Respiratory motion compensation for CT-guided interventions in the liver

Abstract

Computed tomography (CT) guided minimally invasive procedures in the liver, such as tumor biopsy and thermal ablation therapy, require precise targeting of hepatic structures that are subject to breathing motion. To facilitate needle placement, we introduced a navigation system which uses needle-shaped optically tracked navigation aids and a real-time deformation model to continuously estimate the position of a moving target.

In this study, we assessed the target position estimation accuracy of our system in vitro with a custom-designed respiratory liver motion simulator. Several real-time compatible transformations were compared as a basis for the deformation model and were evaluated in a set of experiments using different arrangements of three navigation aids in two porcine and two human livers. Furthermore, we investigated different placement strategies for the case where only two needles are used for motion compensation.

Depending on the transformation and the placement of the navigation aids, our system yielded a root mean square (RMS) target position estimation error in the range of 0.7 mm to 2.9 mm throughout the breathing cycle generated by the motion simulator. Affine transformations and spline transformations performed comparably well (overall RMS < 2 mm) and were considerably better than rigid transformations. When two navigation aids were used for motion compensation instead of three, a diagonal arrangement of the needles yielded the best results.

This study suggests that our navigation system could significantly improve the clinical treatment standard for CT-guided interventions in the liver.

• Image-guided systems
• tracking
• respiratory motion compensation
• needle insertion
• navigation
• deformation model
• interventional radiology

Introduction

Image-guided minimally invasive interventions are nowadays well-established clinical procedures for histopathological diagnostics and tumor therapy. Percutaneous radiofrequency ablation (RFA), for example, has become an accepted alternative to surgical resection in the primary treatment of hepatocellular carcinoma (HCC) and other liver tumors [1], [2]. One of the main challenges related to these interventions is the exact placement of the instrument. So far, commercially available navigation systems have been designed for use with rigid structures such as the skull or the spine, where the target remains in a constant position throughout the intervention. The liver, however, shows significant movement due to respiration [3], [4]. In order to address this issue, several research groups (e.g., those whose work is described in references [5–13]) are currently working on the development of navigation systems for soft tissue interventions. The different approaches to correcting for the complex movement of the liver can be roughly divided into two categories:

Gating techniques [5–9] are based on the assumption that the liver re-occupies the same position at identical points in the respiratory cycle. Consequently, the liver can be approximated as being motionless provided that the intervention is conducted exclusively in end-inspiration or end-expiration.

Marker techniques [10–13] use a set of markers that are placed on the skin [11] (external markers) and/or inside the target organ [10], [12], [13] (internal markers). Throughout the intervention, the markers are continuously located by a tracking system and the position of the navigation target point is estimated with a deformation model.

Table I shows a selection of the liver navigation systems under development. The corresponding accuracy studies generally evaluate the overall targeting accuracy of the system, i.e., they report the mean distance between a reference target position and the final position of the tip of an inserted instrument [5], [8], [9]. Unfortunately, this error depends crucially on the provided visualization scheme and the experience of the user. It is therefore useful to isolate the target position estimation error of a navigation system from the error caused by an inaccurate instrument insertion (as in references [11] and [12]).

Table I.  Selection of soft tissue navigation approaches for the liver.

Authors	Tracking method	Registration method	Motion compensation
Without deformation model
Banovac et al. [5]	electromagnetic	skin fiducials	gating
Nicolau et al. [6]	optical (color-based)	skin fiducials	gating
Nagel et al. [7], [14]	optical (infrared, passive) or electromagnetic	reference frame (equipped with CT markers and optical/electromagnetic markers)	gating, vacuum fixation device
Fichtinger et al. [8]	none (CT image overlay system)	phantom for manually calibrating image overlay system with CT scanner	gating
Khan et al. [9]	optical (infrared, active) and electromagnetic	skin fiducials	gating
With deformation model
Schweikard et al. [10]	stereo X-ray and optical (infrared, active)	internal gold markers and skin markers	deformation model describing correlation between internal and external motion
Khamene et al. [11]	electromagnetic, optical, and image-based (4D MRI for establishing correlation)	plate equipped with magnetic and optical markers	deformation model describing correlation between internal and external motion
Zhang et al. [12], [26]	electromagnetic	needle-shaped internal markers	affine transformation based on marker movement
Maier-Hein et al. [13]	optical (infrared, passive)	needle-shaped internal markers	deformation model based on marker movement

In a previous report [15], we introduced a needle-based navigation system for minimally invasive interventions in the liver, in which a real-time deformation model is used to estimate the position of a navigation target point continuously from a set of optically tracked navigation aids (Figure 1). The accuracy of tracking and CT registration have already been evaluated [15]. In addition, we have shown that the accuracy of the deformation model decreases drastically when only two navigation aids are used for motion compensation instead of three [13].

Figure 1. Soft tissue navigation workflow. [Color version available online.]

In this paper, we assess the target position estimation accuracy of our system in vitro with a custom-designed respiratory liver motion simulator. Several real-time compatible transformations are compared as a basis for the deformation model and are evaluated in a set of experiments using different arrangements of three navigation aids in two porcine and two human livers. Furthermore, we investigate different navigation aid placement strategies for the case where only two needles are used for motion compensation. For a preliminary version of this work, see reference [13].

This paper is organized as follows: First, we give an overview of our soft tissue navigation system. Then, after a brief review of spline-based registration, we describe the implemented real-time deformation model in detail. The subsequent section presents the respiratory liver motion simulator which has been developed for this study. The experiments and results of our work are described, and the paper concludes with a discussion.

Materials and methods

Navigation system

Our soft tissue navigation approach for supporting minimally invasive targeting procedures in the liver has been presented and discussed in a previous report [15]. The workflow is as follows (Figure 1):

1. Preparation: Prior to the intervention, a set of needle-shaped optically trackable navigation aids is inserted into the target region such that the target is contained in the volume spanned by the needles. Next, a planning CT of the target region is acquired.

2. Registration: In the second stage of the procedure, the navigation aids are registered with the planning CT image using a semi-automatic stochastic registration algorithm [15]. In addition, a navigation target point is chosen. Finally, the tracking coordinate system is registered with the CT coordinate system, as described in reference [15] (see also the Deformation model section below).

3. Intervention: During the intervention, the optical tracking system continuously locates the navigation aids, and a real-time deformation model is used to update the position of the target point accordingly. This way, an optically tracked instrument can be visualized in relation to the moving target.

Registration using spline interpolation

While affine schemes can only describe global changes in the object position, spline-based approaches can capture local deformations. The spline transformations used for this study provide a mapping between two 3D spaces given a set of N_C pairs of corresponding control points [16]. The displacement at an arbitrary point is computed using the following equation:where are the coefficients defining the spline, represents the affine portion of the transformation (), and is the basis function of the chosen spline.

In this contribution, we consider thin-plate splines (TPS), elastic body splines (EBS), and volume splines (VS).

Thin-plate splines were originally developed by Harder and Desmarais [17], and were introduced to medical image analysis by Bookstein [18]. They are physically motivated by bended metal plates.

In contrast, elastic body splines are based on a physical model of an elastic material and were specifically designed for 3D applications [16]. They are solutions of the Navier equation, which is a partial differential equation (PDE) that describes the equilibrium displacement of an elastic, homogeneous, isotropic material subject to forces. Davis et al. [16] assumed the underlying force fieldand derived the EBS for different forces [16]. In this paper, we examine two different versions of the EBS:where and |·| represents the Euclidean norm.

Finally, volume splines are a generalization of the univariate cubic interpolating splines when represented with distance functions [19].

The basis functions for the different splines are as follows:where I denotes the 3 × 3 identity matrix, and α and β are functions of the Poisson ratio with the Lamé coefficients λ and μ and thus represent the physical properties of the given material [16].

To determine the coefficients W (see Equation (1)) we exploit the interpolation condition, i.e., the spline displacements must equal the control displacements:Together with some additional constraints, this yields a linear system of equations for the coefficients W, which can be solved analytically [16].

The interested reader may refer to the literature for a more detailed description and comparison of the spline transformations used here [16], [18], [20], [21].

Deformation model

The deformation model of the navigation system was implemented using the open-source toolkits Insight Segmentation and Registration Toolkit (ITK) [22] and Medical Imaging Interaction Toolkit (MITK) [23]. It is based on an interpolator which is used to compute the current position of the target point from a set of corresponding control point pairs representing the initial and current positions of the navigation aids.

In this contribution, we evaluate the suitability of the following real-time compatible transformations as interpolators: Rigid transformations (RIGID), affine transformations (AFFINE), TPS, EBS(r), EBS(r⁻¹), and VS. The Poisson ratio ν has been optimized on a training data set that is disjunctive with the set of experiments used for this study. The best results were achieved for ν = 0.

The deformation model is updated every 100 ms. In each time-step k the coefficients defining the associated transformation are recomputed. The algorithm for the spline transformations is as follows:

1. Initialization (k = 0):

   1. Based on the CT registration results (see registration paragraph of the Navigation system section above) and the initial positions of the navigation aids in the optical tracking coordinate system (first recorded sample), we compute a rigid transformation Φ_TS→CT mapping the coordinate system of the tracking device (TS) to the CT coordinate system (CT). The solution is based on the algorithm of Horn [24] and uses the positions of the optical markers of the N navigation aids in optical tracking coordinates and in CT coordinates, and , as source and target landmarks, respectively.

   2. For each navigation aid i, a set of n = 5 control points in CT coordinates with an inter-point spacing of 1 cm is distributed along the needle beginning at its tip (Figure 2, right). The part of the needle covered by the control points (4 cm) is supposed to roughly represent the part of the needle inside the liver. It is worth mentioning that the number of control points per navigation aid has been determined empirically and does not significantly affect the accuracy of the system. The entire set of control points is defined as

2. Update (k ≥ 1):

   1. The current position of each navigation aid is determined by the optical tracking system and transformed to CT coordinates using Φ_TS→CT.

   2. The current control points are computed:where is defined in an analogous way to P_i.

   3. The current spline coefficients (see Equation (1)) are computed using the control point pairs as described in the previous section.

   4. The current position of the navigation target point (original position) is determined using (1):

In the case of the rigid/affine transformation, steps (c) and (d) of the update algorithm are replaced by the following procedure:

• (c)’ P and Q^k are used as source and target landmarks, respectively, to compute a rigid/affine transformation Φ_0→k following the algorithm of Horn [24].

• (d)' The resulting landmark-based transformation is used to transform the target point:

Figure 2. Sample needle configuration with three navigation aids and one target needle: real needles (left) and virtual representation (right) with corresponding model points (white) on the navigation aids. [Color version available online.]

Respiratory liver motion simulator

In order to allow for an in-vitro evaluation of our soft tissue navigation system, we have developed a custom-designed respiratory liver motion simulator [13] (Figure 3). This is primarily composed of two artificial lungs representing the lobes of the lung and a Plexiglas® plate imitating the diaphragm. To use the simulator, it is necessary to mount an explanted human or porcine liver to the Plexiglas® plate and to connect a lung ventilator to the artificial lungs (Figure 4). This leads to a periodic movement of the liver along the cranio-caudal axis of the artificial corpus. Optionally, a neoprene skin can be attached to the box to allow for the simulation of minimally invasive interventions. We have shown that the generated movement of a liver mounted to the simulator qualitatively resembles the movement of a human liver in vivo [25].

Figure 3. Schematic representation of the respiratory liver motion simulator without skin. [Color version available online.]

Experimental conditions

Two explanted human livers were obtained from patients that underwent liver transplantation at the Department of Surgery of the University of Heidelberg. Informed consent was obtained from the patients in accordance with the Helsinki Declaration. In addition, three porcine livers were purchased from a butcher.

Figure 4. Experimental setup in the computed tomography (CT) room, showing the optical tracking system and respiratory liver motion simulator (without skin) in end-inspiration with a mounted porcine liver. [Color version available online.]

Target position estimation

Various error sources of our navigation system have been discussed in a previous report [13]. In this paper, we assess the target position estimation accuracy, which incorporates the tracking error, the registration error, and the error of the real-time deformation model. For this purpose, we simulated the workflow described in the Navigation system section with the help of the respiratory liver motion simulator introduced in the previous section. A set of 5-degrees-of-freedom (5DOF) navigation aids [15], with a distance of 125 mm between the tip of the needle and the nearest optical marker and an inter-marker distance ranging from 45 mm to 60 mm, was used for this purpose (Figure 2). One needle served as a target while the remaining N = 3 needles were used as navigation aids. The optical tracking system could thus provide a reference position for the target needle over time.

For each porcine liver PL_i (i = 1, 2) and each human liver HL_j (j = 1, 2) used in this experiment, three different navigation aid configurations were examined, where one configuration represents an arrangement of the four needles within the liver as exemplified in Figure 2.

For each configuration, we conducted the following workflow:

1. The four optically trackable needles were inserted “percutaneously” into the liver, such that the target needle was surrounded by the needles serving as navigation aids (Figure 2).

2. A CT scan (Somatom Sensation 16 multidetector row scanner, Siemens, Erlangen, Germany; 0.75-mm slice thickness) in end-expiration was acquired to determine the initial position of the target needle relative to the navigation aids. We applied a semi-automatic stochastic registration algorithm [15]. It should be noted that the expiratory position of the liver was considered to be the location with the most cranial displacement of motion within the torso model.

3. Three data sets were recorded with the Polaris® Vicra™ optical tracking system (Northern Digital Inc. (NDI), Waterloo, Ontario, Canada):

   • Continuous measurement (CONT): Beginning in end-expiration, the motion simulator was activated for a period of 30 seconds and the positions of all four needles were recorded by the optical tracking system for several breathing cycles.

   • Maximal movement (MAX): A timer with the period of the lung ventilator was used to measure the needle positions in one end-expiration phase and ten consecutive end-inspiration phases. Note that the first sample was used for registering the CT coordinate system with the tracking coordinate system as described in the Deformation model section above. This experiment enabled analysis of the performance of the deformation model during maximal organ movement.

   • Minimal movement (MIN): A timer was used to record the needle positions in eleven consecutive end-expiration phases, to simulate an intervention conducted exclusively in one previously determined state in the breathing cycle. Again, the first sample was required for the registration process.

For each experiment defined by a liver ID, a configuration ID, and a measurement type, the target position estimation error was determined as follows:

1. The original target position was defined as a set of m = 5 target points with an inter-point spacing of 1 cm distributed along the registered target needle beginning at its tip. We used several target points instead of just one, in order to consider different depths within the tissue.

2. The first sample of the experiment was used to calculate the transformation Φ_TS→CT mapping the tracking coordinate system to the CT coordinate system (see Deformation model section). Following the notation of the Deformation model section, we computed the mean fiducial registration error (FRE), that is, the mean distance between the target landmarks and the corresponding transformed source landmarks:where |·| represents the Euclidean norm. The standard deviation of the registration error FRE_σ, as well as the root mean square (RMS) and maximum registration error, FRE_rms and FRE_max, were computed analogously.

3. For each sample k > 0, a set of measured target points and a set of estimated target points in CT coordinates were determined:

   • Measured: The target needle position (recorded by the optical tracking system) was transformed to CT coordinates using Φ_TS→CT. Next, m = 5 target points with an inter-point spacing of 1 cm were distributed along the target needle beginning at its tip.

   • Estimated: the original target points T^orig were transformed to as described in the Deformation model section.

4. The mean target position estimation error was then defined aswhere n is the number of recorded samples excluding the first sample (k = 0) which was used for the calculation of the coordinate transformation. Analogously, the standard deviation , the RMS error , and the maximum error were determined.

In order to compute ε^target for a set of experiments, we put all determined estimation errors for the individual experiments in one single vector and calculated the statistics over the entire vector.

In addition, we defined the movement δ^target of the target needle by replacing by in the equations for ε^target. For the RMS movement we thus obtained the following equation:

Placement strategies

It is obvious that the number of navigation aids increases both the potential accuracy and the invasiveness of an intervention. If only two navigation aids are used, the corresponding control points do not span a volume, and the estimation accuracy for the spline transformations decreases drastically [13]. For this reason, we use rigid transformations as the basis for the deformation model in this case. In order to examine whether the placement of the two navigation aids relative to the target is essential for the target position estimation accuracy, we have compared three different placement strategies (Figure 5):

1. Cranio-caudal arrangement: The two navigation aids are arranged parallel to the cranio-caudal axis of the patient. Ideally, the tumor should then be situated between the two needles, as shown in Figure 5 (c_m). Since an exact placement of the navigation aids is difficult, we have defined three subcategories: left shift (c_l), exact placement (c_m), and right shift (c_r).

2. Lateral arrangement: The two navigation aids are arranged laterally. Ideally, the tumor should then be located between the two needles as shown in Figure 5 (l_m). To account for placement error, we have again defined three subcategories: shift up (l_u), exact placement (l_m), and shift down (l_d).

3. Diagonal arrangement: The two navigation aids are arranged diagonally, such that they can potentially capture deformation in both the cranio-caudal and lateral directions. In our experiments, the inter-navigation aid distance for this arrangement was larger than for the two other placement strategies (arrangement on an equally spaced grid; see Figure 5). For this reason, we have only defined two subcategories: left-to-right (d_l) and right-to-left (d_r).

Figure 5. The three navigation aid placement strategies (cranio-caudal, lateral, diagonal) and their subcategories. [Color version available online.]

In order to compare the three placement strategies, we mounted a porcine liver onto the motion simulator and marked a 3 × 3 grid, with a grid cell size of 4 × 4 cm², on the artificial skin (Figure 5). One optically tracked needle was inserted through the grid cell in the middle to represent the tumor. For each arrangement shown in Figure 5, we inserted two navigation aids through the corresponding grid cells and positioned the tracking system accordingly (for a clear view of all tools). Next, we activated the motion simulator and recorded the positions of the three tools for 30 seconds. The initial position of the target relative to the navigation aids was extracted from the first sample recorded by the optical tracking system, i.e., we did not conduct a CT registration, but performed the entire experiment in tracking coordinates. It is worth mentioning that this led to an FRE close to 0 and thus to a lower target position estimation error than would be achieved in practice. Even so, the experiment still allowed us to compare the different placement strategies because the absolute error was not relevant in this context.

Finally, the computation of the target position estimation error was based on the difference between the position of the target needle according to our navigation system (i.e., the deformation model) and its position according to the optical tracking system, as described in the Deformation model section. To obtain a robust result, this experiment was conducted twice for each arrangement (two passes). The results are presented in the following section.

Results

Target position estimation

According to Table II, we obtained a relatively low FRE_rms in the order of 1 mm for all experiments introduced in the preceding section (maximum: 2.6 mm). An analysis of the movement of the target needle in CT coordinates is given in Table III. It can be seen that the RMS movement between expiration and inspiration (dataset MAX) was 14.9 mm in the case of the porcine livers and 10.2 mm in the case of the (heavier and less elastic) human livers, and was primarily in the cranio-caudal direction.

Table II.  Fiducial registration error FRE (in mm) according to Equation (14) for the data sets CONT, MAX, and MIN averaged over six needle configurations (C) in two porcine livers and six needle configurations in two human livers.

	CONT	MAX	MIN
Porcine livers
μ	0.9	1.0	1.0
σ	0.3	0.3	0.3
rms	1.0	1.1	1.0
max	1.3	1.5	1.5
Human livers
μ	1.7	1.1	1.0
σ	0.7	0.1	0.2
rms	1.8	1.1	1.1
max	2.6	1.3	1.4

Table III.  RMS movement of the target needle (in mm) averaged over six configurations in two porcine livers and six configurations in two human livers for the three data sets CONT, MAX, and MIN defined in the Experimental conditions section. The absolute movement as well as the movement along the lateral (x-axis in Figure 3), posterior-anterior (y-axis in Figure 3), and cranio-caudal (z-axis in Figure 3) axes is shown.

	Absolute	x	y	z
Porcine livers
CONT	9.1	1.3	0.9	8.9
MAX	14.9	2.0	1.6	14.6
MIN	1.1	0.4	0.2	1.0
Human livers
CONT	5.4	0.7	1.5	5.2
MAX	10.2	1.0	2.6	9.9
MIN	1.3	0.4	0.5	1.1

The target position estimation error for the different transformations introduced in the Deformation model section and the data sets CONT, MAX and MIN are shown in Tables IV and V for the porcine and human livers, respectively. Depending on the transformation, was in the range of 1.6 mm to 2.2 mm and 1.2 mm to 2.0 mm for the porcine and human livers, respectively, when computed continuously over several breathing cycles (CONT). For the spline transformations, as well as for the affine transformation, it made up approximately 15% of the RMS target movement during maximal organ deformation (MAX). The rigid transformation performed considerably worse, yielding an estimation error of over 20% relative to the target movement in all experiments. When the estimation error was exclusively computed in that state within the breathing cycle in which the CT was taken (in this case, end-expiration), the error difference between the rigid transformation and remaining transformations was reduced drastically (MIN).

Table IV.  Target position estimation error (in mm) for the different transformation types introduced in the Deformation model section and the porcine livers (PL). The results were obtained from six needle configurations in two livers. Mean (μ) error, standard deviation (σ), RMS error (rms) and maximum (max) error are shown for the three data sets CONT, MAX, and MIN defined in the Experimental conditions section. In addition, the RMS error relative to the RMS movement is listed as a percentage.

	RIGID	AFFINE	TPS	EBS(r)	EBS(r^−1)	VS
CONT
μ	1.8	1.4	1.4	1.6	1.4	1.6
σ	1.2	0.8	0.8	1.0	0.8	1.0
rms	2.2	1.6	1.6	1.9	1.6	1.9
max	6.9	3.9	3.7	5.1	3.7	5.0
εrms/δrms	24%	17%	18%	21%	17%	21%
MAX
μ	3.1	2.1	2.1	2.5	2.1	2.4
σ	1.2	0.7	0.8	1.3	0.7	1.2
rms	3.3	2.2	2.3	2.8	2.2	2.7
max	6.6	3.9	3.7	5.0	3.7	5.0
εrms/δrms	22%	15%	15%	19%	15%	18%
MIN
μ	0.9	0.8	0.8	0.9	0.8	0.9
σ	0.3	0.4	0.4	0.4	0.4	0.4
rms	0.9	0.9	0.9	1.0	0.9	1.0
max	1.9	2.0	1.9	1.7	1.9	1.8
εrms/δrms	86%	80%	81%	89%	81%	88%

It is worth mentioning that the target position estimation errors for the porcine livers were generally worse than those for the human livers. When related to the target movement, however, the estimation accuracy was similar (Tables IV and V).

Table V.  Target position estimation error (in mm) for the different transformation types introduced in the Deformation model section and the human livers (HL). The results were obtained from six needle configurations in two livers. Mean (μ) error, standard deviation (σ), RMS error (rms) and maximum (max) error are shown for the three data sets CONT, MAX, and MIN defined in the Experimental conditions section. In addition, the RMS error relative to the RMS movement is listed as a percentage.

	RIGID	AFFINE	TPS	EBS(r)	EBS(r^−1)	VS
CONT
μ	1.7	1.3	1.2	1.1	1.2	1.1
σ	1.1	0.6	0.5	0.5	0.5	0.5
rms	2.0	1.4	1.3	1.2	1.3	1.2
max	5.8	3.1	2.8	2.8	2.8	2.7
εrms/δrms	37%	25%	24%	23%	24%	23%
MAX
μ	2.5	1.7	1.6	1.5	1.6	1.5
σ	1.3	0.6	0.6	0.5	0.6	0.5
rms	2.9	1.8	1.7	1.6	1.7	1.6
max	6.0	3.0	2.7	2.6	2.7	2.6
εrms/δrms	28%	18%	16%	15%	16%	15%
MIN
μ	1.1	1.0	1.0	1.0	1.0	0.9
σ	0.5	0.4	0.4	0.4	0.4	0.4
rms	1.2	1.0	1.0	1.0	1.0	1.0
max	2.3	1.7	1.8	1.7	1.8	1.8
εrms/δrms	88%	78%	78%	78%	79%	78%

To allow for a better comparison of the different transformations considered in this study, we have computed the target position estimation error for the individual needle configurations in Table VI. The best and worst transformations are explicitly listed. In addition, we have visualized the estimation error over several breathing cycles for one sample configuration in Figure 7. Depending on the transformation and the placement of the navigation aids, our system yielded an RMS target position estimation error in the range of 0.7 mm to 2.9 mm throughout the breathing cycle generated by the motion simulator (PL: 0.7–2.9 mm; HL: 1.0–2.4 mm). With the exception of the three configurations (PL2,C1), (PL2,C3), and (HL1,C3), the rigid transformation always yielded the worst result. A careful examination of the experimental data showed that in these cases either the navigation aids or the target needle were placed suboptimally. Figure 6 shows examples of an optimal needle placement (HL1,C1) and a misplaced target needle (PL2,C3).

Figure 6. Left: Model configuration (HL1,C1) with the target needle centered in the volume spanned by the navigation aids. Right: Unfavorable configuration (PL2,C3) with a misplaced target needle. [Color version available online.]

Figure 7. Position estimation error ε^target (in mm) for the tip of the target needle over several breathing cycles for the different transformations and a typical needle configuration (PL1,C3). The movement δ^target of the target serves as the base (BASE). [Color version available online.]

Placement strategies

The target position estimation error for the different placement strategies is shown in Table VII. Both the cranio-caudal arrangement (RMS: 1.4 mm) and the diagonal arrangement (RMS: 1.1 mm) performed considerably better than the lateral arrangement (RMS: 2.5 mm). In the case of the lateral and cranio-caudal placement strategies, the results were particularly good when the target needle was situated between the two navigation aids.

Table VI.  RMS target position estimation error (in mm) for the data set CONT defined in the Experimental conditions section and the individual navigation aid configurations in the porcine livers (PL) and human livers (HL). The error is shown for the different transformation types introduced in the Deformation model section, and the best and worst transformations are explicitly listed.

Experiment	RIGID	AFFINE	TPS	EBS(r)	EBS(r^−1)	VS	Best	Worst
Porcine livers
PL1,C1	2.04	1.48	1.56	1.57	1.55	1.59	AFFINE	RIGID
PL1,C2	2.86	1.82	1.90	2.19	1.83	2.29	AFFINE	RIGID
PL1,C3	2.13	0.90	0.82	0.69	0.81	0.71	EBS(r)	RIGID
PL2,C1	1.92	1.61	1.63	2.84	1.58	2.69	EBS(r^−1)	EBS (r)
PL2,C2	1.68	1.33	1.32	1.32	1.35	1.29	VS	RIGID
PL2,C3	2.09	2.12	2.06	1.99	2.06	2.00	EBS(r)	AFFINE
Human livers
HL1,C1	2.19	1.44	1.20	0.95	1.18	0.98	EBS(r)	RIGID
HL1,C2	2.37	1.06	1.07	1.10	1.07	1.09	AFFINE	RIGID
HL1,C3	2.21	1.13	1.12	1.15	1.16	1.09	VS	RIGID
HL2,C1	1.85	1.35	1.30	1.27	1.31	1.25	VS	RIGID
HL2,C2	1.92	1.78	1.75	1.66	1.74	1.69	EBS(r)	RIGID
HL2,C3	1.37	1.42	1.23	1.14	1.23	1.16	EBS(r)	AFFINE

Table VII.  RMS target position estimation error (in mm) for the different placement strategies shown in Figure 5 (two passes each) and corresponding movement of the target needle. The error relative to the movement is also listed.

Arrangement
Cranio-caudal
cl, pass 1	2.2	5.9	37
cl, pass 2	1.6	4.7	34
cm, pass 1	1.5	4.8	31
cm, pass 2	0.8	4.7	17
cr, pass 1	1.1	5.3	21
cr, pass 2	1.0	5.6	18
All (cranio-caudal)	1.4	5.2	27
Lateral
lt, pass 1	3.0	5.1	58
lt, pass 2	3.1	4.7	67
lm, pass 1	0.9	5.6	17
lm, pass 2	1.1	5.6	20
lb, pass 1	3.6	6.3	58
lb, pass 2	3.1	4.8	64
All (lateral)	2.5	5.3	47
Diagonal
dl, pass 1	1.4	5.2	28
dl, pass 2	1.1	4.8	22
dr, pass 1	1.0	5.7	17
dr, pass 2	0.9	4.9	18
All (diagonal)	1.1	5.1	21

It should be pointed out that the estimation errors for this experiment were generally better than those presented in the previous section because we worked in tracking coordinates and thus obtained an FRE close to 0 (see Placement strategies subsection of Experimental conditions section above).

Discussion

In this paper, we evaluated the target position estimation accuracy of a needle-based soft tissue navigation system for a set of real-time compatible transformation types with a custom-designed respiratory liver motion simulator. The affine transformation and the spline transformations (TPS, EBS, VS) clearly performed better than the rigid transformation, yielding an RMS target position estimation error of less than 2 mm over the breathing cycle generated by a custom-designed motion simulator.

When only two navigation aids are used for motion compensation instead of three, our study suggests a diagonal arrangement of the needles. Comparable results can be achieved with an arrangement parallel to the cranio-caudal axis of the torso. A placement parallel to the lateral axis, on the other hand, should be avoided.

According to our study, there is no clear preference for one of the spline transformations or for the affine transformation. In fact, the needle placement had a greater influence on the target position estimation accuracy than the transformation type. A possible explanation for this phenomenon is the fact that our deformation model aims to capture the motion and deformation of an elastic material with a set of rigid objects. To overcome this problem, we suggest an extension of the deformation model such that the volume defined by the control points on the navigation aids remains constant over time. This would account for the incompressibility of the liver. Alternatively, one could regard the distribution of model points along the needles as noisy: When the volume spanned by the needles decreases, the inter-model point distance should increase. This could possibly be achieved by applying so-called approximating splines [20] which account for landmark (or control point position) errors. If the model points were distributed optimally along the needles, we might obtain more distinguishing results when comparing the different transformations discussed here. In addition, the parameter optimization might then yield a value for ν which is closer to the value for liver tissue (i.e., ν > 0).

Another possible explanation for the fact that the affine transformation performed comparably well relative to the spline transformations is the fact that we used a relatively small number of landmarks for the splines. More information could be obtained from more navigation aids, which, however, would increase the invasiveness of the intervention.

An optimal evaluation of the deformation model would further rely on a perfectly accurate reference position over time. However, the reference target position used for this study was extracted from a rigid object unable to capture the elasticity of the tissue. Furthermore, the needles used were not firmly anchored within the liver and were thus potentially able to move relative to the tissue following insertion. Finally, the target needle possibly altered the natural movement of the liver. The use of an electromagnetic sensor as the target could overcome these problems but would raise new issues such as the registration of the electromagnetic tracking system with the optical tracking system and the implantation of the target. Due to the lower tracking accuracy of electromagnetic systems as compared to optical systems, we assume that the quality of the reference target position achievable with this method would still be worse than that obtained in this study. The use of self-locking needles, on the other hand, could be beneficial.

Despite the drawbacks discussed above, we are one of the first groups (see also references [11] and [26]]) to have isolated the target position estimation error from the overall targeting error of a navigation system. We are thus able to assess the performance of our system independent of the provided visualization scheme and the experience of the user. Furthermore, our evaluation approach enables a report of the estimation error with respect to the state within the breathing cycle generated by the motion simulator.

According to our results, the position of a navigation target point initially marked in a CT scan can be continuously estimated with high accuracy during a minimally invasive intervention even when the patient is breathing. Sufficient accuracy can even be achieved with only two navigation aids, provided that the needles are placed appropriately. A robust targeting precision on the order of several millimeters would certainly decrease the number of CT scans required for targeting a liver lesion and thus lower the radiation exposure for the patient and shorten the intervention time. In addition, precise instrument placement could potentially improve treatment margins in RFA interventions and thus lead to lower recurrence rates. When tumor access is difficult, high position estimation accuracy could further reduce the risk of injury to vital structures.

Several issues still remain to be addressed. In our opinion, clinical acceptance of our proposed method depends crucially on the following questions: (1) Is there a significant benefit in using fiducial needles over skin markers, even if the intervention is conducted in expiration or inspiration only? (2) What is the optimal number of navigation aids, considering the tradeoff between high accuracy and increased invasiveness? (3) Is image guidance needed for inserting the navigation aids? If so, what is the best method?

To answer these questions, we are currently conducting experiments in swine. Based on initial results, we consider two navigation aids to be sufficient for motion compensation provided that the intervention is conducted in expiration (or inspiration) only. In this case, the needles do not need to be positioned close to the target. Ultrasound (US) guidance is helpful for placement of the navigation aids, but as the needles do not have to be inserted deeply into the liver, non-guided placement is also possible. Even though the experiments were conducted in one predefined state within the respiratory cycle, real-time motion compensation turned out to be useful, because the insertion of the instrument led to movements of the target region. Furthermore, we consider fiducial needles to be essential for ensuring high accuracy in the registration of the tracking coordinate system with the image coordinate system, and thus for the overall system accuracy.

In conclusion, we believe that the high target position estimation accuracy of our approach could significantly raise the treatment standard for CT-guided interventions in the liver. To advance the clinical application of our method, we are currently conducting a study comparing the conventional method for CT-guided needle insertions and our approach with respect to complication rates, time required, and accuracy.

Acknowledgments

The present study was conducted within the context of ‘Research training group 1126: Intelligent Surgery - Development of new computer-based methods for the future workplace in surgery’ funded by the German Research Foundation (DFG).

The authors wish to thank Heinrich Rühle, Johann Cieslok, Gernot Echner, Steffen Glasbrenner, Clemens Lang, and Volker Stamm (Research and Development Workshop, German Cancer Research Center) for their valuable contributions to this study. Many thanks also go to Hatice Atmaz and Kerstin Graf (University of Heidelberg, Clinic for Radiology) for the CT data acquisition.