Visualization of Active Devices and Automatic Slice Repositioning (“SnapTo”) for MRI-guided Interventions

Abstract

The accurate visualization of interventional devices is crucial for the safety and effectiveness of MRI-guided interventional procedures. In this paper, we introduce an improvement to the visualization of active devices. The key component is a fast, robust method (“CurveFind”) that reconstructs the 3D trajectory of the device from projection images in a fraction of a second. CurveFind is an iterative prediction-correction algorithm that acts on a product of orthogonal projection images. By varying step-size and search-direction it is robust to signal inhomogeneities. At the touch of a key the imaged slice is repositioned to contain the relevant section of the device (“SnapTo”), the curve of the device is plotted in a 3D display, and the point on a target slice, which the device will intersect, is displayed. These features have been incorporated into a real-time MR imaging system. Experiments in vitro and in vivo (in a pig) have produced successful results using a variety of single and multi-channel devices designed to produce both spatially continuous and discrete signals. CurveFind is typically able to reconstruct the device curve with an average error of approximately 2mm, even in the case of complex geometries.

Introduction

Interventional MRI (1) refers to procedures that involve the manipulation of invasive devices guided by MRI instead of conventional X-ray. It promises to permit a new array of procedures previously attainable only with open surgical exposure, without the radiation exposure of conventional X-ray guidance. Active intravascular devices, such as catheters and guide-wires, contain receiver coils whose signal can be collected separately from the other coils in the MRI scanner. Accurate knowledge of the location and trajectory of the whole device is critical to the success of the procedure and safety of the patient.

Active MR device coils may be classified as being either point-source coils (also known as micro-coils or tracking coils), which produce a very localized single point-like signal, or spatially-extensive coils, which produce a signal along a substantial length of the device shaft. The latter category would include a loopless coil (2) (3) that produces a continuous curve-like signal and can be used for profiling, or a coil that has a discontinuous series of point-sources in a single channel. The key advantage of the spatially extensive coils is that the substantial length of the signal it generates allows the interventionist to see the relative location of the whole device to the surrounding tissue. Loopless coils, in particular, are advantageous as they can be incorporated into more flexible and narrower interventional devices, which are preferable in certain procedures. Furthermore, the gradual decay of their sensitivity allows them to be used for imaging in addition to tracking.

The real time MRI (rtMRI) system described by Guttman et al (4) produces rapidly-updated reconstructions of multiple 2D slices of interest and a 3D display of these slices. This display is crucial to the interventionist's ability to visualize the device as it is maneuvered within the patient. There are two features of the system that are particularly helpful in the visualization of active devices.

The first feature is the coloring of the active device signal. When using active devices, the device channel signals are displayed in a color of the user's choice and blended with the grayscale surface coil images. If a portion of the device is contained within the slice, it may be visualized in relation to the surrounding tissue. However, it is often difficult to locate those portions of the device not contained in the slice (e.g. the tip). Manually repositioning slices to visualize specific parts of the device may be time-consuming and imprecise, possibly compromising patient safety. For example, if the tip of a wire exits the imaging slice unknowingly, tissue injury may result without the operator's knowledge.

This is somewhat addressed by the second feature, device-only projection imaging. To see the entire device, the images can be made non-slice-selective (i.e., infinite slice thickness) by switching off the slice-encode gradient. This allows the entire device to be seen, including sections that were outside the imaged slice.

Although this offers a big improvement in device visualization over thin-slice imaging, it remains difficult to precisely identify the location and orientation of an active device from viewing multiple projection images. Since the image from the device is related to its sensitivity profile modulated by the nearby tissue signal, the device in vivo usually appears inhomogeneous. It thus may be advantageous to automatically determine the trajectory of the entire device and draw a clean line in place of its image.

In this paper, we describe a set of methods that we have implemented in our lab to improve the visualization of the device. The key component is the CurveFind method that computes the 3D trajectory of the active device from a sparse amount of MR data. By 3D trajectory, we mean an ordered set of 3D coordinates of closely-spaced points along the curve-shaped device. From three perpendicular 2D projection images, we are able to robustly compute this trajectory. Note that while a point-source coil can be localized in 3D from merely three echos (k-space lines)(5), the same is not possible, mathematically, for spatially-extensive coils.

This 3D trajectory of the device is used to perform three tasks that improve visualization:

• (1)The automatic re-positioning of one of the imaging slices to contain the active device (SnapTo).
• (2)The plotting of the device curve in a 3D display of the imaged slices.
• (3)The extrapolation of the device curve to the target slice, to help the interventionist maneuver the device to the correct target location.

It is necessary for these tasks to be robust for a wide array of active devices with varying coil characteristics, shapes, and varying numbers of active channels, and for the imaged slice(s) to be located at specific regions of the device --- such as the tip or the shaft.

Theory

Computing the 3D trajectory

The CurveFind algorithm computes the 3D trajectory of the curve from three perpendicular 2D projection images in two steps. First, it builds an approximation to the 3D volume – an image of the active device from three perpendicular projections. Then, it traces the 3D trajectory of the curvilinear active device using a simple predictor-corrector iterative method.

In general, a 3D object is poorly approximated by a reconstruction from merely three projections. In our case, however, the object is sparse. As the sensitivity of the device channel decays rapidly away from the device, the image formed from the device channel alone is zero everywhere except close to the curve-shaped device.

In the first part of the algorithm, we create a product of the three available 2D projections. In particular, from the projections f_X (y, z), f_Y (x, z) and f_Z (x, y), we compute g(x, y, z)fX (y, z) f_Y (x, z) f_Z (x, y) This is illustrated in Figure 1a. The three perpendicular projections f_X, f_Y and f_Z are depicted as three of the faces of a cube. The choice of multiplication rather than addition (as is the case in backprojection (6)) might be seen as analogous to choosing the logical `and' operator instead of the `or' operator in deciding if a voxel of the volume to be reconstructed belongs to the curve or not. The notion of improving the reconstruction of sparse objects by multiplying rather than adding images may be observed in methods such as HYPR and VIPR (7).

Figure 1.

a: The three perpendicular projection images of the active device shown as the sides of a cube (shown in reversed grayscale for clarity). b: The iteration is initialized by picking the voxel of highest magnitude in the product image (large dot). The initial direction (two-headed arrow) is the principal eigenvector of the moment of inertia matrix of the local sub-image. c: The iterative steps in which a slice of the product image is interpolated perpendicular to the estimated curve. These steps are described in detail in d–g. d: The next curve point is initially predicted as described in step (i). The large dot denotes the current point ${\overrightarrow{p}}_i$ The arrow extending from it represents the current curve direction ${\overrightarrow{d}}_i$ e: A local 2D slice h(u₁,u₂) (black-bordered square) is computed as described in step (ii). The vectors ${\overrightarrow{v}}_1$ and ${\overrightarrow{v}}_2$ are represented by the arrows in the plane of the square. f: The centroid (denoted by the center of the large `x') of the local 2D slice is computed as described in step (iii). g: A correction is made to the predicted point by displacing it by the offset of the centroid. The new curve point ${\overrightarrow{p}}_{i+1}$ is the point at the end of the arrow. h: One half of the found curve. i: The whole curve and the SnapTo slice that contains it.

In the second part of the algorithm, we extract the 3D trajectory of the device curve from g(x, y, z) --- the sparse approximation to the 3D volume image of the device that we computed in the first part. Simply thresholding g(x, y, z) (i.e., setting all voxels below a threshold to be zero) and fitting a curve to the resulting image does not work because the signal of the active device is not uniformly strong along its whole length. On the other hand, if we consider a 2D slice in the volume g(x, y, z) that is perpendicular to the device-curve, the location of the device-curve does generally correspond to locally maximal points in that perpendicular 2D slice. We use this fact to trace the complete curve of the device using a simple iterative predictor-corrector method.

Our iterative method is illustrated in Figure 1b–d. To initialize the iterations we pick as our seed point ${\overrightarrow{p}}_0$, the voxel of maximal magnitude in the volume g(x, y, z) (the large dot in the middle of the volume in Figure 1b). To estimate the direction ${\overrightarrow{d}}_0$ of the curve at the seed-point (the double-headed arrow in Figure 1b), we compute the principal eigenvector of the moment-of-inertia tensor of the local volume around that point (See Appendix). This is similar to how in diffusion tensor imaging the principal eigenvector of the diffusion tensor represents the direction of diffusion (8). To compute ${\overrightarrow{d}}_0$ we use a local volume in g(x, y, z)^P (where P ≥ 1), instead of g(x, y, z), in order to accentuate high values and suppress low values and make the product of the projection images sharper/sparser in case the sensitivity of the coil decays slowly. We use P = 4.

Thus, the iterative predictor-corrector algorithm is initialized with a seed point ${\overrightarrow{p}}_0$ and an initial curve direction ${\overrightarrow{d}}_0$ (normalized so that $\Vert {\overrightarrow{d}}_0\Vert =1$. Starting from the seed point ${\overrightarrow{p}}_0$ we estimate one half of the curve by tracing it out in one direction $(+{\overrightarrow{d}}_0)$ and then estimate the other half of the curve by starting from ${\overrightarrow{p}}_0$ again and heading in the opposite direction $(-{\overrightarrow{d}}_0)$. A step-size s is chosen for the algorithm that is small enough to find devices with tight curves and large enough to avoid unnecessary computational cost. For the experiments shown herein, we use s=2.25mm.

Figure 1c illustrates an instant in the middle of the algorithm at which the first i points of the curve $\left(\{{\overrightarrow{p}}_1,{\overrightarrow{p}}_2,.,{\overrightarrow{p}}_i\}\right)$ have been computed. These curve points are shown by the heavy curve in the middle of the volume. The current point ${\overrightarrow{p}}_i$ is shown by the large dot. Notice that the device begins to deviate from the current direction of the estimated curve. The next point ${\overrightarrow{p}}_{i+1}$ in the curve is computed in the following five steps that are illustrated in further detail in Figure 1d–g.

• (i)An initial prediction $\overrightarrow{q}={\overrightarrow{p}}_i+s{\overrightarrow{d}}_i$ is computed using linear extrapolation. In Figure 1d, ${\overrightarrow{d}}_i$ is represented by the arrow extending from the large dot $\left({\overrightarrow{p}}_i\right)$ and $\overrightarrow{q}$ is the point at the end of the arrow.
• (ii)A local 2D slice h(u₁,u₂), centered at the predicted point $\overrightarrow{q}$ and perpendicular to the curve direction ${\overrightarrow{d}}_i$, is computed by interpolating a set of points within the 3D volume g, i.e., $h(u_1,u_2)=g(\overrightarrow{q}+u_1{\overrightarrow{v}}_1+u_2{\overrightarrow{v}}_2)$ where ${\overrightarrow{v}}_1$ and ${\overrightarrow{v}}_2$ are vectors that are perpendicular to each other and to ${\overrightarrow{d}}_i$. The slice h(u₁,u₂) is the black-bordered square shown in Figure 1c and, in close-up, in Figure 1e. The vectors ${\overrightarrow{v}}_1$ and ${\overrightarrow{v}}_2$ are the arrows in the plane of the square.
• (iii)The centroid $(u_1^{\ast },u_2^{\ast })$ of the (L^th power of the) local 2D slice h(u₁,u₂ is computed (see Appendix). The L^th power is used to accentuate high-values and so $(u_1^{\ast },u_2^{\ast })$ represent the centroid of the maximal pixels in the slice. We use L = 20. In Figure 1f, the centroid $(u_1^{\ast },u_2^{\ast })$ is denoted by the large black `x'. As expected, the centroid is displaced from the center of the slice by a few pixels because the device deviates from the initially predicted direction ${\overrightarrow{d}}_i$.
• (iv)The estimated point in the curve ${\overrightarrow{p}}_{i+1}$ is computed by correcting the predicted point $\overrightarrow{q}$ by the location of the centroid, i.e.,${\overrightarrow{p}}_{i+1}=\overrightarrow{q}+(u_1^{\ast }\cdot {\overrightarrow{v}}_1+u_2^{\ast }\cdot {\overrightarrow{v}}_2)$. In Figure 1g, ${\overrightarrow{p}}_{i+1}$ is the point at the end of the arrow extending from the large dot $\left({\overrightarrow{p}}_i\right)$.
• (v)The predicted direction of the next curve point is computed by averaging over the curve direction of the preceding few (J) points.
  $${\overrightarrow{d}}_{i+1}=(1∕J)\sum _{j=i-j+1}^i{\overrightarrow{p}}_{j+1}-{\overrightarrow{p}}_j$$ (1)

  J is chosen to be small enough to capture tight curves of the device but large enough not to be misled by errors in the estimation of immediately preceding curve points. We use J=5 and ${\overrightarrow{d}}_{i+1}$ is normalized to have length 1.

This iterative prediction-correction algorithm stops when the end of the curve is judged to have been reached, i.e., when one of two conditions is met. The first condition is that the magnitude of the point, when re-projected onto the projections, falls below a threshold. The second stopping condition is if the identified curve loops back onto itself. This second condition is verified by comparing every new point to all the previously calculated points in the curve and checking if the new point lies on, or close to, the line-segment connecting any two adjacent points of the existing curve.

Figure 1h shows the curve after the iteration has been stopped. The projection of this curve onto the three perpendicular projection images is also displayed. The estimated curve can be seen to match the projection images correctly. Notice that only half the curve has now been computed. The complete curve is shown by the black curve in Figure 1i.

The projection images of the device might be zero-valued for short sections along the device curve. This might be unintentional --- due to the SSFP banding artifact (9) or signal-loss due to the excitation of a preceding thin-slice, or intentional --- such as when the device coil consists of a discontinuous series of point-sources. In this case, the algorithm as described above might stop prematurely due to the first (“curve-fading”) stopping condition. To overcome this, we introduce an additional check to verify that the iterations should indeed be stopped. When the curve-fading condition is met we consider a longer straight line, in the current curve direction, from the last acceptable curve point. We repeat steps (ii–iv) at points along this line, i.e., we compute the centroid of local 2D perpendicular slices along this line, and re-evaluate the curve-fading stopping condition. We repeat this check using larger local 2D slices, and different curve directions (by averaging over a few curve points by iteratively decrementing J in Eq (1)). We only stop iterations if these additional tests fail. We henceforth refer to this as extending the curve across nulls.

Computing the SnapTo Slice

Now that we have estimated the trajectory of the device, we use it to calculate the SnapTo slice – a 2D slice that contains the desired portion of the active device. Given the 3D coordinates of a set of K points (i.e., {(x₁, y₁, z₁), (x₂, y₂, z₂), ., (x_K, y_K, z_K)}), a 2D plane that best fits those points in a least-squares sense can be computed (10). This plane is parameterized by $\overrightarrow{m}$, the three-element normal to the plane, and b, the perpendicular distance of the plane from the origin. The distance of the k^th 3D point from the plane is then $\left[x_k{y}_k{z}_k\right]\cdot \overrightarrow{m}-b$.

Often the device is oriented such that there is no slice of a given thickness that contains all of it. In this case, the plane that best fits all the curve points in a least-squares sense might only contain a small section of it. The operator is often most interested in visualizing a subsection of the curve-shaped active device, such as the tip and the distal end of the device. The slice, of thickness t that contains the tip and as much of the distal end of the device as possible, is found as follows. First, the best-fit plane of all the curve points is found. If the maximal distance of the points from the slice is greater than 0.5 t, then the farthest curve point from the tip is discarded and the best-fit plane of the remaining points is calculated. This process is repeated until the maximal distance falls below 0.5 t.

The method described above exactly finds the slice of thickness t that contains the tip and as much of the distal end of the device as possible. If it is desired that the device be allowed to be outside of the slice to a limited extent the computation is easily modified. For example the thickness t used in the computation can be increased, or the termination condition of the computation can be modified to allow for the points of the curve to lie outside the slice for a pre-set length.

Methods

We tested CurveFind and SnapTo on a variety of active devices both in a phantom and in-vivo. We describe the setup of the experiments below and the results in the next section.

Imaging System

In our lab a 1.5T Clinical MR scanner (Espree; Siemens Medical Systems, Erlangen, Germany) is connected to a Linux workstation running custom software for rapid image reconstruction and display. This existing real time MRI (rtMRI) system was expanded to incorporate the CurveFind and SnapTo features.

Pulse sequence

Steady-state free precession (SSFP a.k.a True FISP, b-FFE, FIESTA) (11) sequences were selected for rapid, high signal-to-noise ratio (SNR) real-time imaging. The existing SSFP sequence was modified to collect the CurveFind data (three 2D perpendicular projection slices at isocenter, each with FOV 400 mm × 400 mm and “infinite” thickness, i.e., with slice-selection turned off) upon the press of a key at the console. This data is passed to the CurveFind computation method, which estimates the 3D trajectory of the active device. If the user wishes the slice to be repositioned to contain the active device (SnapTo), the sequence then instructs the scanner to change the orientation of the slice.

Display

The existing image display system shows the real-time reconstruction of each slice in a window of its own. In addition it has a window for a 3D display of all the imaged slices so that the interventionist can see the relative 3D spatial location and orientation of the slices, from a user-controlled point of view. We integrate the CurveFind method into the existing visualization system by plotting the curve of the device in the 3D rendering, as shown in Figure 2a.

Figure 2.

a: 3D display of a slice of interest with the curve of the active device plotted in red. The point on the target slice at which the active device is expected to intersect the slice of interest is denoted by the yellow dot. b: A photograph of the Aortic phantom with the guide-wire inside (whose tip is marked by the arrow).

The tip (the green dot) is identified as the end of the curve that has the higher signal strength. It is also useful for the interventionist to know the relationship of the active device to the target slice. We are able to do so by simply extrapolating the computed 3D curve to the target slice and plotting the location of this extrapolated point on the target slice by the yellow dot.

As shown in Figure 3 (top row), three separate windows display the computed curve of the device overlaid on the grayscale projection images. This allows the user to perform a simple visual verification that the device identification is correct and interact with the algorithm if necessary. The interactive features include the ability to flip the direction of the identified device if the tip has been misidentified, and the ability to lengthen or shorten the identified device. This last feature changes the curve-fading stopping threshold of the CurveFind algorithm (as described in the Theory section) and re-computes the 3D trajectory.

Figure 3.

Active guidewire in aortic phantom. Top row shows projection images: Sagittal (a), Coronal (b), and Transverse (c). Bottom row shows the slice before (d) and after (e) SnapTo has been executed. In d the white arrows point to the device (faintly seen in red).

Phantom experiments

An aortic phantom made of soft-silicone and water (Shelly Medical Imaging Technologies, London, Canada) was used to test CurveFind and SnapTo. A custom-made single-channel guidewire was inserted in the phantom as shown in Figure 2b. The active guidewire is the black curve seen inside the transparent phantom whose tip is denoted by the arrow. The rtMRI system was initiated with the imaged slice at an arbitrary orientation. The CurveFind method was initiated by a key-press, the 3D trajectory of the device was computed successfully, and the slice was repositioned to contain the tip of the device (“Snapped-to”).

The 3D trajectory of the curve estimated by CurveFind was verified by comparing it to a 3D volume reconstruction of the device channel. The true trajectory of the curve was identified by applying CurveFind to the 3D volume and visually verifying its correctness. The error of each point in the estimated 3D trajectory was calculated to be the minimum distance of that point to the true trajectory of the device. The average of this error over the whole curve was computed for five different positions of the guidewire.

A two-channel guidewire (12) was used in an aortic phantom. It has one loopless channel along the shaft of the device and a solenoid channel with two point-like signals --- one at the tip and one 2.5 cm away. The device shaft trajectory was first found using the spatially-extensive channel and the tip was found by extending the curve across nulls (as described in the Theory section) using the solenoid channel, and finally refining the tip estimate using the centroid of a local volume. The average of the error in estimating the shaft and the tip were computed for six different positions of the two-channel guidewire by comparing to a 3D volume reconstruction of the device channel.

In order to test CurveFind in more difficult situations, the two-channel guidewire was used in a bath of water with plastic pegs to hold the guidewire in configurations that consisted of more complex turns. The average error in estimating the shaft and tip were computed for six different positions by comparing to a 3D volume reconstruction of the device channels.

Animal experiments

Animal experiments were approved by the NHLBI Animal Care and Use Committee. Animals underwent general anesthesia with inhaled isoflurane and mechanical ventilation. Three porcine experiments were performed with single-channel active guidewires inserted percutaneously via a femoral artery or jugular vein, or a single-channel active needle applied to the chest wall.

Results

Aortic phantom experiments

Figure 3a–c show the console windows of the three perpendicular projections (Sagittal, Coronal and Transverse, respectively) that the CurveFind method collects, with the curve of the single-channel active device overlaid. CurveFind takes less than 0.2 sec to run. Figure 3d and 3e show the imaged slice before and after SnapTo is initiated. In both images, the device channel in red is blended with the grayscale image from the surface coils. It is seen in Figure 3d that the original slice is in a transverse orientation, which is perpendicular to the guidewire (indicated by white arrow). As seen in Figure 3e following SnapTo, the slice contains the distal portion of the active device.

The error in the identification of the shaft of the single-channel guidewire in an aortic phantom are listed in Table 1 and the error in identification of the shaft and tip of the two-channel guidewire in an aortic phantom is listed in Table 2. In both experiments, the errors are almost always less than the voxel spacing of the 3D volume (2mm) and the pixel spacing of the projection images (400 mm / 192 pixels= 2.08 mm/pixel).

Table 1.

Error in identifying a single-channel guidewire.

Expt Number	1	2	3	4	5	Mean +/− SD
Error (in mm)	1.19	1.27	1.09	1.41	1.13	1.22 +/− 0.13

Table 2.

Error in identifying a two-channel guide-wire and its tip.

Expt Number	1	2	3	4	5	6	Mean+/−SD
Error in shaft (mm)	1.25	1.64	1.09	1.49	1.11	1.41	1.33 +/− 0.22
Error in tip (mm)	1.20	0.12	0.64	1.09	1.17	0.96	0.86 +/− 0.42

In interventional procedures, active devices are most often expected to maintain trajectories such as shown in the aortic phantom experiments – with relatively wide curves that do not involve tight turns or closed loops. In order to test the algorithm in more anomalous situations, pegs were used to hold the guidewire in a water bath in more complicated configurations. The errors in identification of the shaft and tip of the two-channel guidewire are listed in Table 3. They are seen to be comparable and sometimes larger than the errors listed in Tables 1 and 2.

Table 3.

Error in identifying a two-channel guidewire with a more complicated configuration

Expt Number	1	2	3	4	5	6	Mean+/−SD
Error in shaft (mm)	3.43	2.12	2.17	1.56	1.39	3.18	2.31 +/− 0.84
Error in tip (mm)	22.32	1.92	1.76	1.57	2.42	1.65	5.27 +/− 8.36

Figure 4 shows projection images from two of the experiments. Figure 4a and b show details of the Sagittal and Coronal projections when the device takes on a tight, closed turn (Experiment #1 in Table 3). The curves identified by CurveFind are the solid black curves overlaid on the projection images. Because of the physics of an antenna that is curved tightly, the signal within this loop in the projections is strong (denoted by the solid black arrow in (a)). The signal along sections of the loop is relatively diminished (dashed black arrow in (a)) because of the tight curve and the presence of the plastic pegs in the water bath (dashed arrows in (b)). CurveFind is misled in the region of these non-idealities and the tip is misidentified in Experiment #1. For comparison the true trajectory, estimated from the 3D volume reconstruction, is shown by dashed black curves. Figure 4c and d show details of the Sagittal and Coronal projections when the device takes on a less tight curve (Experiment #4 in Table 3) and consequently the error is smaller.

Figure 4.

Details of projection images from experiments of guidewire with more complex turns in water bath. Sagittal (a) and Coronal (b) projections of Experiment #1 from Table 3. Dashed arrows point to areas of diminished signal located along the loop of the device and solid arrows point to areas of strong signal within the loop of the device. Sagittal (c) and Coronal (d) projections of Experiment #4 from Table 3. The error in Experiment #4 is lower than that in Experiment #1.

Animal experiments

Animal Experiment #1

To evaluate the accuracy of the CurveFind method in vivo, a 0.035” active guidewire was inserted into the jugular vein of a pig (figure not shown). The device was identified correctly and this was verified by comparing it to a full 3D reconstruction of the device as described in the previous section. The error in estimating the trajectory averaged 1.92 mm over a length of 125 mm along the guidewire.

Animal Experiment #2

The CurveFind method was used with a transfemoral 0.035” active guidewire inserted into the aorta of a pig. Figure 5 shows the three projection slices and Figure 6 shows the imaged slice before and after the SnapTo method is used. Notice that the active device makes a closed loop near the tip inside the left ventricle. Consequently, as in water bath experiment shown in Figure 4a and 4b, the signal within this loop in the Sagittal projection is strong (shown by the white arrows in Figure 5) and the CurveFind algorithm is misled in the neighborhood of this artifact as indicated by the white arrow in Figure 6b. Still, since most of the device is correctly identified (red line), the SnapTo slice does contain most of the distal end of the device (green channel) as desired by the interventionist.

Figure 5.

Transfemoral active guidewire in aorta of a pig. Sagittal, Coronal and Transverse (from left to right) projection images with the found curve of the device overlaid in red. The white arrows point to an area of strong signal within the loop of the device.

Figure 6.

Active guidewire in the aorta of a pig. Imaged slice before (a) and after (b) SnapTo is activated. The device channel image is shown in green in both images. The image in b is the 3D display with the identified curve plotted in red. The breaks in the red curve occur when the identified curve is on the far side of the central plane of the SnapTo slice. The white arrow points to a region in which the device identification is incorrect. The imaged slice is 6mm thick even though it is depicted as infinitesimally thin in the 3D display. Any apparent discrepancy in the position of the red line and the green signal in the proximal guidewire is merely due to the parallax error caused by the non-infinitesimal thickness of the slice combined with the rising of the guidewire out of the plane of the image.

Animal Experiment #3

CurveFind was tested on an active needle entering the chest of a pig. The signal of the needle consists of five discontinuous point-sources (Figure 7a). Figure 7b shows the 3D display of the active needle. CurveFind was able to identify the device because of its ability to extend the device trajectory across nulls.

Figure 7.

Active needle, with a discontinuous signal consisting of a series of point-sources, entering the chest of a pig. a: A closeup of the Sagittal projection image of the device showing the five point-sources. b: 3D display of the imaged transverse slice through the thorax overlaid with the curve trajectory in red.

Discussion

We have presented a robust algorithm that identifies the trajectory of an active device that has a spatially-extensive signal. The advantage of spatially-extensive signals over point-source signals is that the whole device can be visualized in relation to adjacent tissue. While it is well-known that the 3D location of a point-source coil (or other point-like signal source (13)) can be identified with merely three k-space lines (5), the same is not true for spatially-extensive signals. There has been some related work in the field of biplane x-ray fluoroscopy imaging (14).

Unlike previous work (15), CurveFind and SnapTo do not require the device to have a particular shape or recognizable geometric feature or orientation. CurveFind is also robust to discontinuities in the device signal as shown in the aortic phantom experiment (Table 2) and animal experiment #3.

CurveFind is also robust in the case of multi-channel devices that combine a point-source channel with a spatially extensive channel. Consider a device such as that used in the aortic phantom experiment (Table 2). Because of electro-magnetic coupling between the continuous (loopless) shaft channel, shown in Figure 8a, and the discontinuous (solenoidal) tip channel, shown in Figure 8b, the brightest pixels in a projection image of the tip channel do not necessarily correspond to the point-sources. As the device is aligned along the transverse axis, this phenomenon is seen in the transverse projection of the tip channel displayed in Figure 8c. In Figure 8b and Figure 8c, the artifact due to coupling is indicated by the dotted arrow and the point sources are indicated by solid arrows. Because of this phenomenon, neither the conventional three k-space line method (5) nor finding the brightest voxel of the product image of the projections would be successful in identifying the point-source[s] of the tip channel. On the other hand, using CurveFind to first identify the device shaft trajectory from the shaft-channel and then reapplying CurveFind to the tip-channel to extend this trajectory across the nulls, successfully finds both the shaft and the tip of the device because it uses the existing partial knowledge of the location of the device.

Figure 8.

Coupling artifacts. a: Sagittal projection of loopless shaft channel. b: Sagittal projection of solenoidal tip channel. c: Transverse projection of solenoidal tip channel. In b and c the artifact due to electromagnetic coupling is denoted by the dashed arrow, and the true point sources are denoted by whole arrows. In c the brightest pixel is the artifact and not either of the true point sources.

The use of multiple active devices, barring unacceptable levels of electromagnetic coupling between devices, should pose no problem to CurveFind. Since the signal of each device is collected separately, even if the devices cross each other, each individual device should be correctly identified.

The display of the three projection images with the identified device overlaid on it provides a simple method of user verification. While it would be desirable if the method required no human interaction, the user can lengthen or shorten the portion of interest on the device at the touch of a key if necessary. When SnapTo is used multiple times in an experiment, the stopping conditions used during the first instance are stored and reused for the later instances.

Note that the projection images we have displayed have large FOVs and are therefore very sparse. To reduce computational and memory requirements, we apply CurveFind only after (automatically) cropping the projection images to the region adjacent to the device. Furthermore, data requirements can be reduced by methods such as that of Aksit et al. (16) in which a narrow-FOV, aliased, projection image is unwrapped by exploiting the simplicity of the device shape.

In the future, we intend to extend this method to a moving device whose trajectory is dynamically updated from vastly reduced data by exploiting the adjacency of the device position across time. This will allow for an even more seamless incorporation of the tracking of the active device with the real time reconstruction of the slices. In this dynamic case, data requirements can be reduced by choosing the orientation of the projection image appropriately. For example, orienting a projection image almost perpendicular to the plane of the device (i.e., the SnapTo slice) results in an image with a narrow FOV in the phase-encoding direction. Consequently, the projection can be reconstructed from a small number of k-space lines.

CurveFind may also be used with devices that use reverse polarization (17) to separate the signal of the device from the surrounding tissue. The advantage of such devices is that they are not required to be electrically connected to the scanner and therefore avoid RF safety problems. Projection images of such devices are similar to those from active devices and therefore can be used as inputs to the CurveFind algorithm.

Conclusions

We have introduced a fast robust method, CurveFind, to identify the 3D trajectory of an active device from MR projection images. This 3D trajectory is used to improve the interventionist's visualization of the device in three ways: to reposition the imaged slice to contain the device (SnapTo), display the curve of the device in a 3D display of the imaged slices, and extrapolate the location on a target slice, which the device is expected to intersect. We have presented in vitro and in vivo results showing the robustness of the method to differences in the nature of the active device used.

Appendix

The center of mass of a 3D sampled volume h(x₁, x₂, x₃) is the vector [c₁ c₂ c₃] where

$$c_j={\Sigma }_{i_1}{\Sigma }_{i_2}{\Sigma }_{i_3}\widehat{h}(x_{i_1},x_{i_2},x_{i_3})x_{i_j}$$ (2)

and $\widehat{h}(x_1,x_2,x_3)=h(x_1,x_2,x_3)∕{\Sigma }_{i_1}{\Sigma }_{i_2}{\Sigma }_{i_3}h(x_{i_1},x_{i_2},x_{i_3})$ is the normalized volume.

The moment-of-inertia tensor M of the volume is a 3× 3 symmetric matrix $M=\left[\begin{array}{ccc}\hfill m_{11}\hfill & \hfill m_{12}\hfill & \hfill m_{13}\hfill \\ \hfill m_{12}\hfill & \hfill m_{22}\hfill & \hfill m_{23}\hfill \\ \hfill m_{13}\hfill & \hfill m_{23}\hfill & \hfill m_{33}\hfill \end{array}\right]$ where

$$m_{jk}={\Sigma }_{i_1}{\Sigma }_{i_2}{\Sigma }_{i_3}\widehat{h}(x_{i_1},x_{i_2},x_{i_3})(x_{i_j}-c_j)(x_{i_k}-c_k)$$ (3)

The center of mass and moment-of-inertia tensor of a 2D image are similarly computed.