The spatiotemporal evolution of stroke lesions, from acute injury to final tissue damage, is complex. Diffusion-weighted (DWI) and perfusion-weighted (PWI) imaging is commonly used to detect early ischemic changes and attempts to distinguish between permanently damaged and salvageable tissues. To date, 2D and 3D measures of diffusion/perfusion regions at individual timepoints have been widely used but may underestimate the true lesion spatio-temporal dynamics. Currently there is no spatio-temporal 4D dynamic model that simulates the continuous evolution of ischemic stroke from MR images. We determined whether a 4D current-based diffeomorphic model, developed in the field of statistical modeling for measuring the variability of anatomical surfaces, could estimate patient-specific spatio-temporal continuous evolution for MR PWI (measured as mean transit time, (MTT)) and DWI lesions. In our representative pilot sample, the model fitted the data well. Our dynamic analysis of lesion evolution showed different patterns; for example, some DWI/PWI dynamic changes corresponded with DWI lesion expansion into PWI lesions, but other patterns were much more complex and diverse. There was wide variation in the time when the final tissue damage was reached after stroke for DWI and MTT.
Stroke is the third leading cause of death in industrialized countries [
Numerous medical image analysis approaches have been applied to DWI and/or PWI data using 2D or 3D approaches to determine how the ischemic stroke lesions evolve and what factors influence this. Most of these studies evaluated MR (or CT) images of ischemic stroke as static “snapshots” to predict tissue prognosis and its association with clinical outcome [
MTT-DWI mismatch at first acquisition acute timepoint
One explanation for this variation in behavior in DWI and PWI lesions is that methods examining large regions of interest or even voxel-by-voxel-based analyses may not adequately capture the dynamic changes occurring between individual timepoints and their relationship to anatomically important brain regions. A mathematically well-defined 4D dynamic model may help overcome these limitations by providing more detailed and anatomically relevant information on stroke evolution. There is currently no 4D dynamic model available that simulates the continuous evolution of ischemic stroke based on MR or other image types [
To capture the individual differences and enable a model that is as patient specific as possible, we chose a 4D spatiotemporal approach that captures individual differences independent of clinical factors such as stroke severity, the effected vascular territory, or the location of the occluded artery and that did not require any information except for the DWI and PWI lesion outlines. The model is described in detail in the methods section. We used the model to address three aspects of stroke lesion evolution where imaging could provide valuable insight.
Firstly, we modeled individual DWI and PWI lesion dynamic changes separately to identify subregional differences in expansion and contraction of the respective DWI and PWI lesions and determined how well the model fitted the true lesion evolution as represented by the original image data.
Secondly, we explored the pattern of change in the DWI and PWI lesions in relation to each other in individual patients, imputed to 3 hourly time intervals, from the three acquired imaging snapshots spaced many days apart.
Thirdly, we investigated the models prognostic potential by identifying the timepoint at which the PWI/DWI lesions best matched the final observed T2 lesion as an indicative estimate of the “final” lesion damage.
Finally, we would like to emphasize that the aims of the present work were to (a) demonstrate that 4D modeling was possible in stroke, (b) identify the limitations to this approach and potential solutions, and (c) demonstrate the considerable potential for the 4D modeling in advancing our understanding of the dynamics of ischemic stroke lesion evolution.
In order to apply and test this model, we selected eight representative patients (5 males, 3 females) from a study of MR imaging in hyperacute stroke of original sample size 48. Primary study methods were previously described [
All MR images were acquired using a GE Signa LX 1.5-T MR scanner (General Electric, Milwaukee, WI, USA) with a birdcage quadrature coil and a standardised protocol for acute stroke [
A wide range of mathematical studies have focused on computing differences between consecutive scans of the same subject or objects and extracting key features to compare them, for example, to a population. Recently, Durrleman et al. [
This key step improved the generic ability of the new model [ this mathematical representation of surfaces does not require all objects to have the same number of landmarks (normals) to compute the distance between surfaces; the metric of currents densely conserves all the geometric properties of the data (here the normal to the surface) up to a given scale.
Furthermore, Durrleman's approach allows vector features (momentum and velocities of deformation) to be extracted and compared between surfaces. Unlike approaches based on extracting scalar features such as rate of growth, these vector quantities allow more informative mathematical features—such as local curvature and orientation of the shape surface—to be used.
The name “currents” comes from the introduction of a more mathematically precise “way of perceiving a surface,” inspired from Faraday’s law of induction in physics, where the variation of a magnetic vector field
In our case, the space that contains “the magnetic vector field” traversing the shape surface
This sets out a more realistic and efficient framework to represent stroke lesion surfaces as dynamic (rather than static) structures which contract, expand, swell, and shrink in different directions, with variation in the speed of these local changes, without imposing prior assumptions. To estimate the pattern of change in ischemia, we used a sequence of time-indexed surfaces
Considering a source baseline shape
To ensure that the solution at the final time step (
The integration of the estimated velocity field, ultimately, defines the deformation trajectories as geodesic paths between diffeomorphisms. To ascertain these smooth trajectories morphing one shape into another passing by the observed timepoints, we introduce a temporal regression functional
The estimation of the functional
The ultimate estimation of the “spatiotemporal” variability in DWI and MTT lesions will provide us with a clear representation of the similarities and differences between MTT and DWI kinetic patterns and thereafter to evaluate some biological assumptions.
In order to assess the dynamic changes in PWI and DWI lesions across three successive timepoints from acute and subacute stages (from
3D meshed reconstruction of DWI and MTT lesions at three acquisition timepoints. An additional spatial deformation
To show the differences and similarities in the dynamic behavior of the MTT and DWI lesions as they evolve over time, we needed to define appropriate mathematical tools that would adequately set a connection between the changes in the DWI lesion and the MTT lesion as they both evolved with time. This connection is defined as a geodesic diffeomorphism (smooth deformation with a smooth inverse)
Note that the estimation of We firstly compute the norm of the speed at each time step We then extract contracting (corresponding to inward speed direction to the surface) and expanding (corresponding to outward speed direction to the surface) local areas at Finally we compute the mean speed for these contracting and expanding areas over their spatiotemporal evolution for the 8 representative patients, in both DWI and MTT abnormalities.
Estimated DWI/MTT lesion evolution scenarios. (a) DWI (versus MTT) axial slice at 3 timepoints in the first (versus second) column. (b) Estimated DWI/MTT evolution scenarios with estimated velocity norm (speed) in cm/3h. In the Supplementary Material of this paper, we have included a video (Video 1) which visualizes the 4D evolution of both MTT (in red) and DWI (in blue) lesions—as if in “real” time. At
The ability to know precisely at which time the DWI and MTT lesions are most spatially coherent with the final T2-weighted lesion means that we can better evaluate the prognostic potentials of DWI and MTT modalities. To our knowledge, up to this date, detailed information on 4D lesion shape change between one acquisition timepoint and the next is limited [
Time-indexed penumbra and core lesion boundaries combined to final T2-weighted boundary imaged at >1 month. (b) MTT manually delineated penumbra boundaries consecutively at
We also computed, at each time step
The last step was to identify the timepoint
In a similar way, we computed the same measures for the MTT estimated lesion evolution. These specific identified timepoints (
We evaluated the accuracy of our estimation of DWI and MTT lesion evolution by computing the mean and standard deviation (SD) values of the dice index between the estimated and the true lesion volumes at the second and third timepoints for the 8 patients. We found good agreement between the estimated lesion evolution scenarios for MTT and DWI lesions and the observed samples (mean dice SD values: MTT (
Evaluation of the estimated DWI/MTT lesion evolution scenarios. The mean dice index value (a measure quantifying the volumetric overlap between two volumes and ranges from 0 to 1 for the best match) and its standard deviation are computed over the 8 patients between the estimated and the manually delineated DWI/MTT lesions at
DWI |
DWI |
DWI |
MTT |
MTT |
|
---|---|---|---|---|---|
Mean (dice) | 0.90 | 0.90 | 0.86 | 0.76 | 0.80 |
SD (dice) | 0.02 | 0.02 | 0.06 | 0.09 | 0.08 |
We compared the deformation of corresponding DWI and MTT lesion regions to determine any correlations between their contractions and expansions. We first examined lesion behaviour in individual patients and then identified common patterns of lesion change across all eight representative patients.
Figure
Comparison between highly expanding DWI and MTT areas extracted across the spatiotemporal estimated scenarios. As the color ranges from blue to green to red, the different successive areas with high expansion speed are “lit up” at each time step, all mapped back at the baseline lesion shape acquired at
Patient-specific estimated kinetic patterns of change in one patient. (a) The estimated spatiotemporal evolution of DWI (in blue) and MTT (in red) lesions. (b) Detection of highly contracting (versus expanding in (c)) areas in DWI lesion at
We plotted the mean speed of highly contracting and expanding areas for the eight representative patients (Figure
Spatiotemporal mean speed evolution of DWI high contraction and expansion lesion areas for the 8 representative patients and their corresponding areas in the moving MTT lesion. Each box represents a different patient.
We computed the two complementary measures (the dice index and the symmetric distance). We then extracted the corresponding timepoints (in hrs) where the maximum spatial concordance between the two shapes occurred. Both measures produced quite similar results as follows (Table Maximum special closeness between DWI/MTT surface and T2 surface: the dice index averaged for the 8 patients for the spatiotemporal DWI and MTT lesion evolution versus final T2 lesion indicated wide inter-patient variation (DWI dice range 0.0008 to 0.77, median 0.58; MTT dice range 0.003 to 0.63, median 0.39) and similarly wide variation in the temporal symmetric distance for DWI 3.8 to 24.2, median 6.1 mm and MTT 6.1 to 33.2, median 9.8 mm versus final T2. In 5/8 patients, the mean DWI-T2 overlap volume over time exceeded 55% (corresponding to less than 6.2 mm in symmetric distance). This indicates that in most cases there is a good geometric concordance between the T2 and DWI surfaces although this did not necessarily occur at the subacute stage (last acquired DWI image) that is in disagreement with the assumption that acute DWI will grow into the final T2 lesion. Three patients showed almost no MTT-DWI spatiotemporal lesion evolution overlap versus final T2 (mean dice index <0.05). The fact that the dice index did not converge to 1 and the symmetric distance did not fall to 0 mm shows that the time-evolving DWI abnormality does not converge to the final T2 boundary but rather encounters it as it progresses or regresses with time. Time of maximum DWI/MTT surface overlaps with the final T2 surface: the time
Insights into final T2 outcome Columns 1 and 3 show the mean value of dice index over time for the 8 patients between the estimated evolving DWI/MTT lesion boundaries from acute to subacute stages and the final T2 lesion boundary. Columns 2 and 4 show the time corresponding to the maximum value that the dice index reached, where the final T2 lesion is spatially closest to the estimated DWI/MTT evolution. Columns 5 and 7 display the mean value of the symmetric distance over time computed in mm (the spatial discrepancy) between the evolving DWI/MTT boundaries and the final T2 boundary. Columns 6 and 8 depict the time of the “appearance” (in hours) of the T2 within the DWI and MTT evolution scenarios corresponding to the minimum of the symmetric distance that varied with time—for each patient.
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
0.574 |
|
0.682 |
|
6.109 |
|
4.719 |
|
0.598 |
|
0.817 |
|
7.086 |
|
3.828 |
|
0.052 |
|
0.029 |
|
33.23 |
|
24.285 |
|
0.003 |
|
0.227 |
|
28.593 |
|
16.681 |
|
0.007 |
|
0.0008 |
|
23.886 |
|
26.128 |
|
0.364 |
|
0.556 |
|
9.295 |
|
6.151 |
|
0.42 |
|
0.61 |
|
10.45 |
|
6.160 |
|
0.681 | 7 |
0.77 |
|
7.925 |
|
4.713 |
|
We applied a 4D model to evaluate the change in acute stroke lesions from the first few hours to 1–3 months after stroke, to our knowledge, the first time a 4D model has been used to simulate the dynamic evolution of stroke lesions [
This model has some innovative mathematical aspects that we took advantage of, such as (a) there is no need for a point-to-point landmark matching between consecutive surfaces since the metric of currents does not assume any
Looking at the different microscopic phenomenological dynamic models, we notice that they were developed to simulate a voxel-per-voxel pattern of local ischemia using a simplified 1D or 2D geometry of the brain and a set of empirical parameters [
The model also has some key limitations, particularly when applied to a disease such as stroke: the major limitations are that lesions are commonly not a single defect but commonly consist of multiple scattered smaller abnormalities, that the number of these lesion components may change over time, that stroke lesions swell up and shrink, and that no information derived from tissue parameters such as actual perfusion values can be incorporated directly into the model. For the latter a different modeling approach would be needed.
Despite the small sample of only eight representative patients, we saw wide variance in the spatiotemporal interaction between PWI and DWI lesion surfaces in terms of correspondence between areas of high contraction and expansion (Figures
The model also highlighted wide interpatient variability in the time at which the estimated MTT and DWI evolution scenarios matched the final T2 lesion. In 5 patients, the geometric concordance between the moving acute lesion surface and the static final T2 reached its maximum later in DWI data than in MTT (Table
Our study has limitations. We were not able to differentiate dynamic lesion behavior in white and grey matter [
Future technical developments should include the ability to model ischemic lesions variation in the number of components, to address anatomical deformation resulting from lesion swelling rather than true lesion expansion, and to use individual voxels throughout the lesion—for example, derived from DWI/PWI values—rather than just the surface/outline. Indeed, investigating the connection between the estimated speed of the surface evolution and corresponding PWI or DWI values would be very interesting, but this requires radical changes in the mathematical formulation of currents to define “colored” surfaces. Coloring the lesion surface mesh with a perfusion or a diffusion value and tracking their change both in intensity and velocity are an ambitious future improvement of the applied model which is beyond the scope of our current study.
Further testing of the model requires larger data sets including more patient-specific variables and stroke-specific variables such as the site of vascular occlusion as well as acute treatment effects.
To our knowledge this is the first attempt to estimate a continuous 4D PWI and DWI ischemic lesion evolution and use it to evaluate individual patient differences in stroke lesion evolution. Our blinded and prior-free individualized analysis of 8 representative patients of the correspondence in dynamic evolution of DWI and MTT lesions in space and time showed some similarities but also differences in the way the ischemic lesion progressed or resolved. Some of the observations in this proof-of-concept model were partly in line with the mismatch concept, while others contradicted expected lesion behaviors stroke evolution hypotheses such as that acute diffusion abnormality is irreversible and cannot exceed the boundaries of acute perfusion abnormality. We were also able to detect subtle and rapid differences in lesion evolution between DWI and MTT lesions imputed to 3 hourly intervals. The model allows individual lesions and patients to be examined to provide greater insights in speed and time as to what drives stroke lesion evolution and thus other opportunities for developing further interventions. In future this may in turn enhance understanding of stroke pathophysiology and allow greater patient-specific personalized treatment.
The estimation of the final smooth deformation trajectories between lesion shapes is achieved by minimizing a temporal regression functional
The authors do not have any possible conflict of interests with the trademark GE Signa LX 1.5-T MR scanner.
This study was funded by the Scottish Funding Council through the Scottish Imaging Network, A Platform for Scientific Excellence (SINAPSE) Collaboration (