UnwarpingUnwarping

In order to assign an observed response to a particular brain structure, or cortical area, the data must conform to a known anatomical space.

In order to combine data from different scans from the same subject, or data from different subjects it is necessary that they conform to the same anatomical frame of reference.

Voxel-based analyses assume that the data from a particular voxel all derive from the same part of the brain.  Violations of this assumption will introduce artifactual changes in the voxel values that may obscure changes, or differences, of interest. E.g. if movement of the subject in the scanner pushes a voxel from an area of low to high signal, this may register as a false-positive ‘activation’.

Assumptions of statistical tests in functional imaging

Pre-processing steps to cope with violations of Pre-processing steps to cope with violations of these assumptionsthese assumptions

All scans must conform to the same anatomical frame of reference: Realign the data to 'undo' the effects of subject movement during the scanning session. 

Data must conform to a known anatomical space: After realignment the data are then transformed using linear or nonlinear warps into a standard anatomical space. 

Finally, the data are usually spatially smoothed before entering the analysis proper.

Pre-processing steps to cope with violations of Pre-processing steps to cope with violations of these assumptionsthese assumptions

All scans must conform to the same anatomical frame of reference: Realign the data to 'undo' the effects of subject movement during the scanning session. 

!UNWARP!

Data must conform to a known anatomical space: After realignment the data are then transformed using linear or nonlinear warps into a standard anatomical space. 

Finally, the data are usually spatially smoothed before entering the analysis proper.

Errors after realignmentErrors after realignment

After realignment, there can be residual errors in images for a After realignment, there can be residual errors in images for a number of reasons.number of reasons.

The residual variance can be dealt with by assuming that it is The residual variance can be dealt with by assuming that it is related to subject movement.related to subject movement.

One way is to account for subject movement in the design matrix of One way is to account for subject movement in the design matrix of the analysis proper, by including the movement parameters the analysis proper, by including the movement parameters estimated from re-alignment as covariates.estimated from re-alignment as covariates.

Covarying for movement-related errors after Covarying for movement-related errors after realignmentrealignment

However, this may remove activations of interest if they are However, this may remove activations of interest if they are correlated with movementcorrelated with movement

tmax=13.38

No correction

tmax=5.06

Correction by covariation

Problems with covariationProblems with covariationCovariation using movement parameters assumes only rigid Covariation using movement parameters assumes only rigid deformation of the image between scans.deformation of the image between scans.

BUT: images are sampled according to gradients of the magnetic BUT: images are sampled according to gradients of the magnetic field B, in 3 image dimensions. field B, in 3 image dimensions.

ωω = = γγBBωω = resonant frequency B = magnetic field strength = resonant frequency B = magnetic field strength

By applying a gradient field across BBy applying a gradient field across B00, B varies according to , B varies according to position. There will only be one position at which position. There will only be one position at which 11H spins are H spins are precessing at a particular resonant frequency, so can assign precessing at a particular resonant frequency, so can assign resultant signal to this location.resultant signal to this location.

Signals are assigned in 3 image dimensions by applying field Signals are assigned in 3 image dimensions by applying field gradients across Bgradients across B00 in 3 dimensions. in 3 dimensions.

yy z z BB00+G+Gzzzz

BB00 BB00 BB00

BB00-G-Gxxxx x B x B00+G+Gxxxx

BB00-G-Gzzzz

Non-rigid deformationNon-rigid deformationKnowing the location at which Knowing the location at which 11H spins will precess at a particular frequency and H spins will precess at a particular frequency and thus where the signal comes from is dependent upon correctly assigning a thus where the signal comes from is dependent upon correctly assigning a particular field strength to a particular location.particular field strength to a particular location.

If the field BIf the field B00 is homogeneous, then the image is sampled according to a regular is homogeneous, then the image is sampled according to a regular grid and voxels can be localised to the same bit of brain tissue over subsequent grid and voxels can be localised to the same bit of brain tissue over subsequent scans by realigning, this is because the same transformation is applied to all voxels scans by realigning, this is because the same transformation is applied to all voxels between each scan.between each scan.

If there are inhomogeneities in BIf there are inhomogeneities in B00, then different deformations will occur at different , then different deformations will occur at different points in the field over different scans, giving rise to non-rigid deformation.points in the field over different scans, giving rise to non-rigid deformation.

BB00 Expect field strength to be BExpect field strength to be B00 here, so H atoms with signal associated here, so H atoms with signal associated with resonant frequency with resonant frequency ωω00 to be located to be locatedhere.here.In fact, because of inhomogeneity, they are In fact, because of inhomogeneity, they are here.here.

Field inhomogeneitiesField inhomogeneitiesDue to microscopic gradients or variations in magnetic field Due to microscopic gradients or variations in magnetic field strengths that occur at interfaces of substances of different strengths that occur at interfaces of substances of different magnetic susceptibility. E.g., metallic material (ferromagnetic) and magnetic susceptibility. E.g., metallic material (ferromagnetic) and the human body (diamagnetic).the human body (diamagnetic).

Also occurs close to tissue-air and tissue-bone interfaces such as Also occurs close to tissue-air and tissue-bone interfaces such as around frontal sinuses.around frontal sinuses.

Field inhomogeneities have the effect that locations on the image Field inhomogeneities have the effect that locations on the image are ‘deflected’ with respect to the real object.are ‘deflected’ with respect to the real object.

A A deformation fielddeformation field indicates the indicates the directions and magnitudes of directions and magnitudes of location deflections throughout the location deflections throughout the FOV with respect to the real object.FOV with respect to the real object.

igl.stanford.edu/~torsten/ct-dsa.html

Movement-by-inhomogeneity interactionsMovement-by-inhomogeneity interactions

Field inhomogeneities change with the position of the object in the Field inhomogeneities change with the position of the object in the field, so there can be non-rigid, as well as rigid distortion over field, so there can be non-rigid, as well as rigid distortion over subsequent scans.subsequent scans.

The movement-by-inhomogeneity interaction can be observed by The movement-by-inhomogeneity interaction can be observed by changes in the deformation field over subsequent scans.changes in the deformation field over subsequent scans.

The amount of distortion is proportional to the absolute value of the field The amount of distortion is proportional to the absolute value of the field inhomogeneity and the data acquisition time. EPI is particularly sensitive inhomogeneity and the data acquisition time. EPI is particularly sensitive to the effects of magnetic field inhomogeneities because it has long TRto the effects of magnetic field inhomogeneities because it has long TR

Controlling for movement-by-inhomogeneity Controlling for movement-by-inhomogeneity interactionsinteractions

One solution is to explicitly measure field inhomogeneity by use One solution is to explicitly measure field inhomogeneity by use of a of a field-map field-map (available in the “FieldMap” SPM toolbox). (available in the “FieldMap” SPM toolbox). A field A field map then has to be generated for each scan in the time-series.map then has to be generated for each scan in the time-series.

Measurement of field-maps is complicated by noise, and rapid Measurement of field-maps is complicated by noise, and rapid loss of signal towards the edges of the object. loss of signal towards the edges of the object.

In practice, rather than generating a statistical field map for every In practice, rather than generating a statistical field map for every image in the EPI data set, can compute how the statistical maps image in the EPI data set, can compute how the statistical maps are warped over subsequent scans and then unwarp the are warped over subsequent scans and then unwarp the statistical map itself in order to make accurate identification of statistical map itself in order to make accurate identification of activated areas.activated areas.Computing how the images are warped over subsequent scans Computing how the images are warped over subsequent scans requires knowing how the deformation fields change with requires knowing how the deformation fields change with displacement of the subject, i.e. the derivatives of B with respect displacement of the subject, i.e. the derivatives of B with respect to displacement of the subject.to displacement of the subject.

Principles of UNWARPPrinciples of UNWARP

Given the derivative of the field with respect to subject movement, Given the derivative of the field with respect to subject movement, and the movement parameters estimated from realignment, can and the movement parameters estimated from realignment, can predict the non-rigid deformation in the scan series.predict the non-rigid deformation in the scan series.

In practice, we know the non-rigid deformation (in terms of extra In practice, we know the non-rigid deformation (in terms of extra variance after realignment) and the subject movement (movement variance after realignment) and the subject movement (movement parameters) so we can estimate the derivatives of the field Bparameters) so we can estimate the derivatives of the field B0 0 with with

respect to subject movementrespect to subject movement – thus estimate how the field is – thus estimate how the field is

warped over the time series and ‘undo’ this using UNWARP.warped over the time series and ‘undo’ this using UNWARP.

Movements modelled in UNWARPMovements modelled in UNWARP

Translations and rotations in plane perpendicular to BTranslations and rotations in plane perpendicular to B00 will not affect B will not affect B00, , so only need to model derivatives of Bso only need to model derivatives of B00 with respect to rotations out of with respect to rotations out of perpendicular plane, i.e. pitching and rolling perpendicular plane, i.e. pitching and rolling , ..

xx

BB00

y y

z

In UNWARP there is a (default) option to re-estimate the movement In UNWARP there is a (default) option to re-estimate the movement parameters with each unwarp iteration. This is recommended by John parameters with each unwarp iteration. This is recommended by John Ashburner. It is computed via a series of iterations; 1. estimate Ashburner. It is computed via a series of iterations; 1. estimate movement parameters (movement parameters (, ), 2. estimate ), 2. estimate deformation fieldsdeformation fields, , BB0, 0, 3. 3. re-estimate movement with new model of magnetic field Bre-estimate movement with new model of magnetic field B00

Modelling changes in BModelling changes in B00

The field BThe field B00, which changes as a function of displacement , which changes as a function of displacement , , , can be modelled by the first two terms of a Taylor expansioncan be modelled by the first two terms of a Taylor expansion

BB00((, ) = B) = B00 ( (, ) + [() + [(δδBB00/ / δδ) + ( (δδBB00/ / δδ ) ) ]]

The ‘static’ deformation field, The ‘static’ deformation field, Changes in the deformation field withChanges in the deformation field withWhich is the same throughout subject movement. Estimated via iteration Which is the same throughout subject movement. Estimated via iteration The time series.The time series. Procedure in UNWARP.Procedure in UNWARP.Calculated using ‘Fieldmap’ inCalculated using ‘Fieldmap’ inSPMSPMIt is possible to model the next term in the Taylor expansion as well, i.e. the It is possible to model the next term in the Taylor expansion as well, i.e. the

second derivative of B with respect to second derivative of B with respect to , , , but this is not necessary.but this is not necessary.

Applying the deformation field to the imageApplying the deformation field to the image

Once the deformation field has beenmodelled over time, the time-variantfield is applied to the image. effect of sampling a regular object over a curved surface.

The image is therefore re-sampled assuming voxels, corresponding to the same bits of brain tissue, occur at different locations over time.

Advantages of incorporating this in pre-Advantages of incorporating this in pre-processingprocessing

One could include the movement parameters as confounds in the One could include the movement parameters as confounds in the statistical model of activations.statistical model of activations.

However, this may remove activations of interest if they are However, this may remove activations of interest if they are correlated with the movement.correlated with the movement.

tmax=13.38

No correction

tmax=5.06

Correction by covariation

tmax=9.57

Correction by Unwarp

UNWARP: Benefits and LimitationsUNWARP: Benefits and LimitationsAlthough for small movements a limited portion of the total variance is Although for small movements a limited portion of the total variance is removed, the susceptibility-by-movement interaction effects are quite removed, the susceptibility-by-movement interaction effects are quite localised to "problem" areas. For a subset of voxels in e.g. frontal-medial and localised to "problem" areas. For a subset of voxels in e.g. frontal-medial and orbitofrontal cortices and parts of the temporal lobes the reduction can be orbitofrontal cortices and parts of the temporal lobes the reduction can be quite dramatic (>90%).quite dramatic (>90%).

HoweverHowever, UNWARP only tackles one source of variance after re-alignment, , UNWARP only tackles one source of variance after re-alignment, and other errors may arise from:and other errors may arise from:

- - Susceptibility-dropout-by-movement interaction: Field inhomogeneities can also cause signal loss Susceptibility-dropout-by-movement interaction: Field inhomogeneities can also cause signal loss due to through-plane dephasing (which will not be rephased by encoding gradients that are all in-due to through-plane dephasing (which will not be rephased by encoding gradients that are all in-plane).plane).

- - Spin-history effects: The signal will depend on how much longitudinal magnetisation has recovered Spin-history effects: The signal will depend on how much longitudinal magnetisation has recovered (through T1 relaxation) since it was last excited (short TR→low signal). If the subject moves in the (through T1 relaxation) since it was last excited (short TR→low signal). If the subject moves in the direction of increasing slice number between one excitation and the next, then the effective TR direction of increasing slice number between one excitation and the next, then the effective TR will be longer (resulting in increasing signal intensity). will be longer (resulting in increasing signal intensity).

- Slice-to-vol effects: The rigid-body model that is used by most motion-correction (e.g. SPM) - Slice-to-vol effects: The rigid-body model that is used by most motion-correction (e.g. SPM) methods assume that any movement will occur between scans. However there is also movement methods assume that any movement will occur between scans. However there is also movement within scans – leading to further apparent shape changes. within scans – leading to further apparent shape changes.

SummarySummaryMovement-by-inhomogeneity interactions can be accommodated during Movement-by-inhomogeneity interactions can be accommodated during realignment using “realignment using “unwarpunwarp” in SPM5” in SPM5

WARNING!!WARNING!! UNWARP can be computationally intensive, and therefore take UNWARP can be computationally intensive, and therefore take a long time!a long time!

Jezzard, P. and Clare, S. 1999. Sources of distortion in functional MRI Jezzard, P. and Clare, S. 1999. Sources of distortion in functional MRI data. data. Human Brain Mapping, Human Brain Mapping, 8:80-858:80-85

Andersson JLR, Hutton C, Ashburner J, Turner R, Friston K (2001) Andersson JLR, Hutton C, Ashburner J, Turner R, Friston K (2001) Modelling geometric deformations in EPI time series. Modelling geometric deformations in EPI time series. Neuroimage Neuroimage 13: 903-91913: 903-919

John Ashburner’s slides John Ashburner’s slides http://www.fil.ion.ucl.ac.uk/spm/course/#slideshttp://www.fil.ion.ucl.ac.uk/spm/course/#slides

Paul Tofts’ MRI Physics Course at the IoN (slides not yet on the web – Paul Tofts’ MRI Physics Course at the IoN (slides not yet on the web – TBA)TBA)

References