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Abstract -- In liver resection planning, the optimum surgical margin should be selected at the minimum risk, with the help of the processed MDCT data and the expert knowledge of the surgeon. Apart from the volumetric considerations, the manual decision making depends mainly on qualitative analysis, where proper risk estimation is heavily dependent on the surgeon’s experience, sometimes leading to abandoning of possible surgical treatments. Therefore, a quantitative analysis based decision making is essential in order to predict a lowest risk surgical proposal, especially in non segment based atypical resection. In this paper we analyze an approach with a high potential to solve this problem. The proposed method is based on an algorithm for segmented liver, tumor, and vascular territories in MDCT images. Moreover, we propose two independent viewing angles to generate a resection proposal and critically compare them for benefits and draw backs. Keywords—liver resection, preoperative planning, surgical margin optimization, domain knowledge, graph cuts

I. INTRODUCTION

IVER resection today stands as the best treatment for liver cancers, which significantly improves patient’s living standard and hence the surgery is of an utmost

importance and desirable for all the possible cases. However a patient’s eligibly for a lever resection depends on several factors such as, the kind of the tumor (primary or metathesis), the location of the tumor(s) in the vicinity of the major blood supply vessels of liver and the patient’s other chronic liver impairments(ex: cirrhosis, etc ). Therefore the assessment of the risk and the patient’s post-operative conditions preoperatively is a vital factor for a successful resection, which implies that the preoperative planning of liver resections plays a major role [1],[2]. Starting from the acquisition of the abdominal MDCT scan images, the preoperative planning process can roughly be categories in to several steps. First, the CT Images are preprocessed and the liver, lesion(s), and the vasculature are segmented. Then the portal vein, the hepatic artery, their branching, and their blood supply territories are identified. Alternatively, only for segment based resection, in several existing preoperative planning tools the liver segments are approximated. Then for predefined safety margins a virtual resection proposal is generated manually, semi

automatically, or automatically. However the feasibility of such automatically generated proposals are questionable [3] and interactive modifications should be facilitated by the system of interest [4]. Such modifications are done at the preoperative planning phase and even intra-operatively in most recent tools [5],[6]. The other important area in preoperative planning for liver resection is the risk assessment. In the past only the portal vein was taken in to consideration [3], but recent research has proved that all portal vein, hepatic artery and hepatic veins are of major importance when it comes to risk assessment [2],[3].

Irrelevant of the type of the resection, two major questions are to be answered in the preoperative planning process, i.e. whether the patient and the lesions are eligible for surgery and the precise decision of the extent of the surgery. A resection with a sufficient security margin is desirable as it increases the probability of that all the tumor cells being removed leading to better long term outcome. At the same time, a minimum amount of healthy liver should be removed in order to guarantee the post operative liver functions especially in the presence of chronic liver diseases [3]. The conventional safety values are 10mm for the security margin and 25% for the percentage of the remnant liver, however higher values are desirable depending on the above first mentioned factors.

II. PROBLEM FORMULATION

A. Segmentation As the first step the CT images from the various phases are used to identify the liver, tumor and the blood supply, i.e. the vessels of portal vein, hepatic artery and hepatic veins separately. Then those regions are segmented in the CT images. At the time of writing this paper we use manual segmentation procedure, but a suitable semi or fully automated segmentation algorithm can cut down the segmentation time [7]. Once the segmentation process is over the resulting segmentation can be used to generate a 3D model of the system, i.e. the liver, the tumor(s) and the blood vessels [8].

Algorithm for Computational Liver Resection Planning

Nawoda Wadduwage, Nuwan D. Nanayakkara Ruwan Wijesuriya Department of Electronics and Telecommunication Department of Surgery University of Morauwa Faculty of Medicine, University of Kelaniya Katubadda, Moratuwa, Sri Lanka Ragama, Sri Lanka nawoda@ent.mrt.ac.lk, nuwan@uom.lk

L

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B. Approximating blood supply territories The major blood supply to the liver is the portal vein (30%) and hepatic artery (70%). The vessel identification is done by the user. Thus the portal vein and hepatic artery vessel systems can be identified separately. The blood supply territories from these two should be also identified. For this purpose, we assign each voxel to a blood vessel from the two major blood supplies, i.e. each voxel has two specific places of blood vessel from each supply. The assignment procedure is based on the special position of the voxel where the closest blood vessel is assigned to the voxel. The liver voxels are assumed as a set L which is a subset of the entire scan of the abdominal area A, i.e. L A⊂ . The tumor(s) are assigned as T, portal vein as PV and hepatic artery as HA, which are sub sets of L, i.e. TUMOR ⊂ L , PV L⊂ and HA L⊂ . The task is to assign each live voxel to one voxel from Portal vein and one voxel from Hepatic artery.

( )liver portalVeinf V V= ( )liver hepaticArteryg V V=

, ,liver portalVein hepaticArterywhere V L V PV V HA∈ ∈ ∈

The function f (and similarly g) is implemented using the Euclidian distance of each liver voxel which is not an element of PV from the voxels from PV.

( ) ;( ) ,

. . ( ) min{ ( )}

i liver liver i i

liver portalVein

portalVein liver i liver

ED V V V Vf V V

s t ED V ED V

= − ∀=

=

For the elements of PV, a parent voxel is defined so that when the blood vessel is cut by the resection the supplied territories with the branching vessels can be identified.

( )

,portalVein portalVein

portalVein portalVein

parent V V

V V PV

′=′∀ ∈

In order to define the parents for each node the starting points of the vascular structures are identified semi automatically or manually. That means the entering positions of the blood vessels to the liver are identified. Once this is done they act as seed nodes to the parental assignment. Their immediate neighbors are assigned as their children. This routine is repeated for all the element of the set in PV or HA.

1 : ( ) 0

2 :

:3 : ( )

:

, Im

{

portalVein portalVein

portalVein

portalVein portalvein

portalVein

portalVein portalvein

portalVein

Step Parent V V PV

Step Select V A Seed voxel PV

V if V seedStep Parent V

V if V seed

where V An mediateNei

= ∀ ∈

= ∈

==

′ ≠

′ = ( )

. . ( ) 0

portalVein

portalVein

ghbor V

s t Parent V ≠

Step4: Select portalVeinV =AnImmediateNeighborOf portalVeinV

from step 3 Step5: Repeat step 3 until,

( ) 0portalVein portalVeinParent V V PV≠ ∀ ∈

Similarly territories can be approximated for blood drainage with hepatic veins using a function h(Vliver) = VhepaticVein where VhepaticVein ⊂ HV representing hepatic vein voxel set.

C. Defining the security margin We then define a security margin around the tumor according to the required value. The typical security margins of 5mm, 10mm or 15mm are used widely. For larger the security margin, we can guarantee a total removal of all the cancer cells. The volume with this security margin can be taken as the part that must be removed in the surgery hence the voxels that define this part is taken as TUMOR_SM where

_TUMOR SM L⊂ and _TUMOR TUMOR SM⊂ .

III. PROPOSED ALGORITHM

The problem at hand is to find a resection proposal which would define a cutting plane such that as large security margin as possible is taken while as less liver as possible is removed.

A. Classification problem One approach is to look at the problem as a classification problem of liver voxels. We have to classify each voxel in to two sets i.e. the liver portion that is removed (RESECT) and the remaining liver portion (REMNANT). Therefore

RESECT REMNANT L

RESECT REMNANT

∪ =

∩ = ∅

By definition all voxels within the safety margin should be removed. _V TUMOR SM V RESECT∈ ⇒ ∈ However when such part of the liver is removed the dependent blood supply territories are also affected. The conventional method is to assume the part removed is the liver segment that the tumor is on. The liver segment it selves have been defined by analyzing the blood supply vessels. However, research have emphasized the importance of the real scenario in which, the portal vein and hepatic artery supplies blood to the liver while the hepatic veins drain blood from the liver [3]. Therefore, the vessels of all three main blood supply and drainage, which are cut due to the removal of the volume inside the safety margin, should be considered. This involves the affecting regions of the liver due to the blood supply or drainage is lost. i.e. for all,

500

1

1

( _ ); ( ) (1)

V RESECT TUMOR SM V RESECTwhere perent V V

∈ ∩ ⇒ ∈=

Likewise all the voxels in these blood vessels should be assigned to the set RESECT, i.e. Repeat,

( )( )( )

( )

1

1

1 1

;

, ,

For all V RESECT PV HA HV V RESECT

where parent V V

Till For all parent V V RESECT V RESECT

∈ ∩ ∪ ∪ ⇒ ∈

=

= ∈ ∈ All the blood vessels that are being cut due to the removal of tumor (with the safety margin) are assigned to the set RESECT from the position of intersection with the tumor. Then the territories that are affected due to the removal of these vessels should also be assigned to the resection portion of the liver i.e RESECT

( )( )( )( ) ( )( ) ( )( )

1

1 1 1

,

;

For all V RESECT PV HA HV V RESECT

where f V V OR g V V OR h V V

∈ ∩ ∪ ∪ ⇒ ∈

= = =

This way all the voxels that are being affected and hence need to be removed, are classified in to the set RESECT and the complement of RESECT is the set REMNANT. However, the problem with this approach is that there is no guarantee that the resection proposal is realizable. Complicated shaped cuts can hardly be achieved in the real surgery, and the margins that cut the liver surface are not necessarily realizable, where some times the intersection with the liver surface is insufficient to make a surgical cut. Therefore, it is clear that further optimization is needed.

B. Optimization problem

The other angle to see this problem is to view this as an optimization problem, where the optimum cutting plane of the liver should be determined with the lowest risk. However, the constraints remain the same, i.e. the remnant of the liver should be as large as possible and the security margin should be as wide as possible. The problem is to find the optimum tradeoff between the two constraints so that the post operative conditions of the patient is the safest. The risk involved in the surgery can be assessed in several methods from which the volumetric analysis is the most widely used. However, recent research suggests revolutionary new approaches to asset risk depending on the portal vein and hepatic vein blood supply and drainage territories [2]. For above requirements, either a local optimization with details of the optimization process or an energy based global optimization approach can be used. The direct local optimization approach is to use a risk coefficient like the one proposed by Beller et al. and to find a threshold risk

value to determine the operability of the patient. However, such an approach will need a cumbersome testing and evaluation process with a large dataset from patients with different conditions. On the other hand, a global optimization will come handy as we can include more than one criterion in the decision making. However one drawback is that the exact process or the logic behind the resection proposal is lost, but the results can be compared with the manual decision made by an expert. Another major advantage is that, the factors of the expert or the surgeon doing the surgery can be incorporated with the decision making as when it comes to practice the risk involves with the surgery depends on the experience and methodology occupied by the surgeon. In this paper, we propose a global optimization procedure based on graph cuts, which is a segmentation method which can be used for volume segmentation. In this approach, all the voxels of the liver are considered as nodes in the graph. In addition, two special nodes are defined as Source and Sink nodes. These are basically the labels assigned to the voxels depending on them being belonging to resected part (for sink) or the remnant (for source). The T-links are the ones connecting source (and sink) nodes to all the other nodes (voxels). The n-links are the links connecting each voxel with their neighbors. These links are assigned with costs depending on the constraints they represent. The minimum cost cut represent the optimum way of segmenting the two regions and there are a number of algorithms to find this minimum cut. The energy associated with this minimum cost cut is defined below,

Source - remnant

Sink – removed volume

N-links

T-links

T

S

Fig. 1. Representation of nodes and links in a 3D graph for segmentation with a graph cut based algorithm

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{ , }{ , }

( ) ( , )p p p q p qp P p q N

E R L B L Lλ δ∈ ∈

= +∑ ∑

Where 1( , )

0{ p qif L L

Lp Lqotherwise

δ≠

=

The first term Rp refers to the cost associated with the penalty of assigning the label Lp to the node p and the second term refers to the cost of having two neighboring pixels with different labels in some neighborhood of p and q. In our case, since this is a 3D segmentation process, the neighborhood is a 6 voxel neighborhood. Alternatively, a 26 pixel neighborhood can also be defined by taking diagonal connections also in to consideration. Link cost allocation for T-links

We define the n-links to represent the domain knowledge while t-links are used to represent the segmentation results and blood supply territory approximations.

The volume within the tumor(s) must be removed with the blood supply territories. Therefore those voxels must be assigned with the label of the sink , i.e. T. Therefore the cost of assigning the source label S to those voxels should be infinity.

( )pR S p RESECT= ∞ ∀ ∈

Note that in this case the set RESECT must be calculated considering only the tumor and related blood supply territories affected. i.e. the set TUMOR_SM in the equation (1) should be replaced with the set TUMOR and the corresponding set RESECT should be calculated with the algorithm explained above.

The cost of assignment of label T for these voxels is irrelevant as they will never contribute to the energy of the optimum cut. However for the computational purposes, the following assignment is made.

( ) 0pR T p RESECT= ∀ ∈

With this link cost assignment, the optimization problem narrows down to the assignment of the labels for the voxels in the REMNANT part from the previous algorithm i.e. for all p ∈ REMNANT.

The risk of having a narrow safety margin is represented by having the voxels in the near proximity of the tumor a high assignment cost for the label S but this cost should exponentially decrease with increasing distance from the tumor. As for typical values the risk is almost zero for the voxels away from 30mm from the tumor [2].

( ) ( )pR S safety p nearestTumorVoxel

p REMNANT

= −

∀ ∈

The term p nearestTumorVoxel− can be found similarly to the first algorithm explained in the paper. For the function safety an exponentially decaying function, similar to the one shown in figure can be used.

The risk associated with removing larger percentage of the liver is represented by the costs allocated to the assignment of the label T to the voxels of REMNANT. In this case the risk is increased with the number of voxels only. Therefore, we can safely assign a constant value for all the voxels.

( )pR T C p REMNANT= ∀ ∈

Link cost allocation for N-links N links can be used to incorporate the domain knowledge in to the picture as well as other factors affecting the risk of the surgery such as the surgeon’s experience and shapes preferred for cutting planes. One common case is the cutting of the major blood supply and drainage vessels due to the cutting plane. This can be handled by assigning higher values for the N-links within the segmented blood vessels. i.e.

{ , } , ( )( , )p q p q PV HA HVB vessels p q ∀ ∈ ∪ ∪=

The function vessels(p,q) can be defined according to the importance or the amount of blood supply or drainage to the liver. It is reasonable to assume the amount of blood supply is dependent on the cross sectional area of a blood vessel [1]. Therefore, we can define the function vessels as a function of cross-sectional area of the blood vessels containing the voxels {p,q}.

Another common scenario is the popularity of the segment based resection among surgeons. This can be modeled with assigning low cost for the links along a segment margin. Like vise a lot of domain knowledge can be captured in to the optimization procedure.

0 5 10 15 20 25 30 35 40

safe

ty(x

)

x = || p - nearestTumorVoxel || (mm)

Fig. 2. The costing function for safety

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IV. CONCLUSIONS AND FUTURE WORK The surgical procedure liver resection can be improved

with the computationally produced resection proposals. This problem can be viewed as a classification problem and/or as an optimization problem. However, one approach alone may not yield to the best solution. Therefore, a combination of these two is more advantageous. The optimization procedure based on graph-cuts has a higher potential of solving the problem. However, proper implementation of the proposed algorithm is necessary to conclude as no computational complexities were considered in this paper.

The link cost allocation functions defined here should be properly tuned with the medical data so that the risk values are normalized in the optimization procedure. In T-link cost allocation the parameters of function safety and the constant C should be tuned while in N-link cost allocation the optimum parameters for function vessels should be found.

Finally once the entire system is implemented, a complete testing and evaluation is preferred with real clinical data.

REFERENCES [1] Dirk Selle, Bernhard Preim, Andrea Schenk, and Heinz-Otto Peitgen

(2002) “Analysis of Vasculature for Liver Surgical Planning”, IEEE Transactions on Medical Imaging, Vol. 21, NO. 11

[2] S. Beller, S. Eulenstein, T. Lange, M. Niederstrasser, M. Hünerbein, and P.M. Schlag (2009) “ A new measure to assess the difficulty of liver resection” , European Journal of Surgical Oncology

[3] Preim B, Bourquain H, Selle D, Oldhafer KJ, Peitgen HO, “Resection proposals for oncologic liver surgery based on vascular territories”, CARS 2002, CARS/Springer,2002.

[4] O. Konrad-Verse, B. Preim, A. Littmann, “Virtual Resection with a Deformable Cutting Plane“, Proceedings of Simulation und Visualisierung, pp. 203-214 (2004).

[5] C. Hansen, S. Zidowitz, A. Schenk1, K.-J.Oldhafer, H. Lang, H.-O. Peitgen.(2010) “Risk Maps for Navigation in Liver Surgery”, Proc. of SPIE Vol. 7625 762528-3

[6] P. Lamata, A. Jalote-Parmar, F. Lamata, J. Declerck, “The Resection Map, a proposal for intraoperative hepatectomy guidance”, Int J Comput Assist Radiol Surg., 3(3-4), pp. 299-306 (2008).

[7] Soler L, Delingette H, Malandain G et al. “Fully automatic anatomical, pathological and functional segmentation from CT scans for hepatic surgery”, Computer-Aided Surgery, Vol. 6 (3)

[8] Bourquain H, Schenk A, Link F, Preim B, Prause G, Peitgen HO. (2002). “HepaVision2 – a software assistant for preoperative planning in LRLT and oncologic liver surgery”, CARS’2002

Ves

sels

(p,q

)

Cross sectional area of vessels containing {p,q}

Fig. 3. The costing function for vessels

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