which the spins diffuse 
these events can be represented by matrix operators, which depend on the restriction:
q = 1/2π Gstepτ, where Gstep is describes the discretization in gradient amplitude and τ the discretization in time
D – diffusivity, u and λ – eigenfunctions and eigenvalues of the diffusion equation in the restricted geometry
Diffusion signal can be written as a succession of such events:
Phase evolution,
Diffusion evolution,
with m2 = G2/Gstep

9. Theoretical background
Restricted diffusion
3D extension of matrix method (Callaghan 1995, Drobnjak 2011),
based on a multi-propagator approach.
Gradient waveform is discretized (in time and amplitude) and approximated as:
infinitesimal gradient impulses that change the phase of the spins
“empty” time intervals during which the spins diffuse 
these events can be represented by matrix operators, which depend on the restriction: f
q = 1/2π Gstepτ, where Gstep is describes the discretization in gradient amplitude and τ the discretization in time
D – diffusivity, u and λ – eigenfunctions and eigenvalues of the diffusion equation in the restricted geometry
Phase evolution,
Diffusion evolution,

10. Theoretical background
Matrix method signal: Gτ
Gstep
Diffusion signal:
m2 = G2/Gstep, where Gstep is the amplitude of the gradient step

11. Theoretical background
Tissue models
Diffusion signal – weighted sum over different compartments:
Example waveforms for the most common diffusion sequences (single diffusion encoding, oscillating gradient, double diffusion encoding, etc)
Implementation overview

12. Signal validation Aim: compare the MISST generated signal
Tissue substrate
Aim: compare the MISST generated signal
with MC simulations (Camino, Hall et al TMI 2009).
Diffusion substrates of parallel cylinders
Simulation 1
50 random gradient waveforms
Simulation 2
Double diffusion encoding sequences
which vary the angle between the gradients
Results:
signal difference is less than 0.3%
signal is much faster to compute (~ 2 orders of magnitude)

13. Signal validation Simulation 2: Results:
Double diffusion encoding sequences which vary the angle between the gradients
Results:
signal difference between the two methods is less than 0.3%
signal is much faster to compute (~ 2 orders of magnitude)

14. Signal features Simulation 3: Results:
Investigate the diffusion-diffraction patterns of restricted diffusion when increasing G
Results:
Signal shows the well known diffusion-diffraction patterns
Simple analytical models, e.g. Gaussian Phase Distribution approximation, cannot (e.g Balinov 1993)

15. Possible applications – Example 1
Compare the sensitivity of different sequences to features such as axon diameter
Key points:
ODE (N > 1) sequences are more sensitive to axon diameter than SDE sequences (N = 1) in realistic cases of unknown fibre orientation and/ or fibre dispersion (Drobnjak MRM 2015)
SDE
ODE

16. Possible applications – example 2
Analyze the contrast of novel sequences:
Double Oscillating Diffusion Encoding (DODE)
Substrates:
randomly oriented anisotropic pores
Key points:
Signal modulation -> marker of microscopic anisotropy, yet the amplitude varies with frequency
Ianus et al MRM 2016

17. Discussion MISST software packages Limitations
Simulates diffusion signal from a variety of sequences and substrates
Fully flexible user defined waveforms
Algebraic method - 3D extension of the matrix formalism.
Accurate and fast signal computation
Limitations
Simple geometries
Modelling membrane permeability and exchange
Extracellular space → add analytical models
Open source & available for download:

18. Thank you!

19. Questions?

20. Theoretical background
Matrix method signal: Gτ
Gstep
Diffusion signal:
m2 = G2/Gstep, where Gstep is the amplitude of the gradient step