An Integrated Diffusion Map for the Analysis of Diffusion Properties

Rationale and Objectives

To develop an integrated diffusion map (iDM) for evaluation of diffusion properties, including the mean diffusivity and diffusion anisotropy concurrently.

Materials and Methods

The proposed integrated diffusion map consisted of trace and the deviation tensor. It measures the diffusion distributions from a region of interest. Diffusion tensor imaging was acquired from nine healthy volunteers and four patients with acoustic neuroma before and 3 months after the stereotactic radiosurgery. Five regions of interest were selected from healthy subjects and the whole tumor from the patients. The diffusion properties were analyzed in the proposed integrated diffusion map.

Results

In healthy subjects, iDM showed different distributions in regions of interest that can lead to cluster segmentation. In monitoring the treatment response, the number of pixels with meaningful changes in iDM is 12.5% compared to 32.37% in apparent diffusion coefficient and 16.67% in fractional anisotropy. It suggested the effect from radiation therapy might affect the anisotropic diffusion. The interpretation of the diffusion properties, such as changes in mean diffusivity and anisotropy, should be treated in an integrated method.

Conclusions

The integrated diffusion map can be used to analyze the diffusion properties in a comprehensive manner.

Diffusion tensor imaging (DTI) is a technique to describe the microstructural properties of tissues in vivo . Indexes derived from DTI can be divided into two groups, determined by properties related to the diffusivity or anisotropy. The most commonly used indexes are trace and fractional anisotropy (FA). Trace is a reflection of the total measured diffusivity, and FA is often used to quantify the degree of anisotropy. Different anisotropy indexes, such as relative anisotropy and volume ratio , have been compared with their contrast to noise ratio and their susceptibility to noise . In general, FA is preferred because of improved noise immunity and superior contrast to noise ratio in both simulation and in vivo studies compared to relative anisotropy (RA) and volume ratio (VR). A new index, such as InterVoxel Diffusion Coherence, has been proposed to further quantify the diffusion directional coherence .

The change of diffusion related to several diseases can be effectively detected by DTI . Several studies have reported a decline in FA and an increase in mean diffusivity. For example, in epilepsy patients, DTI shows increased diffusivity and reduced anisotropy, suggesting loss of structural organization and expansion of the extracellular space . In patients with multiple sclerosis, trace increased and FA decreased in segmented white matter in the whole multiple sclerosis group compared to their matched controls .

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Theory

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Trace=λ1+λ2+λ3 Trace

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DD=λ21+λ22+λ23−−−−−−−−−−√ D

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Deviation=32((λ1−λ¯)2+(λ2−λ¯)2+(λ3−λ¯)2)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√ Deviation

(

−

)

(

−

)

(

−

)

(Trace3√)2+(Deviation3/2√)2=DD2 (

Trace

)

(

Deviation

)

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$Figure 1, The integrated diffusion map. The x axis is the trace, in units of square millimeters per second. The y axis is the amplitude of the diffusion deviation tensor, in units of square millimeters per second. The circle plotted the amplitude of the diffusion tensor, DD, increased from 1 to 5 in unit of square millimeters per second. The figure showed that at a fixed deviation tensor amplitude of 1 mm 2second, fractional anisotropy (FA) decreases from 1 to 0.2 as the trace increases. FA remains constant in the radial direction, as the diffusivity increased, reflected in the increase of both trace and DD. FA increased from 1 to 1.2166 with the amplitude of the deviation tensor in the vertical direction, as the trace is fixed at 1 mm 2second. Notice that although trace is constant, DD still increased in the y direction.$

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Materials and Methods

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Healthy Volunteers

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Patients with Acoustic Neuroma

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DTI Analysis

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Result

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Table 1

The Averaged FA, DD, and ADC from Healthy Volunteers

Callosal splenium Lentiform nucleus External capsule Thalamus Subcortical white matter FA 0.82 ± 0.18 0.24 ± 0.10 0.55 ± 0.16 0.39 ± 0.05 0.61 ± 0.04 ADC (mm 2 /second) 0.77 ± 0.40 0.66 ± 0.08 0.70 ± 0.09 0.71 ± 0.02 0.77 ± 0.06 DD (mm 2 /second) 1.58 ± 0.42 0.71 ± 0.19 0.92 ± 0.18 1.30 ± 0.41 1.53 ± 0.14

The regions of interest included callosal splenium, lentiform nucleus, external capsule, thalamus, and subcortical white matter in the parietal lobe. FA (fractional anisotropy) is dimensionless. Both DD and ADC (apparent diffusion coefficient) are in units of square millimeters per second.

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Table 2

The Percentage Change in Patients Measured from fDM and iDM

Changed Unchanged Integrated 12.5 ± 3.6 87.5 ± 3.6 fDM Increase Decrease 15.22 ± 3.9 17.15 ± 2.7 67.63 ± 3.2

The fractional anisotrophy (FA) and apparent diffusion coefficient (ADC) were calculated for each individual subject within the whole volume of tumor, selected from consecutive slices, before and after the stereotactic radiosurgery. The number of pixels of changes was calculated from fDM. In the integrated diffusion map, only with or without significant changes was shown. iDM, integrated diffusion map; fDM, functional diffusion map.

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Discussion

An iDM for Diffusion Evaluation

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In Healthy Volunteers

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Monitoring Tumor Response after Treatment

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References

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An Integrated Diffusion Map for the Analysis of Diffusion Properties

Rationale and Objectives

Materials and Methods

Results

Conclusions

Theory

Materials and Methods

Healthy Volunteers

Patients with Acoustic Neuroma

DTI Analysis

Result

Discussion

An iDM for Diffusion Evaluation

In Healthy Volunteers

Monitoring Tumor Response after Treatment

References

Further Reading

A Novel Approach to Nodule Feature Optimization on Thin Section Thoracic CT

Abstracts of Funded National Institutes of Health Grants

Application of Computer-aided Diagnosis (CAD) in MR-Mammography (MRM)