Reconstruction and error detection of blood vessel network from ultrasound volume data

Transcription

1 Reconstruction and error detection of blood vessel network from ultrasound volume data Kohji Masuda, Antoine Bossard, Yuki Sugano, Toshikazu Kato and Shinya Onogi Graduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology, Japan. Abstract Recently, we described a reconstruction method of the blood vessel network by 3D thinning to detect vessels bifurcations, which is applied to the control of microbubbles in vivo. However, that method did not include error detections and was only verified on a very simply shaped artificial blood vessel. In this paper we propose a system including an abstraction method for the blood vessel network. Such a model is then analyzed through graph theory and error patterns in the reconstructed network. We proceeded in vitro by acquiring volume data from an artificial capillary with multi-bifurcations whose diameter ranges from 0.5 to 2.0mm and with different flow velocities. We were able to reconstruct the blood vessel network of an in vitro artificial capillary with multi-bifurcations. Results show that our system successfully reconstructed the corresponding networks as much as the limitation of resolution of echography. 1. Introduction Blood vessel network (BVN) reconstruction from CT and MRI data is a well-discussed topic and several approaches have already been published [1, 2]. Regarding the ultrasound modality, BVN reconstruction by ultrasound has not been developed because of significantly lower resolution than that of CT and MRI. However, it has been proved recently that reconstructing the blood vessel network by using the ultrasound modality has a great potential for applications. For example, due to their high degree of echogenicity, microbubbles are commonly used in echography as they can be easily observed. Under the effect of ultrasound pulses, microbubbles start oscillating and thus generate heat and shock waves. Hence microbubbles have proven popular when it comes to thermal therapy or drug delivery [3-5]. Even if microbubbles are well adapted to observation via ultrasound, the control of their flow in vivo remains challenging. To apply to an in vivo method realizing an active control of a flow of microbubbles [6-8], a reconstruction method of the BVN is required as it is not directly observable. As mentioned earlier, by using CT or MRI threedimensional images, one can reconstruct the BVN, including vessels bifurcations. However, in vivo microbubbles cannot be controlled within such equipments. Effectively, even if a BVN reconstruction is obtained by preprocessing, the configuration of the blood vessels, that is the positions of the vessels bifurcations, will be changed by several factors like respiration. Therefore, echography is the only modality to have a constant update of the BVN that enables realtime reconstruction and tracking of blood vessels and their bifurcations positions. In this paper, we describe a system reconstructing the BVN in three dimensions from ultrasound volume data, including vessels bifurcations absolute position for aforementioned applications. The measurement system we are proposing in this research can be separated into three main steps as shown in Fig.1. First, a tracker is set onto the ultrasound probe and the transducer. So, we can track in real-time their positions and orientations with a position sensor. Second, the structure of the blood vessels is reconstructed by applying image processing to the acquired threedimensional volume data. Third, we apply a thinning operation onto the BVN reconstruction to be able to detect vessels bifurcations. Fig.1 System configuration /13/$31.00 c 2013 IEEE CBMS

2 2. Theory 2.1 Extraction of blood vessels construction Volume rendering is an important step in the process of extracting blood vessels from the acquired volume data. First, we eliminated noise in the volume data by using opening and closing filters. To extract blood vessels, we applied a marching cubes method [9], which is able to extract a polygonal mesh from successive two-dimensional slices as obtained from the DICOM file. Subsequently, blood vessels are rendered as three-dimensional objects and polygons. We have applied this rendering process to the color Doppler information embedded in the DICOM file so as to obtain blood flow information in our reconstruction of the BVN. Then we obtain a binary image representing blood vessels: red vessels indicating a blood flow towards the ultrasound probe and blue vessels indicating a blood flow moving away from the ultrasound probe. After obtaining blood vessels as volume objects, an additional processing is applied so as to precisely locate vessels bifurcations and end points. For this purpose, we shall reduce volume-rendered vessels to a one-voxel-wide center line: this is a thinning operation. For a voxel (i, j, k) and Q the background area (voxels not part of an extracted vessel object), let the distance l ijk be defined as min{(i-x) 2 +(j-y) 2 +(k-z) 2 (x,y,z) Q}. From there, by erasing voxels from extracted vessels objects in ascending order of l ijk, we obtain the center line of blood vessels. Concretely, objects resulting from the previous rendering operations are eroded in a way that they become a one-voxel-wide object. We describe below this algorithm in details. (i) Categorize voxels of extracted objects having the smallest distance l ijk based on the number of neighboring background voxels. (ii) Erase deletable voxels of the category whose number of neighboring background voxels is the highest. (iii) Apply (ii) to each category. (iv) Repeat (i) to (iii) for deletable voxels of extracted objects until there is none. So, by erasing voxels in descending order of their number of neighboring background voxels, irrelevant holes and other noise are ignored when extracting center lines. This process is illustrated in Fig.2. Once reduced to their respective center lines, blood vessels can be scanned to detect bifurcations and end points. This can be easily done by performing a neighborhood analysis for each pixel of a center line. Fig.2 Detection of vascular bifurcation using 3-dimension thinning. 2.2 Abstraction of the BVN and basic correctness measurement In this section, we recall the definition of the induced graph of an original BVN reconstruction [10]. A graph G = (V, E) is a pair of a set V of vertices and a set E of edges where E!V!V. The degree of a vertex u " V, denoted by d(u), is the number of edges incident to u. A path is an alternate sequence of distinct vertices and edges. A cycle is a path with one additional edge linking its two extremities. The length of a cycle is defined by its number of edges. Depending on the original BVN reconstruction, we can induce different kinds of graphs. Some basic data is required though to construct a most basic induced graph. So, an original BVN reconstruction must include information locating blood vessels bifurcations and their end-points. From there, a mapping of the union of the set of all bifurcations and of the set of all end-points to a set V of vertices is performed. Then, the set E of edges is obtained by simple pixel connectivity analysis between bifurcations and endpoints. If no other information is provided by the original BVN reconstruction, the induced graph obtained is a simple undirected, graph. In the case blood flow directions are known, we can obtain a directed graph as described hereinafter. Correctness measurement of an original BVN reconstruction can be obtained by performing the traversal of the corresponding induced graph as Depthfirst Search (DFS) or Breadth-first Search (BFS) [11]. So, one can check easily several properties of the induced graph, and more precisely we shall define error patterns to give a correctness indication. For instance, a degree greater than three, or a cycle of length three are very likely to indicate an error in the original BVN reconstruction as shown in Fig.3, where the error patterns are represented as A and B. 498 CBMS 2013

3 Fig.3: An original BVN reconstruction (left) and the corresponding induced graph (right) including two error patterns: a degree of 4 (A) and a cycle of length 3 (B). 3. Experiments Let us now apply our method to an in vitro artificial capillary with multi-bifurcations made of poly(vinyl alcohol) by grayscale lithography whose diameter ranges from 0.5 to 2.0 mm and with a maximum flow velocity of 20 mm/s. We have designed the capillary model as shown in Fig.4. The external size was 180!70!8 mm 3. The inflow path of 2 mm was repeatedly divided into two lower courses to constitute the artificial capillary until the middle of the model, where the minimum diameter was 0.5 mm. After the middle of the model, courses converged towards the outflow of the model in the opposite way to the inflow towards the middle. In this model, the diameters of the paths in the same x- coordinate are uniform. The diameters and the section areas corresponding from A to E in Fig.4 are shown in Table 1 to guarantee a constant flow velocity in any part of the model. Finally, one should note that sound velocity and density of this capillary are similar to those of water. A B We compared capillary reconstructions obtained from the following different settings: flow velocity, gain and MI (Mechanical index) value. Volume data was acquired by using a matrix array probe equipped on a 3D-capable echography (iu22, Philips). The transducer (X6-1), whose frequency ranges from 1 to 6 MHz, is built on a state-of-the-art technology involving a matrix phased array with more than 9,200 elements, thus producing high-resolution images [12]. The experimental setup has been represented in Fig.5. Definition of the position and angle of the probe is shown in Fig.6. Fig.5 Experimental setup. Fig.6 Definition of the position of the probe. 4. Results Fig.4: Construction of the artificial blood vessel of the capillary model. Table 1: The diameters and the section areas of the capillary model.! " # $ % & %'()*+*,!-)).!"# $"% $"# #"& #"' /*0+'12!(,*(!-)) 3. ("$% $"') #"&* #"% #"! In the experiment, BVN reconstructions were realised from power Doppler information as it produced echograms of higher quality than colour Doppler for capillary visualisation. Concretely, we have taken samples varying the following parameters: ultrasound probe position, flow velocity, echography gain, and echography MI value (output power index). These parameters were selected as follows. First, we chose two different probe positions. Position 1 sets the parameters of Fig.6 as follows: h =20 mm,! =0 deg, CBMS

4 " =45 deg. Position 2 sets the parameters of Fig.6 as follows: h =20 mm,! =38 deg, " =45 deg. Then, we selected three different flow velocities: 5, 10 and 20 mm/s. Lastly, echography gain was set to 30%, 40% and 50%, and echography MI value was set to 0.3, 0.5 and 0.7. So, in total, we have acquired 54 samples. For each sample, we manually selected a treedimensional rectangular region of interest (ROI) containing the capillary so as to analyse only the relevant area. The bifurcation level L1 is the nearest bifurcation level to the probe, whereas L8 is the farthest. The reconstruction results obtained from a representative set of samples is given in Fig.7. Practically, these results correspond from volume data acquisition in the following experimental conditions: environmental parameters are fixed to a 20 mm/s flow velocity and Position 1, whereas echography parameters vary (gain and MI value). reconstructions have detected all bifurcations at that bifurcation level and flow velocity. We can observe that when the diameter of the path was greater than or equal to 0.7 mm, the reconstruction reliability is high. Additionally, we can see that a path of diameter less than 1 mm could not be properly reconstructed. Fig.8 Detection rate at each bifurcation level. Fig.7 Reconstruction results of the capillary with the following parameters: Position 1 and 20 mm/s flow velocity. Finally, we measured the average bifurcation detection rate at each bifurcation level (L1 to L3, as described in Fig.4) in the capillary, which is distinguishing bifurcations vessels diameters. 54 samples were collected under various conditions as explained previously. The results for Position 1 are given in Fig.8 (a), while those for Position 2 are given in Fig.8 (b). Note that a rate of 100% for a given flow velocity and bifurcation level means that all capillary 5. Discussion Let us compare the results obtained at bifurcation levels near (L1) and far (L3 and beyond) from the probe. First we can observe that reconstructed areas closer to the probe (e.g. L1) have a greater reliability compared to farther areas (e.g. L3). For example, at a flow velocity of 10 mm/s in Position 1, bifurcation detection rate is 88% in L1 and only 56% in L3. A similar discussion holds for all flow velocities and both probe positions. Second, we can observe that a higher flow velocity also positively impacts the bifurcation detection rate. For example, in Position 2 and at level L2, a 5 mm/s flow velocity has a 43% detection rate while at 10mm/s it is up to 100%. Importantly, the results obtained are reasonable: the reliability of Doppler information depends directly on flow velocity and probe distance. Precisely, the higher the flow velocity, the higher the Doppler output power, and the same holds for distances: a closer probe produces a higher Doppler output power. 500 CBMS 2013

5 So, we could observe and quantitatively measure optimal volume data acquisition conditions in the context of our capillary model reconstruction. Lastly, our results showed no significant differences between data acquired in Position 1 and data acquired in Position 2. This can be explained by the fact that setting! =38 deg for Position 2 will at the same time decrease the Doppler output power down to 0.79 (cos!) times that in Position 1. However the difference is not significant enough to be clearly reflected by our results. Probe positioning as defined for Positions 1 and 2 can be a great asset to improve reconstruction though. For example, one can think of using spatial absolute coordinates [13] of the probe and detected bifurcations to perform a merging operations between all the separate data obtained. Finally, our results interestingly hint at the hardware limitations of the echography and its transducer as for the detection (and subsequent reconstruction) of thin blood vessels. Effectively, blood vessels bifurcations located at levels L4 and L5 were not detected in any condition and parameters; by looking at the corresponding reconstruction, one can easily understand that the ultrasound probe fails to acquire any Doppler data regarding vessels of diameters less than or equal to 0.7 mm. 6. Conclusions In this paper, we have described a novel method for the three-dimensional reconstruction of the blood vessel network, including error detection in reconstruction. Several experiments were conducted, validating our method. We were able to reconstruct the BVN of an in vitro artificial capillary with multi-bifurcations. Our results notably showed the hardware limits of the ultrasound probe used in this study regarding thin blood vessels. Future works include improving the BVN reconstruction accuracy. For example, one can think of using an ultrasound transducer of higher frequency to detect thin blood vessels that were not detected. Then, merging the two results would lead to a more complete reconstruction. Acknowledgements This research is granted by the Japan Society for the Promotion of Science (JSPS) through the Funding Program for Next Generation World-Leading Researchers (NEXT Program). References [1] M.Schwenke, A.Hennemuth, B.Fischer, O.Friman: Blood flow computation in phase-contrast MRI by minimal paths in anisotropic media, Proceedings of the Medical Image Computing and Computer-Assisted Intervention Conference 6891: pp , [2] M.A.Gülsün, H.Tek: Robust vessel tree modeling, Proc. of the Medical Image Computing and Computer- Assisted Intervention Conference 5241: pp , [3] N.Kudo, K.Okada, K.Yamamoto: Sonoporation by single-shot pulsed ultrasound with microbubbles adjacent to cells, Journal of Biophysics 96(12): pp , [4] K.Yasui, J.Lee, T.Tuziuti, A.Towata, T.Kozuka, Y.Iida: Influence of the bubble-bubble interaction on destruction of encapsulated microbubbles under ultrasound, Journal of Acoustical Society of America 126(3): pp , [5] E.Stride, N.Saffari: The potential for thermal damage posed by microbubble ultrasound contrast agents, Ultrasonics 42: pp , [6] R.Koda, J.Koido, T.Ito, T.Mochizuki, K.Masuda, S.Ikeda, F.Arai, Y.Miyamoto, T.Chiba: Experimental study to produce multiple focal points of acoustic field for active path selection of microbubbles through multi-bifurcation Japanese Journal of Applied Physics 52: 2013 (in press). [7] K.Masuda, R.Nakamoto, N.Watarai, R.Koda, Y.Taguchi, T.Kozuka, Y.Miyamoto, T.Kakimoto, S.Enosawa, T.Chiba: Effect of existence of red blood cell in trapping performance of microbubbles by acoustic radiation force, Japanese Journal of Applied Physics 50: 07HF11, [8] R.Nakamoto, K.Masuda, N.Watarai, Y.Taguchi, T.Kato, T.Yoshinaga, Y.Miyamoto and T.Chiba: Evaluation of local density enhancement of microcapsules in artificial blood vessel under emission of focused ultrasound, American Institute of Physics (AIP) Conference Proceedings, 1359: pp , 2011 [9] W.E.Lorensen, H.E.Cline: Marching cubes: A high resolution 3D surface construction algorithm. Computer Graphics 21(4): pp , 1987 [10] A.Bossard, T.Kato, K.Masuda: Supporting reconstruction of the blood vessel network using graph theory: an abstraction method, Proc. of the 34th International Conference of the IEEE Engineering in Medicine & Biology Society: pp , [11] R.Sedgewick: Algorithms in C++ Part 5: Graph Algorithms, 3rd ed., Addison-Wesley Professional, [12] Y.Sugano, S.Onogi, A.Bossard, T.Mochizuki, K.Masuda: Development of a 3D Reconstruction of Blood Vessel by Positional Calibration of Ultrasound Probe, Proc. of the 5th Biomedical Engineering International Conference: BME , [13] S.Onogi, Y.Sugano, T.Yoshida, K.Masuda: An accurate calibration method of ultrasound images by center positions of a metal ball, Proc. of the 34th International Conference of the IEEE Engineering in Medicine & Biology Society: pp , CBMS