Imaging method based on fractal surface-filling or space-filling curves

p0001Imaging methods based on self-similar area or space-filling curves

p0002Description; The present invention relates to an image forming method and associated apparatus for nuclear magnetic resonance, which are based on self-similar area or space-filling curves, the magnetic resonance or magnetic resonance based on the fact that atomic nuclei (and in particular atomic nuclei in molecules) emit, are excited by radio waves and in turn radio waves, the nuclear magnetic resonance effect may be further and more particularly in the imaging can be utilized in the following cores:^{, 3}C, ¹⁵N, ^{1 29}Xe, ³He, ²³so what ^{, 7}0, reason is the self-rotation - the spin - of protons. This spin creates a moving electric charge a small, nuclear magnetic field that interacts with the magnetic moments of neighboring protons, so arises Depending on the environment, a characteristic magnetic moment of the entire molecule.

p0003For MR measurements on the human body offer

p0004Waser fabric cores, since they occur most frequently by far. If the examined person exposed to a strong static magnetic field, then orient the spins the protons in the body by this external magnetic field. In general, a high frequency electromagnetic field is applied perpendicular to the static magnetic field. At a certain frequency, the Larmor frequency, the spins are deflected, they resonate.

p0005If this excitation pulse now shut, "fold" the spins of protons in their original direction back - and lose energy they emit as radio waves, the magnetic portion of this radiation can be measured by a receiver coil and finally analyzed on a computer..

p0006By the time precisely defined switching on an additional gradient magnetic field (layer selection) are the spins of the protons excited in layers. The returned radio waves are precisely localized when using read and phase gradient; there arise pixels that can be assembled to form a two-dimensional image. Thus, the magnetic resonance is a method frequently used, non-invasive for the investigation of the human body. The functional magnetic resonance imaging is used for example for the representation of local brain activity,

p0007A fast image acquisition allows the so-called EC / io planar imaging (EPI), This is a fast measuring technique may be included in a single excitation pulse of the entire k-space (2D), from EPI are when reading the k-space lines added gradient.

p0008EPI is by far the fastest method of MR imaging. The classic EPI sequence uses a single excitation and then collects all data in gradient echo, an MR image can be created so in less than 1 00 ms.

p0009There are spin-echo and gradient-echo EPI sequence of the variants. The gradient echo variant (V-sensitivity) is used for the measurement of brain activity. The functional MR imaging in this case based on the BOLD effect: Blood Oxygen Level Dependent- Effect. The spin-echo variant (T₂-sensitive) used after the excitation pulse 1 a 80 ° RF pulse in order to minimize field inhomogeneities. Using an additional 1 80 ° pulse can be recorded with the EPI also T, weighted images. The pure gradient echo variant is particularly suitable for cardiac imaging. In EPI, the frequency coding oscillates (with continuously or plateau intervals), whereby a series of gradient echo is generated.

p0010Unlike the conventional MR imaging techniques of phase encoding is switched during reading, this way, all echo a different phase encoding: the raw data matrix is ​​filled line by line with alternating direction.

p0011When gradient echo signal is generated by switching a pair of dephasing and rephasing gradients. To this end, the frequency coding is switched on directly after the excitation pulse with a negative polarity. He first caused the fanning of the spins. Then switch it to a positive polarity. Now the spins are brought back into phase (rephasing), and it comes to echo.

p0012When using cut repetition a tilt angle provides less than 90 ° a better signal-to-noise ratio than a 90 ° Pulse. To illustrate this, only one (the first) excitation pulse is first considered. For example, an excitation pulse with a flip angle of 20 ° produces a still sufficient transverse magnetization of 34% of the maximum value. The longitudinal magnetization is in this case 94% of the maximum value. It is the next excitation pulse again a high longitudinal magnetization available. In the case of short repetition (T_R small compared with T.) a stronger MR signal is generated therefore with a smaller tilt angle than with a 90 ° pulse.

p0013The longitudinal magnetization recovers faster, the smaller it is. After each deflection by the angle of tilt If the remaining longitudinal magnetization initially smaller than before. She is recovering but then each faster the smaller it is. After several excitation pulses creates a balance between these two opposing tendencies. The longitudinal magnetization and thus the signal is then after each pulse of equal size, this equilibrium state is also referred to as steady-state,

p0014However, the variation of the tilt angle does not change, only the signal-to-noise ratio, but also the contrast behavior of the MR image. The so-called Ernst angle results for a certain repetition time T_R and the tissue-dependent T- -time a maximum signal. For diagnostic purposes, however, one chooses a tilt angle at which the signal is not necessarily optimized to noise ratio, but rather the contrast.

p0015For T. weighted images produces a larger tilt angle than the

p0016Ernst angle better T. -Contrast in Proton density weightings is a smaller tilt angle is desirable.

p0017Because the gradient echo sequence is very fast and very short repetition times T_R to T₂may have -time (down to 8 ms at the fastest sequences), is from the previous suggestion still a residual transverse magnetization left. There are 2 ways to deal with this fact: The transverse magnetization is destroyed or used.

p0018The so-called FLASH method (Fast Low Angle Shot) is destroyed by means of the FLASH sequence, the remaining transverse magnetization before the repeated excitation pulse by a spoiler gradient, i .e. it adjusts itself after a few excitation pulses of the Steady State of the longitudinal magnetization, Only this is used for imaging. A disadvantage of the methods described above, particularly in the echo-planar imaging, is the high sound generation associated therewith. This is due to the effect of the Lorentz force on the within the magnetic field gradient coils, which are traversed by a time (with frequencies around 500 Hz) varying current having a strength of several amperes. With increasing magnetic field strength increases, the sound intensity of the gradient switching processes, this make often in the form of loud knocking sounds, with some devices as clayey noise noticeable. Consequently, limiting the noise depending on the task to be handled by the subject ( "task") is adversely required.

p0019In auditory experiments, limitations arise from the fact that the image recording noise can mask the stimuli partially Furthermore generates this noise as an additional acoustic stimulus, a difficult to control activation of auditory areas, the effects of the image pickup noise on the auditory cortex are the subject of intensive research. Moreover, formed in the Ec o-planar imaging with moderate lines Readout adversely procedural "ghosting" - artifacts. "Ghosting" artifacts caused by superimposing the actual image with an offset in the phase-coding image. From the prior art, an application of Hilbert curves in the field of MR imaging is also known and has been in: "Detecting Discriminative Functional MRI Activation Patterns Using Space Fllllng Curves" D.Kontos, V.Megalooikonomou, N.Ghubade, C .Faloutsos, EMBC2003, S.963-966 disclosed. It merely is an evaluation of the already recorded (conventional) MR data in terms of patterns that are characteristic of a disease, carried. By the Hilbert curve 3D data sets are mapped to 1 D data structures, which are then compared with each other.

p0020In view of the disadvantages described above, it is therefore an object of the present invention to provide a method and an apparatus that enable a quieter compared implementation and improve the imaging and claim the device compared less and reduce the demand on these.

p0021This object is represented by the generic method having the features of claims 1 and 7 and by Vorrich. ung solved according to claim 1. 3 Vorteilhaf te Ausgestali ments result from the dependent claims

p0022The inventive imaging method for nuclear magnetic resonance provides that a sample applied a konstan.es sfaiiεches Magneifeld Typically, the magnetic field at s.ai iscne gegenwartigen MR tomograph weιsτ a Strong between e^x ao, 25 and 1 0 t on. The basic field is required to guarantee a minimum size of Sιgnal-to-smoke-Verhaltmsses When using hyperpolarisier.en nuclei the basic field may consist of comparatively very small. have all, ciso less than 0, 25 T,

p0023The konslan + e sta. ic magnetic field is superimposed by a Zusaizfeid The additional field has the property for each point at least one grating surface within the sample volume at each point of Gilterebene, only e'nrna another, occurring field strength value to have, it can not be aabei involve several Giiterflachen and these must be mandatory pianar it may be spherical or cylindrical surfaces uie sample is also stimulated by a hochfrequenres, alternating electromagnetic field the inventive imaging method further provides that the light emitted by the excited sample solenoid see radiation is recorded and evaluated to Bildgenerlerung by using the so predefined additional field, a varying gradient zeiϊlich omitted gelιngτ folglicn, a magnetic resonance (MR) -Bιld with a single

p0024take high-frequency excitation onne time varying gradient, which in turn thus verounaene Schallentwickiung advantageously prevents, the field can be swept gehalτen temporally constant over several measurements, making a broadband radio-frequency excitation necessary. Or it may be switched by using a narrow-band excitation compared for each measurement. For narrow-band excitation, the resonant frequencies of spins in close proximity, which is achieved for example by switching off the additional field are. In a broadband excitation, the additional field may persist, which is easily to carry. In the method according to the invention further, the light emitted by the excited sample electromagnetic radiation is read and evaluated for Bildgenerlerung.

p0025According to another embodiment of the method the additional field is described by area or space-filling curves, these curves have a one-one mapping of the field strength value and point of the grid. Due to the one-one mapping between position and frequency, the image reconstruction may be performed by a 1 D Fourier transformation, a raw data array is filled with data and converted into an MR image by means of a 1 D Fourier transform, the measuring a plurality of surfaces, for example, carried out sequentially. Thus, the object to be examined is transported for example to the measuring arrangement by or through it or individual segments of the measurement arrangement activated sequentially. The additional field is described by area or space-filling curves. For example, it is being constructed by L-systems around curves as Peltgen et al. Described in "Chaos and Fractals", This box jumps are advantageously reduced between adjacent points, which in turn minimizes artifacts. The reason for this is that the for möalichst ootimale Erfülluna the Eindeutiakeitsbedinauna hops required in the field strength only approximate can be met (steady transition of the field intensity between adjacent grid points, outlay for field production). A uniqueness violation condition exists z. B. when two different locations are mapped to a frequency in the spectrum. It can not be ascertained, the location from which a signal originates. Provisionally, the signal may then each divided equally between both places. This leads to a blurring of the image, particularly along lines which are between regions with very different field strengths. The so-defined magnetic field is generated, for example, with a current-carrying coil arrangement which is determined by a numerical optimization. This is a magneto-static calculation, the differences from the predetermined magnetic field values ​​and the numerically determined values ​​are to be minimized.

p0026Another mode of the invention provides that a plurality of regions of the sample are the same, ie measured parallel in time, For example, this is achieved in that a measuring device is used, which is configured multiple times. This method can be carried out very quickly.

p0027In a further advantageous variant of the invention, echoes are generated. This is a fast measuring technique, which are, for example, is spin-echo and gradient. To generate the echoes is provided in a further embodiment that the additional field changes sign on the tent. By a change of sign can be prepared analogously to known MR imaging produce gradient, but not for individual k-space lines, but for an entire image at one time, this allows the implementation of a fast spectroscopic MR imaging: an excitation and receiving several consecutive echo images. In another embodiment of the method, the additional field is described by a Hilbert curve, a special spatial and area-filling curve. If the Hilbert curve is based on, resulting in a hierarchical artifact structure, ie there is a negative correlation between artifact size and frequency. Thus, a compromise is advantageously achieved because weak artifacts can be tolerated more than strong.

p0028The inventive method can be used to measure current distributions or magnetic fields, characterized in that no gradients are switched, no (undesirable) currents can be induced in the sample,

p0029Another alternative imaging techniques for the nuclear magnetic resonance provides that in the sample by means of high frequency excitation, a spatially detectable transverse magnetization is generated. By switching of imaging gradient occurs, for example, a spatially resolved measurement of the transverse magnetization. It takes place in a Datenakquisltionsphase the readout of the signal along self-similar, space-filling curves, and from the data obtained is formed a raw data matrix. Using a Fourier transform an image is extracted from the raw data matrix, In known processes the raw data matrix is ​​generated (so-called k-space) by line or by sampling on circular paths. In the conventional cellular EPI-sampling of the (often operated with virtually maximum amplitude) read gradient alternates between each k-space line, whereby the sequence typical noises with frequencies of the order of 500Hz. "Sequence" refers to the sequence of radio frequency excitations, gradient pulses and data acquisitions In the inventive method the sign of the gradient changes significantly more often, almost every k-space point;.. Which practically corresponds to a sequence of EPI'Blips' With Blip 'a gradient pulse is referred to, which is required for changing from one k-space line to the next. This has the consequence that the Gradientengeräusche advantageously be moved to a higher frequency range (at a resolution of 64x64 of frequencies around 500Hz frequencies to 32000Hz). this effect can be used advantageously for performing auditory brain imaging studies because they are strongly affected by gradient partly, in part, this is because the human ear is particularly sensitive in relevant for voice generation frequency range.

p0030Complicated and expensive measures for reducing sound generation by passive or even active

p0031Sound attenuation can be advantageously eliminated by the inventive process. Sequence technical measures for noise reduction are made according to the prior art in the Verlαngsαmung the k-Rαum-Reαdouts and the reduction of k Rαumzeilen, which adversely increases the measurement time and reduces the resolution of the measurement. The inventive method also avoids prolonged 'gradient plateaus¹, Resulting in a relief of the gradient amplifiers respectively, results in lower technical demands on the gradient amplifiers. Another advantage of the image coding according to the invention consists in a reduction of the periodicity of Gradientenzeitverlaufs, are in turn reducing mechanical resonances of the imaging device.

p0032According to another embodiment of the inventive method, the space-filling trajectory described by a Hilbert curve. In the Hilbert curve (trajectory) adjacent k-space points are sampled at similar points in time, whereby possible artifacts spread evenly over the k-space, a similar procedure exists in methods for color space reduction position space images when ( "dither algorithms ").

p0033Another embodiment provides that the Datenakquisation done in segments, ie the k-space is divided into individual segments, which in turn are scanned along a space-filling curve ( "hybrid method"), ie, for each segment, an excitation pulse is generated. Segmentation may be particularly advantageous if the relaxation times are short,

p0034The above method can advantageously be realized with known and existing devices for magnetic resonance imaging, for example, the pulse sequence is adjust. Another embodiment of the method provides that the image coding takes place in 3 dimensions. It is therefore suitable for the so-called echo Volumar imaging. This is a three-dimensional EPI wherein is advantageous to forego the layer selection.

p0035A- further embodiment provides that parts of the measuring arrangement can be moved to the sample over or through the sample or individual gradient coils are activated in sequence.

p0036The invention further relates to devices for carrying out the processes described above in each case with the connected thereto advantages. According to a first device, a constant, static magnetic field is provided, which acts on a sample. The apparatus includes means for generating an additional field that is superimposed on the static magnetic field and in any point of the grating surface has a different field strength values ​​within the sample volume in at least one grating surface. Further, means for generating a high-frequency electromagnetic alternating field, whereby the sample is excited, is provided in a particularly simple variant, the means for generating a high-frequency electromagnetic alternating field, a the total sample enclosing RF transmit / receive coil. The means for reading serve the registration of the light emitted by the excited sample electromagnetic radiation, further comprising means for evaluating and Bildgenerlerung. For example, it concerns with the devices to known MR imaging devices. By using the so predetermined Zusαtzfeldes can be dispensed with a time-varying gradient. It succeeds thus, a magnetic resonance (MR) image with a single radio frequency excitation without taking time varying gradient, which in turn the sound generation associated therewith binds advantageous

p0037According to a further embodiment of the device according to the invention, the means for generating an additional field a micro-coil assembly. For example, it is known as micro coil array, as used in the surface measurement or in biology or biochemistry for screening systems. The field may be generated, for example, with microcoils, which are arranged on a rectangular area like a matrix (n × n), the sample is, for example, on these coils or adjacent to these on immediately. To describe the additional field, for example, by a Hilbert curve, a special spatial and area-filling curve, the currents of microcoils are defined by the values ​​along this Hilbert curve with linear increase in field strength along the curve, another device of the invention provides that means are provided for generating a detectable transverse magnetization in a sample. The apparatus further provides means for data acquisition of a signal along a self-similar, space-filling trajectory. Furthermore, means are provided for data analysis, forming a raw data matrix from the acquired data and gain from the raw data matrix with a Fourier transform image. The device of the invention advantageously provides for a reduction or frequency shift of the "sequence" noises. The effect can be beneficial for performing auditory Gehi nbildgebungs studies are used because they are strongly affected by gradient sometimes. In part this is because the human ear is particularly sensitive in relevant for voice generation frequency range, Complicated and expensive measures for reducing sound generation by passive or even active sound attenuation can advantageously be dispensed with in the inventive device. The device can be comparatively easily maintained because prolonged 'gradient plateaus "are avoided, resulting in a relief of the gradient amplifiers or less technical demands on the gradient amplifier shown Another advantage of the image coding according to the invention consists in a reduction of the periodicity of Gradientenzeitverlaufs, are in turn reducing mechanical resonance of the imaging device.

p0038The Flauren: Figure 1 is a 3D representation of a two-dimensional Hilbert curve. The z-coordinate is the date on which the corresponding k-space point is reached or the strength of the additional field as a function of position.

p00392a shows an example of the k_χComponent of a Hilbert trajectory for a resolution of 64x64 voxels.

p0040Figure 2b shows an example of the k component of a Hilbert trajectory for a resolution of 64x64 voxels. Figure 3α shows the x-component of Grαdientenfeldes for coding the Hilbert Trαjektorie that results by time derivation from the k (t) curve. Figure 3b shows the y-component of the gradient field for the coding of the Hilbert trajectory that results from the time derivative of k (t) curve.

p0041Summary: The present invention relates to an imaging method and apparatus for nuclear magnetic resonance. The method provides a hand in front of a picture coding by an additional field, which has a different, once occurring field strength value for each point of a 2-dimensional grid area within ö.e ^ sample, v / ie it z. B. in on itself like, area- or . SFC curves based fields is the case, the other hand, a readout of the resonance behavior of a sample can be provided along a space-filling or surface-filling curve, In the first variant can be added without time-varying gradient, a magnetic resonance (MR) -Biid with a single radio frequency excitation what Schailenfwickiung associated advantageously prevents, in the second variant, the noise generated in the readout are advantageously moved to a different frequency range where the human ear has a lower sensitivity, addition as the device is released and the technical requirements for these reduced. Further, it can be carried out with known and existing devices.