Diffusion magnetic resonance imaging (dMRI) is currently the only technique that can non-invasively detect the structural integrity of white matter microscopic tissue. Among them, diffusion tensor imaging (DTI) based on Gaussian model is the most popular dMRI technique, which has been widely used in the study of various clinical diseases [1-3]. However, recent studies have found multidirectional fiber tracts within voxels of many tissues in the brain [4]. Since the spatial resolution of dMRI is generally in millimeters and the diffusion of water molecules is in micrometers (1 mm = 1000 microns), there are thousands of diffusion species in a single voxel, and the average diffusion of water molecules does not necessarily conform to Gaussian distribution. Therefore, DTI is limited by the single Gaussian model and cannot reveal multidirectional fiber bundles within a voxel. Diffusion spectrum imaging is a model-independent multi-b value and multi-directional q-space imaging [5]. This method uses the probability density function to describe the complete spatial distribution of the diffusion motion, and can accurately identify local complex interlaces with excellent angular resolution. fibers travel. With the development of diffusion spectrum imaging (DSI), a lot of research work has been carried out around improving data acquisition methods, reducing scanning time, increasing angular resolution, and popularizing clinical applications, making this method a popular method in the field of diffusion imaging. a research hotspot.
1 Basic principles of diffusion spectrum imaging
1.1 Principle
In the Stejskal-Tanner experiment, the diffused signal decays exponentially with phase discretization e:
(1)
S0 represents the MRI signal without applying the diffusion gradient, Φ represents the phase dispersion caused by the diffusion gradient, and SΔ represents the MRI signal after applying the diffusion gradient. Assuming that the interval Δ between the two diffusion sensitive gradients is much larger than the gradient duration δ, the discrete phase of the water molecule is:
. In the formula, 
is the echo vector, γ is the magnetic spin ratio of hydrogen protons, and 
is the diffusion gradient. r is the relative displacement of the water molecule during the diffusion time Δ, 
and 
is the position of the water molecule at the beginning of the first diffusion gradient magnetic field and the second diffusion gradient magnetic field, respectively. If the average diffusion of water molecules is regarded as the expected value, then the relationship between the diffusion signal and the diffusion probability density function can be obtained as follows:
(2)
(probability densityfunction, PDF) represents the density of the average relative spin displacement within a voxel.
In order to exclude the influence of macroscopic motion (such as head movement) [6], DSI uses the signal modulus to perform inverse Fourier transform to obtain the probability density function:
(3)
The one here is obtained by Fourier transform, so we call it the diffusion spectrum.
Although the theory of DSI requires that the interval time of the diffusion gradient magnetic field is much larger than the duration of the diffusion gradient magnetic field, in practical applications, this assumption is generally not satisfied due to the limitation of hardware conditions. Wedeen et al. [6] further confirmed that even if the diffusion gradient magnetic field duration cannot be ignored, equation (3) still holds.
1.2 Data collection and processing
DSI uses a Cartesian grid strategy to collect q-space data points within a sphere. Under normal circumstances, the number of gradient directions of the scanning sequence needs to be at least 200, and the maximum b value needs to be more than 8000 s/mm2, resulting in a scanning time of tens of minutes or even more than 1 hour, which seriously hinders its clinical application. The routine processing steps of DSI data are as follows: (1) Data denoising (for example, adding Hanning window function, card threshold, wavelet denoising, etc.); (2) Perform 3D inverse Fourier transform on the mode of the diffuse signal to obtain PDF; (3) Perform radial integration of PDF to obtain the orientation density function (ODF) of water molecule diffusion, and use ODF to describe the orientation distribution of fiber bundles; (4) Use ODF to calculate some quantitative indicators (such as generalized fractional anisotropy, GFA) ; (5) Using ODF-based streamlined algorithm for fiber bundle tracking [7].
2 Methodological study of diffusion spectrum imaging
The biggest disadvantage of DSI is that the data collection time is too long, which leads to patients who may not be able to tolerate the termination of the experiment and serious head movement problems. In addition, excellent post-processing methods can improve the angular resolution of ODFs, thereby revealing more reliable and complex microstructures.
2.1 Improvement of data collection efficiency
Since the diffusive contrast in q-space is positive and spherically symmetric, it has been proposed to sample DSI data using a hemispherical shell [8]. The results show that compared with global shell sampling, hemispheric shell sampling can not only halve the scan time, but also preserve the angular resolution comparable to that of the global shell. By optimizing the maximum b value and the number of directions of the DSI acquisition strategy, Kuo et al. [9] found that the maximum b values of DSI-515 and DSI-203 correspond to 6500 and 6500 respectively under the condition of ensuring better signal-to-noise ratio and angular resolution. 4000 s/mm2 is sufficient, and the reduced maximum b value can significantly shorten the scan time. From the perspective of sequence, Reese et al. [10] proposed a synchronous image refocusing plane echo sequence, which can excite two slices at a time by changing the radio frequency pulse, and the echo signals of each phase-selected slice will be recorded separately, and the MRI signal will be reconstructed in the MRI signal. When the data is divided into 2 arrays, after Fourier transform, each slice produces an image, which reduces the scanning time by nearly half. [11] proposed a new non-Cartesian grid acquisition method (body-centered-cubic, BCC), which acquires the center point of each unit cell instead of the grid point. The sampling density is twice that of grid sampling. In the case of comparable precision and accuracy, the optimal b value and number of directions of BCC sampling are lower than those of grid sampling, which can effectively reduce the scanning time by 30%. Yeh et al. [12] proposed a reduced-encoding DSI (RE-DSI) method combined with a double Gaussian model, assuming that the diffusion signal of biological tissue follows a double Gaussian curve distribution, collects data with low q values, and then uses the double Gaussian model. Fit data with high q values. The experimental results show that RE-DSI can not only reduce the scanning time but also ensure a relatively high fiber bundle orientation accuracy and signal-to-noise ratio. Recently Menzel et al. [13] tried to apply compressed sensing technology to DSI and found very surprising results. When the acceleration factor R is equal to 4, the key information of water molecule dispersion (such as ODF, diffusion coefficient and kurtosis) can be preserved, and the corresponding undersampling of DSI-128 and DSI-515 can reduce the scanning time to 6 min respectively and 26 min, which has basically met the clinical requirements and provided a reference for promoting the clinical application of DSI.
2.2 Improve angular resolution
DSI assumes that the direction of the maximum value of the diffusion orientation density function (dODF) of water molecules is the direction of the fiber bundle, but in fact it is not the real fiber bundle direction. In order to improve the estimation of fiber bundle orientation, HARDI's research has used deconvolution to obtain the fiber orientation density function (fiberorientation density function, fODF) [14]. Data validation shows that the angular resolution of fODF and the accuracy of fiber bundle tracking are better than dODF, and it is more suitable for describing the direction of fiber bundles. Canales-Rodríguez et al. [15] believed that the FT in the DSI algorithm occurred in the full q space, but the actual MR data for 3D FT was limited, so the PDF obtained by conventional DSI processing was not real, but the real PDF and A convolution of a point spread function. They obtained the true PDF by deconvolution and then radially integrated it to obtain the ODF. The results show that the ODF after deconvolution processing is more satisfactory in the precision, accuracy and stability of revealing intersecting fiber bundles. In order to perform the same deconvolution process on the data of different acquisition strategies, Yeh et al. [16] established a new mixed diffusion model, using the spin density function (similar to ODF) to describe the diffusion behavior of water molecules, the The average diffusion is weighted by different diffusion components. The researchers collected QBI (q-ball imaging), DSI and GQI (generalized-sampling imaging) human brain data, and processed these three data accordingly to obtain dODF, and then deconvolved dODF and a feature function to obtain fODF. The data results show that compared to dODF, fODF is more accurate and reliable for the inspection of small-angle (45° and 60°) intersecting fiber bundles and the evaluation of some tiny fiber bundles. To further improve the accuracy of fODF, Yeh et al. [17] recently proposed a diffusion decomposition method. This method treats the fODF as the solution of a regression equation and evaluates the fODF using the LASSO (least absolute shrinkage and selection operator) algorithm, which uses L1 regularization to promote the sparsity of the regression equation solution. Simulation data results show that the fODF derived from diffusion decomposition is more capable of revealing intersecting fiber bundles than the restricted deconvolution method and baseball model, even at low signal-to-noise ratios. The most prominent finding of this study is that due to the very high angular resolution of the fODF after diffusion decomposition, the fODF obtained by diffusion decomposition of 30-QBI and 40-DSI data are comparable to the characteristics of 252-QBI and 202-DSI data, respectively. The reduction in the number of directions can drastically shorten the scan time. operator) algorithm evaluates the fODF, which utilizes L1 regularization to promote sparsity of solutions to regression equations. Simulation data results show that the fODF derived from diffusion decomposition is more capable of revealing intersecting fiber bundles than the restricted deconvolution method and baseball model, even at low signal-to-noise ratios. The most prominent finding of this study is that due to the very high angular resolution of the fODF after diffusion decomposition, the fODF obtained by diffusion decomposition of 30-QBI and 40-DSI data are comparable to the characteristics of 252-QBI and 202-DSI data, respectively. The reduction in the number of directions can drastically shorten the scan time. operator) algorithm evaluates the fODF, which utilizes L1 regularization to promote sparsity of solutions to regression equations. Simulation data results show that the fODF derived from diffusion decomposition is more capable of revealing intersecting fiber bundles than the restricted deconvolution method and baseball model, even at low signal-to-noise ratios. The most prominent finding of this study is that due to the very high angular resolution of the fODF after diffusion decomposition, the fODF obtained by diffusion decomposition of 30-QBI and 40-DSI data are comparable to the characteristics of 252-QBI and 202-DSI data, respectively. The reduction in the number of directions can drastically shorten the scan time.
3 Application research of diffusion spectrum imaging
DSI's initial applied research aimed to reveal a more realistic microstructure. In recent years, with the development of MR hardware, the improvement of scanning time and angular resolution, DSI has been gradually applied to clinical disease research, and breakthrough progress has been made.
3.1 Revealing the microstructure
Due to the failure to detect multidirectional fiber bundles, tissues such as tongue, muscle, and esophagus contain a large number of complex muscle fibers arranged in an orderly manner, and DTI cannot reveal their complete tissue structure. Gilbert et al. [18-19] applied DSI technology to the structural inspection of the bovine tongue and esophagus, and found that there are a large number of multidirectional fiber bundles in these tissues, and successfully revealed the bovine tongue and esophagus using a streamlined tracking algorithm based on DSI-ODF. The complete fiber bundle structure and the underlying dynamic characteristics of this complex fiber arrangement composition and physiological function were also resolved. Takahashi et al. [20] used DTI and DSI to explore the age-dependent changes in the structure of cat brain fiber tracts. The DSI results showed that the nerve fiber bundles from the thalamus to the cortex were smooth at first and had few branches. However, the insensitivity of DTI to multidirectional fiber bundles prevents it from revealing such changes in fiber bundle structure. Schmahmann et al. [21] used DSI technology to identify 10 long connecting fiber tracts in the monkey brain. In some brain regions with obvious crossing fiber tracts, such as the optic chiasm, the center of the semiovale, etc., DTI tracking technology cannot identify and DSI successfully visualized the crossing direction of these fiber tracts. More importantly, the structures of all fiber bundles revealed by DSI were in good agreement with the results of automated radiohistological tracking. Hagmann et al. [22] used DSI and resting-state fMRI to study the brain structure and function of five subjects and found that many human brain hubs (such as posteromedial cortex, medial frontal lobe, superior temporal lobe) identified by white matter tractography Cortex, etc.) correspond exactly to the core brain regions of the default network, and there is a robust correlation between the structural and functional connectivity of the brain. At the same time, similar modular features to functional networks were found, providing important evidence for further research on the interrelationship of structural and functional connections in the brain. Granziera et al. [23] scanned 4 healthy female subjects and used DSI tracking technology to show the neural circuit patterns in the cerebellar cortex, deep and brainstem nuclei, and between the thalamus. This is the first time researchers have revealed the complex network connections of the cerebellum , the results are consistent with previous histological studies in animal models. Recently, Wedeen et al. [24] used DSI technology to track the structure of the main fiber tracts in the brain. By analyzing and comparing the spatial relationship between each fiber tract and its adjacent parallel and perpendicularly intersecting fiber tracts, they found a breakthrough in human and four kinds of monkey brain fibers. The beam orientation conforms to a simple geometric distribution, the results of this study Not quite in line with the complex microscopic structure of the brain as we understand it in "ideas". Based on this discovery, theoretically, we can map or predict the fiber bundle structure of any microscopic tissue in the brain using some simple mathematical models, which provides a new perspective for the study of neural connectomics.
3.2 Application in clinical diseases
Due to the accuracy of DSI in revealing microscopic tissue structure, the reliability of fiber tract tracking, and the improvement of data collection methods in recent years, it has gradually been applied to some clinical disease research, including ADHD, psychosis, stroke and autism. Wait. Tang et al. [25] used DSI technology to study the integrity of the corticospinal tract in the lower extremities of patients with subcortical stroke. By comparing the GFA values of the corticospinal tracts of the lower extremities with disabilities and normal lower extremities, they found that the GFA of the lower extremities with disabilities was significantly reduced, and the GFA Values are highly correlated with motor function of the lower extremities. Wu et al. [26] used DSI tracking technology to study changes in the integrity of the frontal-striatal circuit in ADHD children. It was found that the integrity of all four fiber tracts of the frontal-striatal circuit in children with ADHD was disrupted, and the integrity of the fiber tracts of the orbitofrontal back to the caudate nucleus was significantly associated with the patients' clinical symptoms of attention deficit. These findings Provides a basis for the hypothesis that frontal-striatal circuit defects are the underlying pathological mechanism of ADHD. Griffa et al. [27] used DSI technology to find some core brain regions that lead to the loss of brain network integrity in schizophrenia patients, such as the orbitofrontal gyrus, middle frontal gyrus, inferior frontal gyrus and parietal lobe. Further graph analysis revealed that the topological properties of the patient's core brain regions and the structure of the fiber tracts connecting them were altered compared to the normal group, and they formed a more dispersed network through a rearrangement of the shortest paths. These findings shed light on an important pathological mechanism of impaired brain connectivity in patients with schizophrenia. Wu et al. [28] used DSI technology to study the relationship between structural and functional networks in psychotic patients with auditory verbal hallucinations. It was found that the integrity of the bilateral ventral fiber tracts and the right dorsal fiber tracts and the functional laterality of the dorsal pathway were reduced in the patient group, and the integrity of the right dorsal pathway and the functional laterality of the dorsal pathway were reduced. Laterality had a significant positive correlation while functional laterality of the dorsal pathway was negatively correlated with the structural integrity of the right dorsal pathway and clinical scores. These findings successfully reveal the relationship between the underlying structural and functional changes in schizophrenia with auditory-verbal auditory hallucinations, advancing the understanding of the pathological mechanisms of the disease.
4 Problems that still exist
Methodological studies of DSI have optimized its scanning efficiency and post-processing methods, and clinical studies are increasing, but we still face some challenges. Most of the existing DSI clinical studies mainly use hemispherical shell sampling data in 102 directions and an optimized maximum b value of 4000 s/mm2. However, the scanning time is still as long as about 16 minutes (3T-MR), which is still unbearable for patients. , so these studies generally involve a relatively small number of subjects, which may make the final statistical results less reliable. Although the synchronous image refocusing echo plane sequence acquisition, BCC sampling, compressed sensing and other technologies mentioned earlier can reduce the scanning time, these methods are difficult to implement and difficult to generalize. How to find a simple and feasible data with short scanning time The acquisition method is the focus of our future research; the current research on the methodology and application of DSI is mostly based on the directional part of the PDF, ODF, and does not pay attention to its radial information. Previous studies have shown that the radial information of PDF is related to the destruction of axonal structure and microstructure. Recently, based on the multi-spherical shell sampling method, researchers have proposed some new models [29] to directly study PDF and related the nature of quantitative indicators. The results show that PDF is more stable and less affected by noise than ODF, and fiber bundle tracking is more accurate. However, these models have their own interpretations of the q-space signal, and the models also have their own advantages and disadvantages. This requires us to further explore to find a model-independent PDF research method; most of the current clinical application studies of DSI use a single quantitative indicator GFA, which is obviously not comprehensive for disease detection. GFA and FA are highly correlated and it is also affected by partial volume effects. The value of GFA may not be comparable for different reconstruction methods, because the accuracy and angular resolution of ODF obtained by different reconstruction methods are not the same. In addition, different sampling methods and b values will also affect the value of ODF. In order to overcome the problem of GFA, Yeh et al. [17] proposed a new indicator quantitative anisotropy (QA), QA is defined for each fiber bundle direction, it is calculated from the peak direction of ODF and FA and GFA are for each voxel, which is their maximum difference. Using QA as a threshold when doing fiber bundle tracking can reduce the partial volume effect while filtering out some false fiber bundles. In future research, we need to combine other indicators, such as P0 or MSD based on PDF radial information [30], to conduct a more comprehensive and comprehensive detection of pathological structures. Different indicators may have different sensitivities to different diseases. May be able to reveal lesion information from different angles.
5 Summary
In summary, although DSI still has some problems in data acquisition and post-processing methods, due to its advantages in revealing multi-directional fiber bundles, the structure of fiber bundles it detects is more realistic and reliable, which indicates that DSI Potentially huge value in clinical application, some preliminary clinical disease studies have proved this. However, limited by software and hardware, the clinical promotion of DSI technology is still very slow. There is a long way to go for future research. It is gratifying that DSI has made our understanding of the human brain a step further. With the development of science and technology, we believe that DSI technology will replace DTI in the near future and become the magnetic resonance diffusion. The new mainstream technology in imaging.
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