The present disclosure relates to measurement and monitoring of magnetic resonance imaging. In particular, the disclosure relates to an optical system for measurement of the position of a rigid body in space adapted for applications in the field of magnetic resonance imaging.
Computerized tomography (CT), magnetic resonance imaging (MRI), and positron emission tomography (PET), coupled with developments in computer-based image processing and modeling capabilities have led to significant improvements in the ability to visualize anatomical structures in human patients. This information has become invaluable in the diagnosis, treatment, and tracking of patients. The technology has been recently been expanded to be used in conjunction with real-time interventional procedures.
MRI is a known method of creating images (referred to as MR images) of the internal organs in living organisms. The primary purpose is demonstrating pathological or other physiological alterations of living tissues. MRI has also found many niche applications outside of the medical and biological fields such as rock permeability to hydrocarbons and certain non-destructive testing methods such as produce and timber quality characterization. Superb image contrast for soft tissues and high spatial resolution have established MRI as a prepared imaging technology. MRI is unique in that many tissue properties can be simultaneously observed.
The MRI process requires a highly accurate and stable target. This is a consequence of the process by which medical MRI functions. Medical MRI relies on the relaxation properties of excited hydrogen nuclei in water. When an object is placed in a powerful, uniform magnetic field, the spins of the atomic nuclei with non-zero spin numbers align in one of two opposite directions: parallel to the magnetic field or antiparallel.
The difference in the number of parallel and antiparallel nuclei is only about one in a million. However, due to the vast quantity of nuclei in a small volume, the nuclei sum to produce a detectable change in field strength. The magnetic dipole moment of the nuclei then moves in a gyrating fashion around the axial field. While the proportion is nearly equal, slightly more nuclei are oriented at the low energy angle. The frequency with which the dipole moments process is called the Larmor frequency. The tissue is then briefly exposed to pulses of electromagnetic energy (RF pulse) in a plane perpendicular to the magnetic field, causing some of the magnetically aligned hydrogen nuclei to assume a temporary non-aligned high-energy state.
In order to selectively image the different voxels (3-D pixels) of the material in question, three orthogonal magnetic gradients are applied, slice selection, phase encoding and frequency encoding. Usually, the three gradients are applied in the X, Y, and Z directions. Any small shift in the position of the patient with respect to these fixed gradient axes will alter the orientations and positions of the selected slices and result in poor imaging.
In order to create an MR image, spatial information must be recorded along with the received tissue relaxation information. For this reason, magnetic fields with an intensity gradient are applied in addition to the strong alignment field to allow encoding of the position of the nuclei. A field with the gradient increasing in each of the three dimensional planes is applied in sequence. This information is then subsequently subjected to a Fourier transformation by a computer that transforms the data into the desired image and yields detailed anatomical information results.
With conventional anatomic MR imaging, the presence of moving biological tissue is problematic. The tissue produces image artifacts, degrades the quality of the images, and complicates the interpretation of MR images. The typical appearance of such image artifacts takes the form of “blurring,” or a characteristic “motion ghost” in the phase encoding direction associated with incorrectly encoding the spatial frequencies of a moving object that is assumed to be static.
Through the process of MRI, anatomy can be defined in great detail, and several other biophysical and metabolic properties of tissue, including blood flow, blood volume, elasticity, oxygenation, permeability, molecular self-diffusion, anisotropy, and water exchange through cell membranes, can also be represented. Conventional anatomical MR imaging uses this spin-echo, gradient-echo, and inversion recovery sequencing. There are other methods of MR that are currently being used, including magnetic resonance spectroscopy (MRS), apparent diffusion coefficient (ADC) mapping, diffusion-weighted imaging (DWI) and its derivatives of diffusion tensor imaging and tractography, perfusion imaging, permeability imaging, MR angiography (MRA), and functional MRI (fMRI). As the techniques of MR become more precise, there is corresponding need for increased accuracy and the tracking of the patient during the MR procedure. See, E. F
Functional MRI (fMRI) measures signal changes in the brain that are due to changing neural activity. An fMRI scan is completed at a low resolution but at a very rapid rate (typically once every 1-3 seconds). Increases in neural activity cause changes in the MR signal via a mechanism called the BOLD (blood oxygen level-dependent) effect. Increased neural activity causes a corresponding increased demand for oxygen, which is responded to by the vascular system, which increases the amount of oxygenated relative to deoxygenated hemoglobin. Because deoxygenated hemoglobin attenuates the MR signal, the vascular response leads to a signal increase that is related to the neural activity. The use of MRI to measure physiologic and metabolic properties of tissue non-invasively requires dynamic imaging to obtain time-series data.
The fMRI process relies on neurovascular coupling that results in transient increases in blood flow, oxygenation, and volume in the vicinity of neurons that are functionally activated above their baseline level. Signal changes due to the blood oxygenation-level-dependent (BOLD) effect are intrinsically weak (only several percent signal change from baseline at 4.0 T or less). In addition, as BOLD imaging is typically coupled with a repetitive behavioral task (e.g., passive sensory, cognitive, or sensorimotor task) to localize BOLD signals in the vicinity of neurons of interest, there is significant potential for fMRI to be confounded by the presence of small head motions. Specifically, such motion can introduce a signal intensity fluctuation in time due to intra-voxel movement of an interface between two different tissues with different MR signal intensities, or an interface between tissue and air. Random head motion decreases the statistical power with which brain activity can be inferred, whereas task-correlated motion cannot be easily separated from the fMRI signal due to neuronal activity, resulting in spurious and inaccurate images of brain activation. In addition, head motion can cause mis-registration between neuroanatomical MR and fMR images that are acquired in the same examination session. This latter point is important because the neuroanatomical MRI data serve as an underlay for fMRI color maps, and mis-registration results in mis-location of brain activity. An analogous problem exists for aligning anatomical and functional MR images performed on different days.
Lack of motion in current MRI examinations anatomic motion is very important. Most aspects of human motor system performance require the patient to execute a movement as part of the behavioral task that is imaged to visualize brain activity. Movements can be very simple (e.g., self-paced finger tapping) or more complex (e.g., visually-guided reaching). Such examinations require both that the desired movement is performed in a well-controlled or well-quantified fashion, and also that the movement does not induce task-correlated head motion that confounds the ability to observe brain activity using fMRI. Perhaps the most complicated scenario involves combining use of virtual reality (VR) technology with fMRI, to determine brain activity associated with VR tasks for assessment and rehabilitation of impaired brain function. Such applications are important because they provide the opportunity to visualize brain activity associated with tasks that generalize well to everyday behavior. For example, position tracking would be required to provide a visual representation of a virtual hand operated by a data glove in a virtual environment.
The problem of motion tracking within an fMRI environment has been well documented in published medical literature describing various aspects of motion detection and quantitation. See, Seto et al., NeuroImage, 14:284-297 (2001); Hajnal et al., Magn. Res. Med., 31: 283-291 (1994); Friston et al., Magn. Res. Med., 35:346-355 (1996); Bullmore et al., Human Brain Mapping, 7: 38-48 (1999); Bandettini et al., Magn. Res. Med., 30:161-173 (1993); Cox, Comp. Med. Res., 29:162-173 (1996); Cox et al., Magn. Res. Med., 42:1014-1018 (1999); Grootoonk et al., NeuroImage, 11:49-57 (2000); Freire et al., IEEE Trans. Med. Im., 21(5):470-484 (2002); Babak et al., Mag. Res. Lin., 19:959-963 (2001); Voldye et al., Magn. Res. Med., 41:964-972 (1999), which are each incorporated by reference.
As the clinical applications of MRI expand, there is a concurrent requirement for improved technology to visualize and determine the position and orientation of moving objects in the imaging field. Improvements in position tracking technology are required to advance the resolution and quality of the MRI, including the ability to image the anatomy of a patient, the imaging of tissue functions, the use of MRI data for other imaging tasks, and interventional applications.
For anatomical and functional MRI applications, as well as interventional MRI, there is the additional need to register data from other imaging systems to provide comprehensive and complementary anatomical and functional information about the tissue of interest. Data registration allows different images to be overlaid, or to'ensure that images acquired in different spatial formats (e.g., MRI, conventional x-ray imaging, ultrasonic imaging) can be used to view the same spatial location. While some algorithms exist for performing such registrations, computational cost would be significantly reduced by developing technology that enables data from multiple different imaging modalities to be inherently registered by measuring the patient's orientation in each image with respect to a common coordinate system.
By detecting, tracking, and correcting for changes in movement, data acquisition can be synchronized to a specific target. As a consequence, MR data acquisition is gated to a specific position of the target, and by implication, to a specific position of a specific target region.
U.S. Pat. No. 6,067,465 to Foo, et al. discloses a method for detecting and tracking the position of a reference structure in the body using a linear phase shift to minimize motion artifacts in magnetic resonance imaging. In one application, the system and method are used to determine the relative position of the diaphragm in the body in order to synchronize data acquisition to the same relative position with respect to the abdominal and thoracic organs to minimize respiratory motion artifacts. The time domain linear phase shift of the reference structure data is used to determine its spatial positional displacement as a function of the respiratory cycle. The signal from a two-dimensional rectangular or cylindrical column is first Fourier-transformed to the image domain, apodized or bandwidth-limited, converted to real, positive values by taking the magnitude of the profile, and then transformed back to the image domain. The relative displacement of a target edge in the image domain is determined from an auto-correlation of the resulting time domain information.
There is often a need in neuroimaging to examine changes in brain images over long periods of time, such as the waxing and waning of MS lesions, progressive atrophy in a patient with Alzheimer's disease, or the growth or remission of a brain tumor. In these cases, the ability to determine the position of anatomy as a function of time is extremely important to detect and quantify subtle changes. High-spatial resolution is a basic requirement of 3D brain imaging data for patients with neurological disease, and motion artifacts a consequence of movement during scanning pose a significant problem. If a patient does not stay completely still during MR neuroimaging the quality of the MR scan will be compromised.
Many of the advantages of MRI that make it a powerful clinical imaging tool are also valuable during interventional procedures. The lack of ionizing radiation and the oblique and multi-planar imaging capabilities are particularly useful during invasive procedures. The absence of beam-hardening artifacts from bone allows complex approaches to anatomic regions that may be difficult or impossible with other imaging techniques such as conventional CT. Perhaps the greatest advantage of MRI is the superior soft-tissue signal contrast available, which allows early and sensitive detection of tissue changes during interventional procedures.
MR is used for procedures such as “interventional radiology”, where images produced by an MRI scanner guide surgeons in a minimally invasive procedure. However, the non-magnetic environment required by the scanner, and the strong magnetic radio frequency and quasi-static fields generated by the scanner hardware require the use of specialized instruments. Exemplary of such endoscopic treatment devices are devices for endoscopic surgery, such as for laser surgery disclosed in U.S. Pat. No. 5,496,305 to Kittrell, et al, and biopsy devices and drug delivery systems, such as disclosed in U.S. Pat. No. 4,900,303 and U.S. Pat. No. 4,578,061 to Lemelson.
Prior art attempts at tracking motion using cross-correlation and other simple distance measurement techniques have not been highly effective where signal intensities vary either within images, between images, or both. U.S. Pat. No. 6,292,683 to Gupta et al. discloses a method and apparatus to track motion of anatomy or medical instruments between MR images. The invention includes acquiring a time series of MR images of a region of interest, where the region of interest contains the anatomy or structure that is prone to movement, and the MR images contain signal intensity variations. The invention includes identifying a local reference region in the region of interest of a reference image and acquired from the time series. The local reference region of the reference image is compared to that of the other MR images and a translational displacement is determined between the local reference region of the reference image and of another MR image. The translational displacement has signal intensity invariance and can accurately track anatomy motion or the movement of a medical instrument during an invasive procedure. The translational displacement can be used to align the images for automatic registration, such as in myocardial perfusion imaging, MRA, fMRI, or in any other procedure in which motion tracking is advantageous. One of the problems with this disclosure is that the application and implementation of this methodology has proven difficult.
U.S. Pat. No. 5,947,900 to Derbyshire, et al. and U.S. Pat. No. 6,559,641 to Thesen disclose different correction schemes. The first is a correlation coefficient is used to determine the translational displacement. The second converts images to a binary form by thresholding and cross-correlation to create a signal peak which is plotted as the translational displacement.
U.S. Pat. No. 6,516,213 to Nevo discloses a method to determine the location and orientation of an object, while the body is being scanned by magnetic resonance imaging (MRI). Nevo estimates the location and orientation of various devices (e.g., catheters, surgery instruments, biopsy needles) by measuring voltages induced by time-variable magnetic fields in a set of miniature coils, said time-variable magnetic fields being generated by the gradient coils of an MRI scanner during its normal imaging operation. However, the method disclosed by Nevo is not capable of position tracking when imaging gradients are inactive, nor is it capable of measurements outside the sensitive volume of the imaging gradients.
Other systems are known. For example, fast imaging is known to “freeze” motion within the fMRI acquisition time frame, in combination with use of head restraints to limit motion. It is still possible to achieve poor activation image quality if patients exhibit task-correlated motion. This problem is particularly manifest in specific patient populations (e.g. dementia, immediate post-acute phase of stroke). Furthermore, image-based coregistration algorithms suffer from methodological limitations. Consequently, the resulting co-registered images still can suffer from residual motion contamination that impairs the ability to interpret brain activity.
Another method of tracking the position of a patient in an MRI is disclosed in U.S. Patent Application 2005/0054910 to Tremblay, et al., published Mar. 10, 2005. In this approach, a reference tool is fixed to a stationary target as close as possible to the centre of the sensitive measuring volume of an MRI-compatible camera system. There are several drawbacks of this approach, including the requirement of a second “tracking” component that must be calibrated with a dummy object, the position ambiguity due to the configuration of this approach, and the inherent limitation of the resolution provided by this approach.
U.S. Pat. No. 6,879,160 to Jakab describes a system for combining electromagnetic position and orientation tracking with magnetic resonance scanner imaging. Jakab discloses a system where the location of a magnetic field sensor relative to a reference coordinate system of the magnetic resonance scanner is determined by a tracking device using a line segment model of a magnetic field source and the signal from a magnetic field sensor. However, resolutions provided by the Jakab invention are not precise.
There is consequently a need for improved patient movement tracking techniques in medical imaging. There is a need for improved patient movement tracking that can function in adverse environments including high strength magnetic and/or radio frequency fields without the tracking mechanism exerting its own RF pulse or magnetic field. There is a need for improved patient movement tracking techniques that can be performed in real time. In particular, but without limitation, there is a need for real time tracking of a patient's head position in a high field strength fMRI without disrupting the scanning by the fMRI.
Disclosed is a monocular optical system and associated three point pose algorithm optimized for real-time motion tracking in MRI applications. The optical fiducial is lightweight and facilitates closely coupled patient motion measurements in six degrees of freedom (“6 DOF”). Angular and translational accuracies are in the range of 100 microradians (0.005 degrees) and 10-100 microns. Due to the nature of the target and the use of a single camera, the x, y translation resolutions are approximately an order of magnitude better than the z direction resolution. However, the z value specifications are still well within the requirements for motion tracking and correction in MRI applications, and if necessary, may be improved by adding an additional turning mirror in the system, thus eliminating the need for a perspective-based measurement for z translation.
For both inherent patient motions and those correlated with commanded tasks in fMRI, good temporal agreement is observed between motion parameters derived from the camera and those produced by the PACE algorithm for low frequency motions. The aliasing inherent in the MRI measurements is apparent for higher frequency motions, and the movements monitored by PACE diverge from those measured with the camera. These divergences in measured motion parameters promise improved image quality with the camera system implemented to provide real-time feedback to the scanner gradients for prospective motion correction.
In one aspect, the monocular optical system is used as a motion alarm incorporating a monitor and graphical user interface to provide for an audible and visible alarm of excessive patient motion based on a measured centroid motion of an optical fiducial target.
The placement and small footprint of the instrument accommodates a wide range of additional equipment that is demanded by the complex and sophisticated protocols that are required by MRI applications. The IR illumination system improves imaging time and accuracy without impacting the patient or imaging protocols.
The exemplary embodiments disclosed find particular use in radiological scanning such as MRI scanning where image data is captured over a relatively long period of time (seconds to minutes) and motion artifacts cause image corruption. Although common in MRI scanning, the image distortion is especially problematic for patients with involuntary tremors, for young patients and for injured patients. Often these motion artifacts are not discovered until after the scan has completed, thus resulting in an immediate re-scan, or are later discovered by the radiologist necessitating rescheduling the patient for a rescan.
It is possible to determine rigid body positions of the 6-DOF motion using a single camera. Disclosed is a single camera motion measurement system capable of precise relative 6-DOF measurements in the scanner environment using no in-scanner calibration. A simple multiple disc optical fiducial target is used in combination with an IR illuminator and the single camera. A program for extracting rotational and translational motion implements a special case of the 3-point pose problem that has no ambiguity in measured motion parameters and that converges quickly in a successive approximation for a limited range of rotations.
Projector 12 illuminates projector screen 13 along light path 23. Light path 24 is established between projector screen 13 and the patient eyes via two-way mirror 3 and patient mirror 7 mounted above head coil 11 and patient's head. Light path 25 is established between IR illuminator 4 and optical fiducial target 5. LED light from light path 25 reflects from optical fiducial target 5 along light path 26, through 2-way mirror to the CCD detector of camera 2. Optical fiducial target 5 is preferably mounted to the patient's head and protrudes from the side of head coil 11 through slot 6 preferably at an angle to keep the LED light and IR illuminator out of the field of view of the patient (see
Continuing with
In the exemplary embodiment, the fMRI scanner typically requires the display of photographic images to the patient to effect brain stimulation using a patient projection system such as the projector, screen and a patient mirror as described. In other embodiments involving radiological tests not requiring photographic brain stimulation, the two-way mirror is not utilized. The optical fiducial target can be positioned above the patient's head, if the projection system is not utilized, and to the side if the projection system is utilized.
Camera 2 is positioned nominally 2.5 m from the target. At this distance, the 3T magnetic field strength of MR magnet 10 falls off to the point where it does not substantially interfere with the electronics in the camera or the communication link to the control room. Also, at this distance, camera 2 does not interfere with the activities of nurses and technicians. Camera 2 is preferably constructed from metals such as copper, aluminum, brass, or a non-magnetic alloy as much as is possible to avoid interaction with the magnetic field of MR magnet. In the preferred embodiment camera 2 is Vision Components model VC4438.
Camera 2 is equipped with on-board processor 17 sufficient to enable calculation of 6-DOF data. On-board processing avoids transmission of image data to the controller or monitor over RF communication links in the scanner room. A communications link 18 is established between on-board processor 17 and controller 28. Another communication link 19 is established between on-board processor 17 and a motion monitor 29. An advantage of this architecture is the reduced communication bandwidth on communications links 18 and 19, which are typically serial communications links. In the preferred embodiment, suitable on-board processor 17 is the TI TMS 320 digital signal processor from Texas Instruments Corporation.
In an alternate embodiment, the CCD element is replaced by a CMOS image sensor.
In another alternate embodiment, camera 2 is equipped with a low-power laser pointer 101 (less than 5 mW) to aid the scanner operator in aligning the patient, the optical fiducial target, the IR illuminator and the camera.
In yet another embodiment, camera 2 is equipped with a shielded video cable connected to the motion monitor for sending a video signal to align the patient and optical fiducial target prior to an MR image scan. The video signal can be disabled by the scanner operator via the motion monitor to avoid interference with an MRI image scan.
IR illuminator is preferably controlled by the motion monitor, but can be controlled by on-board processor 17 though communications link 102 prior to and during an MR image scan in order to adjust contrast and backlighting levels for best performance. Alternatively, the IR illuminator can operate in a “constant on” fashion without control.
Motion monitor 29 is programmed to operate a graphical user interface, GUI 27, for alerting MRI personnel of unacceptable patient movement during an MR image scan. Motion monitor 29 is preferably a personal computer, which can be either a desktop computer or a laptop computer, configured to run the GUI and to interface with the MR controller.
Integration of the motion tracking system allows for images to be projected on a screen for visual fMRI stimuli. Two-way mirror 3, preferably a partially Al-coated glass substrate mirror (1.2 m×2.4 m), 85% reflecting and 15% transmitting to support high-quality optical imaging, is substituted for a standard high reflectivity mirror. Camera 2 thus remains invisible to the patient and obtains an unobstructed view down the magnet bore during the scan. The 6-DOF data is collected by camera 2 by imaging optical fiducial target 5 through two-way mirror 3.
Due to the invariance of their centroids under translation and rotation, a set of circular shaped optical objects offer good performance as the optical fiducial target. This is especially true for binary images, since as the image of the optical fiducial target moves across the CCD detector the time series of detected images progress through a series of representations with various pixels changing black/white states. The use of a set of circular shaped objects ensures that many pixels in the detected images do not change at once and that the reported position moves semi-smoothly as the target image translates across the CCD. Higher accuracy is found to be obtained with a set of at least three circular shaped objects covering a large area of camera 2 field of view. A higher zoom level, set by zoom lens 16, yields higher precision measurements, but at the cost of a lower range of movement. The position of camera 2 is preferably fixed so that zoom lens 16 can have a fixed focal length. Alternatively, zoom lens 16 has an adjustable focal length.
A preferred optical fiducial target is shown in
The attachment of the optical fiducial target to the patient must meet a number of constraints including human factors, fMRI scanner constraints and metrology considerations. The target movements must faithfully correlate with the movement of a patient's head and brain for accurate image correction, which necessitates a relatively close and rigid attachment of the optical fiducial target to the patient's head. Since fMRI protocols may extend for one and even two hours, it is also essential that the attachment be comfortable to the patient. The attachment must also be quick and efficient to install due to scanner throughput considerations. A further constraint is that the optical fiducial target must be clearly visible to the camera through a compact and often cluttered scanner bore.
Referring to
Referring to
A first embodiment of the motion measurement system includes a motion alarm. The motion measurement system detects patient movement in real time and provides immediate feedback to the scanner operator who may then take immediate corrective action such as termination of the scan early, settling the patient and performing a rescan. The immediate feedback is in realized in a first form as a motion alarm alerting scanner operator of patient movement in excess of a pre-defined adjustable threshold. The immediate feedback is realized in a second form as a trend graph of patient movement.
The trend capability preferably includes storage and trend calculations of 6-DOF data so that the graph of patient motion is allowed to extend into the past and preferably includes trend calculations using between 1 second and 1000 seconds of motion data.
A second embodiment of the motion measurement system is a motion tracking and correction system. The motion correction system detects patient movement in real time and provides real-time motion data to the MRI controller which takes immediate corrective action by adjusting the MRI images according to the motion data.
The on-camera processor is programmed to carry out a set of steps to continuously determine the three rotation angles and the three translation distances of the motion (6-DOF) of the optical fiducial target. In
At step 41, a preliminary signal processing of the raw CCD pixels is performed to threshold the image data and compress the image into binary pixels. The optical target identification step 42 then captures the image of the optical fiducial target including an image of the set of circular optical objects and an area filter discards any circular objects below a fixed area. At step 44, the centroids of the remaining circular optical objects are calculated in the order in which the circular objects are located and reported in step 42. The on-camera processing function searches for circular objects using a raster scan of data rows from upper left to lower right. Since the optical fiducial target is free to rotate with the patient's head, this introduces the possibility of inconsistent reporting order for the circular objects. To allow for inconsistent reporting orders, the physical areas of the circular objects (for example, the areas of T1, T2, T3 in
Pincushion distortion of the lens, can cause errors in the precise determination of x and y coordinates of centroids and thus in the remaining four degrees of freedom. By modeling the effect of the pincushion as a calibrated parabaloid, these errors are numerically corrected in step 46.
In the descriptions of the remaining steps, an optical fiducial target having a set of three circular discs as in
The distance X from the camera lens to the optical fiducial target is approximately known. A scale factor S is first calculated relating the number of pixels to a linear measure at each circular object. The scale factor allows calculation of the expected CCD-measured relative positions of the targets for a given set of rotation angles. At step 48 of perspective correction, the distance X and scale factor S are used to calculate the expected positions of the circular objects for zero rotation.
Equations 1, 2 and 3 define standard rotation matrices:
Equation 4 relates the second and third circular object post-rotation positions relative to the first circular object in terms of their pre-rotation positions relative to the first circular object:
Rz Ry Rx (xn-x1, yn-y1, zn-z1)T=(x′n-x′1, z′n-z′1)T (4)
where Rz, Ry, and Rx are the rotation operators, n is an object index, x, y, and z are the expected CCD measures of the circular object centroids at zero rotation for a given lens focal length and camera-to-fiducial target distance, and x′, y′, z′ are the circular object relative positions as measured directly from the CCD pixels.
The rotation angles θx, θy and θz satisfy the relation:
Rz Ry Rx (xn-x1, yn-y1, zn-z1)T−(x′n-x′1, y′n-y′1, z′n-z′1)T=0 (5)
where θx is the rotation angle about the x-axis, θy is the rotation angle about the y-axis and θz is the rotation angle about the z-axis.
For n=2 and n=3 (second and third circular objects) this yields a coupled system of six equations, shown expanded below as Equations (6) through (11):
{(x2-x1)cos(θy)−[−(y2-y1)sin(θx)+(z2-z1)cos(θx)] sin(θy)} cos(θz)+[(y2-y1)cos(θx)+(z2-z1)sin(θx)] sin(θz)−(x′2-x′1)=0 (6)
−{(x2-x1)cos(θy)−[−(y2-y1)sin(θx)+(z2-z1)cos(θx)] sin(θy)} sin(θz)+[(y2-y1)cos(θx)+(z2-z1)sin(θx)] cos(θz)−(y′2-y′1)=0 (7)
(x2-x1)sin(θy)+[−(y2-y1)sin(θx)+(z2-z1)cos(θx)] cos(θy)−(z′2-z′1)=0 (8)
{(x3-x1)cos(θy)−[−(y3-y1)sin(θx)+(z3-z1)cos(θx)] sin(θy)} cos(θz)+[(y3-y1)cos(θx)+(z3-z1)sin(θx)] sin(θz)−(x′3-x′1)=0 (9)
−{(x3-x1)cos(θy)−[−(y3-y1)sin(θx)+(z3-z1)cos(θx)] sin(θy)} sin(θz)+[(y3-y1)cos(θx)+(z3-z1)sin(θx)] cos(θz)−(y′3-y′1)=0 (10)
(x3-x1)sin(θy)+[−(y3-y1)sin(θx)+(z3-z1)cos(θx)] cos(θy)−(z′3-z′1)=0 (11)
This system may not be solved directly since the equations contain CCD-measured z coordinates. A single CCD camera can only directly locate the x and y coordinates of the circular objects with the required fidelity. A rough estimate of z is possible using perspective and known fiducial target geometries; however, this estimate is not suitable for high definition 6-DOF measurements. The coupling of Equations (6)-(11), as well as the lack of a CCD z measurement, requires an iterative successive approximation to solve. At step 50, the rotation angles are extracted by estimating θx, θy and θz given a set of x′ and y′ CCD measurements of the circular object centroids by successive approximation in an iterative loop.
At step 72, θx(0) and θy(0) are compared. If θx(0) is found to be larger, θx (1) is set to θx (0) and step 76 is performed to estimate θy(1), substituting θx (1) for θx and θz=θz (1)=0 in Eq. 6 and solving iteratively for θy(1) using Newton's method. At step 78, θz(1) is estimated using the previously estimated values for θx(1) and θy(1) by solving Eq. 10 iteratively for θz (1) using Newton's method. Steps 74, 76 and 78 are repeatedly performed in a loop using successive angle estimates to recalculate θx(k), θy(k) and θz(k) for k iterations. The loop is checked for termination at step 80 wherein steeps 74, 76 and 78 are repeated until a set number of iterations have been reached or until the change in the estimates falls below a predetermined value. The change in estimates can be characterized for example by the sum |θx(k)-θx(k−1)|+|θx(k)-θx(k−1)|+|θz(k)-θz(k−1)| for the kth iteration. If the angle extraction step is terminated at step 80, the rotation angles θx, θy, and θz are reported as θx(k), θy(k) and θz(k). Note that at step 74, the angle θx(k) is estimated using θy(k−1) and θz(k−1).
If θy(0) is found to be larger than θx (0) at step 72, then θy (1) is set to θy (0) and step 86 is performed to estimate θx(1), substituting θy (1) for θy and θz=θz (1)=0 in Eq. 7 and solving iteratively for θx(1) using Newton's method. Next, at step 88, θz(1) is estimated using the previously estimated values for θx(1) and θy(1) by solving Eq. 9 iteratively for θz (1) using Newton's method. Steps 84, 86 and 88 are repeatedly performed in a loop using successive angle estimates to recalculate θy(k), θx(k) and θz(k) for k iterations. The loop is checked for termination at step 90 wherein steps 84, 86 and 88 are repeated until a set number of iterations have been reached or until the change in the estimates falls below a predetermined value. The change in estimates can be characterized for example by the sum |θx(k)-θx(k−1)|+|θx(k)−θx(k−1)|+|θz(k)-θz(k−1)| for the kth iteration. If the angle extraction step is terminated at step 90, the rotation angles θx, θy, and θz are reported as θx(k), θy(k) and θz(k). Note that at step 84, the angle θy(k) is estimated using θx(k−1) and θz(k−1).
The rotational angle extraction process of step 50 is preferably limited to 20 iterations with 10 iterations of Newton's method used for each angle estimation. For the preferred on-board camera processor, step 50 typically completes in less than 1 millisecond of execution time. The process terminates at step 91.
For an iterative method to converge to the correct solution, it is desirable that the error decrease with each iteration. For this reason the target geometry is selected such that the quantity (x′2-x′1) chiefly responds to θy (with lesser influence by θx and θz) and that (y′2-y′1) is mostly a measure of θx (with lesser influence by θy and θz).
Returning now to
z′1=(D−mD′)L/D (12)
At step 52, all of the 6-DOF measurements are scaled from units of pixels to millimeters in target dimensions, using the target range and lens focal length. Step 52 completes the measurement of 6-DOF in the optical fiducial coordinate system.
In another embodiment system, the stalk of the optical fiduciary target incorporates MRI-readable fiducial marks at known locations. At step 53, the MRI scanner locates the MRI-readable fiducial marks during a calibration to determine the spatial relation between MRI-readable fiducial marks and the optical fiducial target. With the known and fixed spatial relation between the MRI-readmarks and the optical fiducial target, transformation of the 6-DOF measurements from the optical fiducial coordinate system to the MR scanner isocenter coordinate system is accomplished by the on-board image processor using a set of homogenous transforms.
At step 54, the 6-DOF are reported to the MR scanner controller in MR scanner isocenter coordinates (see step 163 of second embodiment method 160 in
An operational test of the on-camera processing function was performed, wherein a target was rotated by a known amount and the rotation measured using a simulated CCD camera. The angle extraction step was run on the resulting data and the recovered angles were compared to the known rotations. For small angles the algorithm converges rapidly to the correct angle, with convergence to sub-microradian (sub milli-degree) error levels achieved within 20 cycles.
In order to test the accuracy of pose determination and proper operation of the system a series of laboratory and scanner tests were performed. These included bench tests of calibrated motion and direct measurement of subject motion in the MRI scanner in both quiescent and task-based scenarios. Subject head motions measured by the optical camera were compared to MRI image-based motion parameters while bench tests were compared with callipered measurements.
First a static bench target was measured to establish the intrinsic noise of the measurement system. A stationary optical fiducial target was mounted to a pneumatically isolated floating optical table. Assuming complete vibration isolation by the table, this test measured the apparent motion caused by finite convergence of the algorithm combined with other hardware and software limitations, and benchmarks the best attainable precision of the instrument. The data for the static tracking experiment is shown in Table 1, column 1. The rms errors for angle measures were each <75 microradians (0.005 degrees) and for the x and y linear measures were less than 2 microns. The rms error for the z linear measure was 15 microns. The lower performance of the z linear measure is mainly due to the monocular measurement setup but is still much better than is required for radiological motion correction. For these tests, as for measurements in the scanner, the target was mounted 2.5 m from the CCD and a 75 mm focal length lens was used.
Two additional bench tests were made to determine linearity and accuracy of the motion tracking system for a moving target. For these tests, the fiducial was mounted on precision, calibrated motion-control stages and the motion measured by the camera was compared with the directly measured calibrated motion. The error between the two is a combination of impairments in the optical and the mechanical measurements.
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Since a system or algorithm error could manifest as a coupling between the various motions, a compound test jig comprising both translation and rotation stages was constructed. Testing was conducted using multiple successive rotations and translations. Over 1 cm translations the divergence from a linear fit, for x, y and z translations was 6.0, 4.0 and 108 microns rms, and over 100 milliradian (5 degree) rotations for θx, θy, and θz, the errors were 277, 170 and 232 microradians rms (0.016, 0.0097, and 0.013 degrees) respectively (Table 1, column 2). Since this is a multiply coupled mechanical system, these errors represent the camera measurement system error plus any errors due to the mechanics plus errors due to mechanical misalignment. This is a worst-case measure of the limits of system performance, and confirms the system is suitable for use in most MRI applications.
Obtaining calibrated motion in the MRI scanner environment is problematic due to the presence of strong magnetic fields. For example, a typical optical-bench micrometer constructed of steel would become a dangerous projectile when brought close to the scanner bore. For this reason a target was attached to the head coil of the scanner and the motion of the static target was observed, similar to the static bench test. The θx, θy, and θz, motions were less than 300 microradians rms (0.017 degrees); translational motion errors measured in x and y were less than 10 microns rms and for z were less than 100 microns rms (Table 1, column 3). This represents camera system errors plus any vibration induced motion caused by the scanner, which are within acceptable bounds.
In another series of tests, the motion measurement system was operated during an MRI image scan while a patient was speaking aloud. In
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Table 1 shows a comparison of system performance for static bench measurements (column 1), six axis dynamic bench test with calibrated motions (column 2) and static measure of scanner structure (column 3). Increased errors for the six axis tests are attributed to the more complex test setup causing mechanical error stack-up. Column 1 and 2 measurements were taken on a pneumatically vibration isolated optical bench. Column 3 data were taken with the scanner in idle mode and the target fixed to the scanner head coil. Errors for the movement test (column 2) are in relation to a best linear fit. Since image correction requires only differential position measurement, actual errors may be expected to be less than these by a factor of the square-root of two.
This application claims priority to Provisional Patent Application No. 61/310,703 filed on Mar. 4, 2010.
Number | Date | Country | |
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61310703 | Mar 2010 | US |