Assessment of passive muscle elongation using DTI: Correlation between fiber length and diffusion coefficients

Valentina Mazzoli^{1,2,3}, Jos Oudeman^{1}, Marco A Marra^{3}, Klaas Nicolay^{2}, Nico Verdonschot^{3}, Andre M Sprengers^{3}, Martijn Froeling^{4}, Aart J Nederveen^{1}, and Gustav J Strijkers^{5}

Mechanisms of muscle contraction and force generation in healthy subjects and patients with muscle disorders is an intensely studied topic and relevant for numerous clinical applications. Diffusion Tensor Imaging offers unique opportunities as it provides both architectural parameters as well as information on tissue status. DTI in skeletal muscle has been shown to be sensitive to transient effects including joint positioning as well as fiber lengthening and shortening [1]. Increased water diffusion perpendicular to the axis of the fiber was reported in the soleus and gastrocnemius muscle during plantarflexion and this was empirically explained with an increase in muscle cross sectional area, although no connections were made between changes in fiberlength and diffusion coefficients. Understanding this connection could be useful for a better modeling of muscle (patho)physiology.

The **aim** of this study is to investigate the
relationship between changes in diffusion parameters and fiberlength in the
lower leg as a result of muscle shortening/lengthening in passive stretch.

The right lower leg
of 5 male healthy volunteers (27±2 years) was scanned using a 3T Philips
Achieva scanner. A custom-built device was used to fixate the foot in 3
different positions (15° dorsiflexion, neutral and 30° plantarflexion). A
SE-EPI DTI scan with the following parameters was used: FOV: 192x156 mm^{2};
TE/TR: 51.63/11191 ms; matrix size: 64x52; 50 slices; voxel size: 3x3x5 mm^{3};
12 diffusion encoding directions; b-value: 400s/mm^{2}. Each measurement
was performed twice on the same subject within the same measurement day.

A mDixon scan was performed for each foot position and used for anatomical reference. Four different muscle groups were segmented from the out-of-phase scan: soleus (SOL), extensor digitorum longus (EDL), fibularis longus (FL) and tibialis anterior (TA).

The DTI data were
fitted to a tensor model using a WLLS algorithm, and diffusion parameters (λ_{1},
FA and RD=(λ_{2}+λ_{3})/2) were calculated.

Fiberlength was
calculated after automatic tendon segmentation, using a method previously
described [2].
Changes in length
and diffusion parameters are expressed as relative change with respect to the
neutral position (ΔX_{dorsi}=X_{dorsi}-X_{neutral} and ΔX_{plantar}=X_{plantar}-X_{neutral}).

Next, muscle fibers
were modeled as cylinders with constant volume. In order to test the model, percentage
changes in the square of fiber radius calculated from the change in fiberlength
were correlated with measured percentage changes in radial diffusivity (according
to Einstein’s equation of diffusion r^{2}=2Dt).

Our results show significant negative correlations in all investigated muscles between the changes in RD and the changes in fiberlength with respect to neutral foot position. The general change in fiberlength from dorsiflexion to plantarflexion position is in agreement with results previously obtained using ultrasonography[3].

Different muscles showed different rate of change in fiberlength and diffusion parameters. In particular it was observed that plantarflexor muscles (SOL and FL) lengthened in dorsiflexion and decreased their radial diffusivity, while the opposite behavior was observed for the dorsiflexor muscles (EDL and TA).

On the other hand, λ_{1} did not show significant changes
with foot positions, indicating that intracellular proteins and other barriers that
hinder diffusion of water molecules in the axial direction are not influenced
by the change in length of the structure.

The rate of change in diffusivity perpendicular to the fiber is in agreement with expected changes in the square of the radius, indicating that in first approximation muscle fibers can be adequately described by a simple cylindrical model and that changes in RD can be used to predict changes in fiberlength. In fact assuming a cylindrical model and using Einstein’s equation, we obtain that the product between the diffusivity and the length is constant.

Taken together, our data shows that DTI is a valuable tool in the assessment of muscle passive elongation and shortening, and suggest that RD could be used in the assessment of muscle functioning and abnormalities. These findings advance the physiological interpretation of diffusion coefficients derived from the tensor model and could potentially have an important role in biomechanical models of muscle functioning.

Figure 1: Relative
changes in λ_{1}, RD and FA plotted against relative change in
fiberlength. Differences are calculated with respect to the neutral foot
position. The line that best fits the data is indicated in red.
Correlations between
the variables are summarized in Table 2.

Table 1:
Pearson correlation coefficient (r) and p-value (p) calculated between the
relative change in fiberlength and λ_{1}, RD and FA respectively.
Underlined values indicate a significant correlation (p<0.02) between the
relative change in fiberlength and the relative change in diffusion parameters.

Figure 2:
Percentage change in radial diffusivity (RD) plotted against percentage change
in the square of the radius. The change in radius was calculated from measured
changes in fiberlength, assuming a cylindrical model with constant volume.

Table 2:
Pearson correlation coefficient (r) and p-value (p) calculated between the
relative change in radial diffusion and square of the radius. Underlined values
indicate a significant correlation (p<0.005). Significant positive correlation
is observed for all muscles, in agreement with Einstein’s equation of
diffusion.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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