SYSTEM AND APPARATUS FOR SIMPLIFIED DIFFUSION IMAGING FITTING USING A ROTATIONAL INVARIANT DICTIONARY

A computer-implemented method includes: generating a set of simulated diffusion signals based on a corresponding set of diffusion sampling parameters and a corresponding set of micro structural model parameters, wherein the diffusion sample parameters correspond to magnetic resonance (MR) parameters, and wherein the microstructural model parameters characterizing a microscopic diffusion with a spatial orientation; processing the set of simulated diffusion signals based on the corresponding set of diffusion sampling parameters to generate a first set of output metrics, wherein the first set of output metrics are associated with the spatial orientation; consolidating multiple sets of output metrics into a dictionary, wherein each set of the multiple sets of output metrics are generated by processing a corresponding set of simulated diffusion signals and associated with a corresponding spatial orientation; applying the dictionary to a set of acquired diffusion MR signals; and generating at least one macroscopic diffusion feature that is orientation invariant.

TECHNICAL FIELD

This description generally relates to magnetic resonance imaging (MRI).

BACKGROUND

MRI is a noninvasive medical diagnostic technique in which the absorption and transmission of high-frequency radio waves are analyzed as they irradiate the hydrogen atoms in water molecules and other tissue components placed in a strong magnetic field. MRI provides soft-tissue images with superior contrast compared to other imaging modalities and has therefore become widely used for human imaging. Diffusion imaging is an MRI method that produces in vivo magnetic resonance images of biological tissues sensitized with the local characteristics of molecular diffusion, generally water. Diffusion imaging thus allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and non-invasively. Molecular diffusion in tissues is not free, but reflects interactions with many obstacles, such as macromolecules, fibers, and membranes. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state.

SUMMARY

In one aspect, implementations provide a computer-implemented method that includes: generating a set of simulated diffusion signals based on a corresponding set of diffusion sampling parameters and a corresponding set of microstructural model parameters, wherein the diffusion sample parameters correspond to magnetic resonance (MR) parameters for acquiring MR signals, and wherein the microstructural model parameters characterize a microscopic diffusion with a spatial orientation; processing the set of simulated diffusion signals based on the corresponding set of diffusion sampling parameters to generate a set of output metrics, wherein the set of output metrics are associated with the spatial orientation; consolidating multiple sets of output metrics into a dictionary, wherein each set of the multiple sets of output metrics are generated by processing a corresponding set of simulated diffusion signals and are associated with a corresponding spatial orientation; applying the dictionary to a set of acquired diffusion MR signals; and subsequently generating at least one macroscopic diffusion feature that is orientation invariant.

The applying may include: processing the set of acquired diffusion MR signals to generate a set of acquired metrics; and based on the set of acquired metrics, performing a lookup at the dictionary to generate the at least one macroscopic diffusion feature. The set of acquired diffusion MR signals may be associated with a corresponding set of diffusion sample parameters.

The at least one macroscopic diffusion feature may include: an apparent fiber diameter, and an apparent fluid fraction. The output metrics may include: a mean diffusivity MD, an axial diffusivity AD, a radial diffusivity RD, a fractional anisotropy FA, and a compartment fraction fResfor restricted motion, a compartment fraction fHinfor hindered motion, and a compartment fraction fFrefor free motion. The diffusion sampling parameters may include: a b-value b, a normalized gradient vector g, a mixing time Δ, and a pulse width δ. The microstructural model parameters may include: a radius r, an intracellular diffusivity D0, a fluid fraction ρ, a parallel diffusivity D1, and a fluid diffusivity Dρ.

The processing may include: performing one or more diffusion fittings of the set of simulated diffusion signals. The one or more diffusion fittings may include: a model-based de-noising, or a diffusion tensor imaging (DTI) fitting.

The consolidating may include: averaging the multiple sets of output metrics, and wherein said averaging comprises one of: an arithmetic mean, a geometric mean, or a median.

In another aspect, implementations may provide a computer system that includes at least one computer processor configured to perform operations of: generating a set of simulated diffusion signals based on a corresponding set of diffusion sampling parameters and a corresponding set of microstructural model parameters, wherein the diffusion sample parameters correspond to magnetic resonance (MR) parameters for acquiring MR signals, and wherein the microstructural model parameters characterizing a microscopic diffusion with a spatial orientation; processing the set of simulated diffusion signals based on the corresponding set of diffusion sampling parameters to generate a set of output metrics, wherein the set of output metrics are associated with the spatial orientation; consolidating multiple sets of output metrics into a dictionary, wherein each set of the multiple sets of output metrics are generated by processing a corresponding set of simulated diffusion signals and are associated with a corresponding spatial orientation; applying the dictionary to a set of acquired diffusion MR signals; and subsequently generating at least one macroscopic diffusion feature that is orientation invariant.

The operation of applying a set of acquired diffusion MR signals to the dictionary may include: processing the set of acquired diffusion MR signals to generate a set of acquired metrics; and based on the set of acquired metrics, performing a lookup at the dictionary to generate the at least one macroscopic diffusion feature. The set of acquired diffusion MR signals may be associated with a corresponding set of diffusion sample parameters.

The at least one macroscopic diffusion feature may include: an apparent fiber diameter, and an apparent fluid fraction. The output metrics may include: a mean diffusivity MD, an axial diffusivity AD, a radial diffusivity RD, a fractional anisotropy FA, and a compartment fraction fResfor restricted motion, a compartment fraction fHinfor hindered motion, and a compartment fraction fFrefor free motion. The diffusion sampling parameters may include: a b-value b, a normalized gradient vector g, a mixing time Δ, and a pulse width δ. The microstructural model parameters may include: a radius r, an intracellular diffusivity D0, a fluid fraction ρ, a parallel diffusivity D1, and a fluid diffusivity Dρ.

The operation of processing the set of simulated diffusion signals may include: performing one or more diffusion fittings of the set of simulated diffusion signals. The one or more diffusion fittings may include: a model-based de-noising, or a diffusion tensor imaging (DTI) fitting. The operation of consolidating multiple sets of output metrics may include: averaging the multiple sets of output metrics, and wherein said averaging comprises one of: an arithmetic mean, a geometric mean, or a median.

Implementations according to the present disclosure may be realized in computer implemented methods, hardware computing systems, and tangible computer readable media. For example, a system of one or more computers can be configured to perform particular actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions.

The details of one or more implementations of the subject matter of this specification are set forth in the description, the claims, and the accompanying drawings. Other features, aspects, and advantages of the subject matter will become apparent from the description, the claims, and the accompanying drawings.

DETAILED DESCRIPTION

MRI can be made sensitive to the motion of molecules. Regular MRI acquisition utilizes the behavior of protons in water to generate contrast between clinically relevant features of a particular subject. The versatile nature of MRI renders it capable of producing contrast related to the structure of tissues at the microscopic level. In an MRI image, water molecules in a sample are excited with the imposition of a strong magnetic field. This causes many of the protons in water molecules to precess simultaneously, producing signals in MRI. In weighted images, contrast is produced by measuring the loss of coherence or synchrony between the water protons. When water is in an environment where it can freely tumble, relaxation tends to take longer. In certain clinical situations, this altered relaxation can generate contrast between an area of pathology and the surrounding healthy tissue.

To sensitize MRI images to diffusion, the magnetic field strength (B1) is varied linearly by a pulsed field gradient. Since precession is proportional to the magnet strength, the protons begin to precess at different rates, resulting in dispersion of the phase and signal loss. Another gradient pulse is applied in the same magnitude but with opposite direction to refocus or rephase the spins. The refocusing will not be perfect for protons that have moved during the time interval between the pulses, and the signal measured by the MRI machine is reduced.

In order to localize this signal attenuation to obtain diffusion images, one has to combine the pulsed magnetic field gradient pulses used for MRI (aimed at localization of the signal, but those gradient pulses are too weak to produce a diffusion related attenuation) with additional “motion-probing” gradient pulses. Summarizing all the gradient terms in a “b factor” (which depends only on the acquisition parameters), the signal attenuation of the non-diffusion signal S0can be characterized as:

S=S0exp(−bD), or

Here, b is gradient strength, and D, or ADC is the apparent diffusion coefficient indicating that the diffusion process is not free in tissues, but hindered and modulated by many mechanisms (restriction in closed spaces, tortuosity around obstacles, etc.)

In the context of applying diffusion imaging to quantify muscle fibers, a major challenge is to reliably and non-invasively estimate the muscle fiber diameter using a cylinder model. A solution to this challenge can render it feasible to depict microstructural changes of the muscle following pathologic insult, which can aid in the diagnosis and treatment of neuromuscular conditions.

For parameter fitting of diffusion imaging data, complex models may involve many parameters related to the radial and angular dimensions of diffusivity. Previously reported approaches generally focus on fitting either the radial or angular dimensions, alone, to simplify the fitting process. Under conventional wisdom, fitting for both radial and angular diffusivity is feasible, but it is computationally intensive and can result in poor convergence of the fitted solution.

Notably, the diameter is in the radial direction, for which a rotationally-invariant method would be better suited. The first technical challenge is to identify a robust, rotationally-invariant way to fit the model, for example, a cylindrical model. To this end, simple, rotationally-invariant metrics, as proposed in the literature, are not directly related to the more complicated fiber diameter model. Other approaches that leverage rotationally-invariant basis functions generally include parameters that operate by virtue of complicated mathematical analytics for relating cylinders to these basis functions. Such may not lend itself to a practical solution in most cases.

The second technical challenge is to find an efficient way to fit the cylinder model to the estimation muscle fiber diameter. While various optimization methods can be used, these methods tend to be computationally time consuming. Moreover, these methods have focused on angular diffusivity, and are not rotationally-invariant. A dictionary method can be efficiently applied for look-up. Furthermore, if the size of the dictionary can be reduced, computational time can be decreased.

FIG.1shows an example of a magnetic resonance imaging (MRI) system5with a solenoid magnet for imaging knee joints. The MRI system5includes a workstation10having a display12and a keyboard14. The Workstation10includes a processor16that is a commercially available programmable machine running a commercially available operating system. The workstation10provides the operator interface that enables scan prescriptions to be entered into the MRI system5. The workstation10is coupled to four servers including a pulse sequence server18, a data acquisition server20, a data processing server22, and a data store server23. The work station10and each server18,20,22and23are connected to communicate with each other.

The pulse sequence server18functions in response to instructions downloaded from the workstation10to operate a gradient system24and an RF system26. Gradient waveforms necessary to perform the prescribed scan are produced and applied to the gradient system24that excites gradient coils in an assembly28to produce the magnetic field gradients Gx, Gy and Gz used for position-encoding MR signals. The gradient coil assembly28forms part of a magnet assembly30that includes a polarizing magnet32and a whole-body RF coil34.

RF excitation waveforms are applied to the RF coil34by the RF system26to perform the prescribed magnetic resonance pulse sequence. Responsive MR signals detected by the RF coil34or a separate local coil (not shown inFIG.1) are received by the RF system26, amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server18. The RF system26includes an RF transmitter for producing a wide variety of RF pulses used in MR pulse sequences. The RF transmitter is responsive to the scan prescription and direction from the pulse sequence server18to produce RF pulses of the desired frequency, phase and pulse amplitude waveform. The generated RF pulses may be applied to the whole body RF coil34or to one or more local coils or coil arrays (not highlighted inFIG.1).

The RF system26also includes one or more RF receiver channels. Each RF receiver channel includes an RF amplifier that amplifies the MR signal received by the coil to which it is connected and a detector that detects and digitizes the I and Q quadrature components of the received MR signal.

The pulse sequence server18also optionally receives patient or subject data from a physiological acquisition controller36. The controller36receives signals from a number of different sensors connected to the patient, such as ECG signals from electrodes or respiratory signals from a bellows. Such signals are typically used by the pulse sequence server18to synchronize, or “gate”, the performance of the scan with the subject's respiration or heartbeat.

The pulse sequence server18also connects to a scan room interface circuit38that receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit38that a patient positioning system40receives commands to move the patient to desired positions during the scan by translating the patient table41.

The digitized MR signal samples produced by the RF system26are received by the data acquisition server20. The data acquisition server20operates in response to instructions downloaded from the workstation10to receive the real-time MR data and provide buffer storage such that no data is lost by data overrun. In some scans the data acquisition server20does little more than pass the acquired MR data to the data processor server22. However, in scans that require information derived from acquired MR data to control the further performance of the scan, the data acquisition server20is programmed to produce such information and convey it to the pulse sequence server18. For example, during prescans, MR data is acquired and used to calibrate the pulse sequence performed by the pulse sequence server18. Also, navigator signals may be acquired during a scan and used to adjust RF or gradient system operating parameters or to control the view order in which k-space is sampled. In all these examples the data acquisition server20acquires MR data and processes it in real-time to produce information that is used to control the scan.

The data processing server22receives MR data from the data acquisition server and processes it in accordance with instructions downloaded from the workstation10. Such processing may include, for example, Fourier transformation of raw k-space MR data to produce two or three dimensional images, the application of filters to a reconstructed image, the performance of a back projection image reconstruction of acquired MR data; the calculation of functional MR images, the calculation of motion or flow images, and the like.

Images reconstructed by the data processing server22are conveyed back to the workstation10where they are stored. Real-time images are stored in a data base memory cache (not shown) from which they may be output to operator display12or a display42that is located near the magnet assembly30for use by physicians. Batch mode images or selected real time images are stored in a host database on disc storage44. When such images have been reconstructed and transferred to storage, the data processing server22notifies the data store server23on the workstation10. The Workstation10may be used by an operator to archive the images, produce films, or send the images via a network to other facilities.

As shown inFIG.1, the RF system26may be connected to the whole body RF coil34while a transmitter section of the RF system26may connect to one RF coil152A and its receiver section may connect to a separate RF receive coil152B. Often, the transmitter section is connected to the whole body RF coil34and each receiver section is connected to a separate local coil152B. In this illustration, RF receive coil152B can be a phased array coil. In some cases, the phased array coil is a receive-only coil. In other cases, the phased array coil functions as both a transmitter and a receiver (also known as a transceiver).

For additional context, an MRI scanner can be adapted to perform diffusion imaging. For example, in combination with innovative gradient waveforms and timing, a variety of diffusion MR techniques enable the measurement of the restricted diffusion of water in tissue to capture the spatial distribution of diffusion, which can be anisotropic. These MR techniques include, for example, diffusion weighted imaging and diffusion tensor imaging (DTI). For context, DTI can produce not only neural tract images but also images of the muscle—including heart muscle—as well as other tissues such as the prostate.

In DTI, each voxel has one or more pairs of parameters: a rate of diffusion and a preferred direction of diffusion—described in terms of three-dimensional space—for which that parameter is valid. The properties of each voxel of a single DTI image can be calculated by vector or tensor math from six or more different diffusion weighted acquisitions, each obtained with a different orientation of the diffusion sensitizing gradients. In some methods, hundreds of measurements—each making up a complete image—are made to generate a single resulting calculated image data set. The higher information content of a DTI voxel makes it extremely sensitive to subtle pathology in the brain. In addition, the directional information can be exploited at a higher level of structure to select and follow neural tracts through the brain—a process called tractography.

In more detail, during image acquisition, the image-intensities at each position are attenuated, depending on the strength (b-value) and direction of the so-called magnetic diffusion gradient, as well as on the local microstructure in which the water molecules diffuse. The more attenuated the image is at a given position, the greater diffusion there is in the direction of the diffusion gradient. In order to measure the tissue's complete diffusion profile, one needs to repeat the MR scans, applying different directions (and possibly strengths) of the diffusion gradient for each scan.

Various brain and muscle pathologies may be detected by measuring anisotropy and diffusivity. As mentioned, the underlying physical process of diffusion causes a group of water molecules to move out from a central point, and gradually reach the surface of an ellipsoid or cylinder if the medium is anisotropic, or the surface of a sphere in the case of an isotropic medium. The ellipsoid formalism functions also as a mathematical method of organizing tensor data. Measurement of an ellipsoid tensor further permits a retrospective analysis, to gather information about the process of diffusion in each voxel of the tissue. Once each voxel has been measured from six or more directions, the spatial distribution of the diffusion for each voxel can be characterized based on information from the ellipsoid tensor. The diffusion is thus quantified as a tensor to characterize, for example, anisotropic properties in space.

Various implementations of the present disclosure can perform orientation-invariant diffusion fitting by constructing an orientationally-invariant dictionary for the fitting. As shown inFIG.2, diagram200illustrates an example of generating an orientationally-invariant dictionary according to some implementations. This diagram200includes forward model201and fitting segment211. During forward model201, diffusion sampling parameters202and desired microstructure model parameters203are combined and correlated to generate the diffusion signal205. Examples of diffusion sampling parameters include: a b-value, a gradient amplitude, a pulse width (e.g., associated with the gradient waveform), a mixing time (e.g., characterizing the temporal separation between two gradient waveforms surrounding, for example, a 180 degree inversion radio-frequency pulse), a gradient direction (e.g., in a three dimensional space), and a q-value (e.g., a value in q space for characterizing the motion of slow-diffusion component). As to the microstructural model parameters, examples can include: fiber diameter, spherical diameter, cell size, and axon diameter. The forward model201can combine diffusion sampling parameters202and desired microstructural model parameters203to generate diffusion signal205, which can be simulated. Such diffusion signal205, as well as diffusion sampling parameters, are then processed by the fitting block206to generate diffusion metrics207. These metrics can include mean diffusivity, radial diffusivity, axial diffusivity, fractional anisotropy, and fraction of compartments of diffusivity such as the restricted fraction, hindered fraction and free fraction. In addition, the acquired diffusion data204, which is fed separately into the fitting block206to generate the metrics (acquired)208that are computed for the forward model diffusion signal205.

FIG.3is a diagram300illustrating an example of feeding metrics for each model parameter set and orientation according to some implementations. In more detail, diagram300shows the next step that constructs a dictionary. As illustrated, diagram300involves feeding the metrics (model) for each model parameter set (1 to P) and orientation (1 to N). These instances of metrics (model) are illustrated by metrics (model)207A (from orientation 1, parameter set 1), metrics (model)207B (from orientation N, parameter set 1), and metrics (model)207C (from orientation N, parameter set P). These instances of metrics are averaged across all orientations302to generate an averaged metric-by-parameter dictionary303. This averaging is typically best depicted by an arithmetic mean, although geometric mean and median may also apply.

FIG.4is a diagram400illustrating an example of using the metrics (acquired) and the dictionary to look up microstructure model parameters according to some implementations. Here, the metrics (acquired)208are provided to look-up block401, along with the earlier generated dictionary303as inputs. The dictionary303is used to look-up the output model parameters based on the incoming instance of metrics (acquired)208. In turn, the look-up block401identifies microstructure model parameters203. As illustrated, the application of the dictionary allows the microstructure model parameters203to be generated in one look-up operation, rather than a lengthy fitting and optimization process, which can be timing consuming and prone to inaccuracies due to, for example, local minima during a typical simplex search or gradient descent search.

FIG.5is a diagram500illustrating an example of applying the orientation-invariant diffusion fitting for a muscle fiber diameter application according to some implementations. Diagram500includes a forward model501and a fitting segment502that demonstrate an example of applying the orientation-invariant diffusion fitting to investigating a muscle fiber diameter, based on a combination of steps fromFIGS.2-4. Here, the solid line arrows indicate the model processing and dashed lines indicate acquired data processing. As illustrated, diffusion sample parameters502(including, for example, b-value, b, normalized gradient vector g, mixing time Δ, and pulse width δ) and cylinder model parameters503(including radius r, intracellular diffusivity D0, fluid fraction ρ, parallel diffusivity D1and fluid diffusivity Dρ) are combined to generate diffusion signal505. Diffusion sample parameters502and diffusion signal505are provided to fitting block506for DTI fitting and model-based de-noising. Fitting block506generates output metrics507that are rotationally-invariant. Examples of such output metrics include mean diffusivity MD, axial diffusivity AD, radial diffusivity RD, fractional anisotropy FA, and compartment fractions for restricted fRes, hindered fHinand free fFre. In general, mean diffusivity characterizes diffusion as a scalar quantity. In comparison, axial diffusivity, and radial diffusivity characterize diffusion along a respective direction. Fractional anisotropy refers to a fraction of the diffusion that is anisotropic. By way of background, most fluids and some homogeneous solid materials like gels, diffusion is the same in every direction. These substances are called isotropic and are characterized by a single diffusion coefficient (D). Biological tissues, on the other hand, are highly structured and typically have different diffusion coefficients along different directions and are called anisotropic. Virtually all biological materials demonstrate some degree of anisotropy. White matter is highly anisotropic because of the parallel orientation of its nerve fiber tracts. Other tissues demonstrating significant anisotropy include skeletal muscle and peripheral nerves. Free water diffusion describes the random (Brownian) motion of water molecules due to thermal agitation, in the absence of any obstacles. Hindered and restricted diffusion are two distinct processes that result from fundamentally different behavior of spins within different tissue compartments, which may be either intra- or extracellular depending on the type of tissue being modeled. In the context of muscle fiber diffusion anisotropy, the number of orientations used can be 30 for muscle fibers, although this could be increased to >100 for highly anisotropic axons in the brain or just 6 for more isotropic tissue. A collection of the metrics (model) can be averaged across various orientations512to generate dictionary513. The diffusion data acquired with the same diffusion sampling parameters504are fed into the same fitting block506to obtain the acquired metrics507. The acquired metrics are then provided along with the dictionary513for a processor to look up the dictionary514to identify output parameters515. Looking up the table usually involves finding the values in the dictionary that best approximate the acquired metrics, such as the nearest neighbor value in the dictionary. In some cases, examples of the output parameters include apparent fiber diameter AFD=2r and apparent fluid fraction AFF=ρ.

FIGS.6A to6Dshow results from the muscle fiber diameter example ofFIG.5according to some implementations. In particular,FIGS.6A to6Drespectively shows the metrics of mean diffusivity (MD), fractional anisotropy (FA), compartment fractions for restricted fResand compartment fractions for free fFreas a function of fiber diameter r for a range of apparent fluid fraction ρ.

FIG.7shows examples from analyzing muscle fiber diameter for two subjects according to some implementations. In particular,FIG.7shows results from two clinical examples: a healthy subject in panels a to d, and a patient with spontaneous, bilateral upper extremity neuropathy (i.e. Parsonage-Turner syndrome leading to severe muscle weakness) in panels e to h. As to the healthy subject, panels a and b respectively show coronal MRI T2-weighted images from the left and the right brachial plexi, while dashed line in panels a and b shows the respective muscle fiber diameter maps of the oblique axial diffusion acquisition for panels c and d. The coronal Dixon water images from panels a and b confirm no muscle edema patterns in the healthy subject. Regarding the patient with spontaneous neuropathy, panels e to f show the coronal MRI T2-weighted images from the left and the right brachial plexus while panels g to h show the respective muscle fiber diameter maps of the oblique axial diffusion acquisition. A comparison between the two subjects demonstrate that the patient has reduced diameter relative to the healthy subject. In particular, results from the healthy subject demonstrates high AFD in the left (c) and right (d) shoulder muscles. As to the patient, clinical exam reported deltoid weakness on the left (g) and right (h), and infraspinatus and supraspinatus (not shown) weakness only on the right. The result of right deltoid and infraspinatus muscles (2/5 British Medical Research Council muscle grade testing) being weaker than the left (3/5) was consistent with AFD on the right (h) being lower than the left (g). Arrows point to denervated muscle identified on MRI, green arrows to non-denervated muscle.

In an additional study, 30 subjects underwent both electromyography (EMG) and 3-Tesla MRI for suspected neuropathy. In this study, diffusion imaging was also performed to obtain the apparent fiber diameter (AFD). For EMG, motor unit recruitment (MUR) and denervation potentials were assessed. Linear mixed models were used to estimate AFD differences between EMG grades. Significant AFD decreases (by −11.04 to −21.58 μm, p=0.0136) were observed with all abnormal motor unit recruitment (MUR) grades as compared to ‘full’ MUR (mean of 78.35 μm). Significant changes in AFD were also observed with increased denervation potentials (by −16.25 to −18.66 μm, p<0.0001). This additional study further confirms the robustness of the implementations described in this disclosure.

As used herein, the terms “about” and “approximately” are meant to cover variations that may exist in the upper and lower limits of the ranges of values, such as variations in properties, parameters, and dimensions. In one non-limiting example, the terms “about” and “approximately” mean plus or minus 10 percent or less.

The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., a central processing unit (CPU), a FPGA (field programmable gate array), or an ASIC (application specific integrated circuit).