A Novel Shaft-to-Tissue Force Model for Safer Motion Planning of Steerable Needles
Michael Bentley, Caleb Rucker, Chakravarthy Reddy, Oren Salzman, Alan Kuntz
aa r X i v : . [ c s . R O ] J a n A Novel Shaft-to-Tissue Force Model for Safer Motion Planning ofSteerable Needles
Michael Bentley , Caleb Rucker , Chakravarthy Reddy , Oren Salzman , and Alan Kuntz Abstract — Steerable needles are capable of accurately tar-geting difficult-to-reach clinical sites in the body. By bendingaround sensitive anatomical structures, steerable needles havethe potential to reduce the invasiveness of many medical proce-dures. However, inserting these needles with curved trajectoriesincreases the risk of tissue shearing due to large forces beingexerted on the surrounding tissue by the needle’s shaft. Suchshearing can cause significant damage to surrounding tissue,potentially worsening patient outcomes. In this work, we derivea tissue and needle force model based on a Cosserat stringformulation, which describes the normal forces and frictionalforces along the shaft as a function of the planned needle path,friction parameters, and tip piercing force. We then incorporatethis force model as a cost function in an asymptotically near-optimal motion planner and demonstrate the ability to planmotions that consider the tissue normal forces from the needleshaft during planning in a simulated steering environment anda simulated lung tumor biopsy scenario. By planning motionsfor the needle that aim to minimize the tissue normal forceexplicitly, our method plans needle paths that reduce the riskof tissue shearing while still reaching desired targets in thebody.
I. I
NTRODUCTION
Bevel-tip steerable needles have the potential to provideminimally-invasive access to anatomical sites deep in thehuman body [1], [2], [3], [4]. These needles leverage asym-metric tip forces to curve around anatomical obstacles duringneedle insertion, enabling accurate targeting of clinically-relevant sites that are difficult or impossible to reach safelywith traditional needles (see Fig. 1). In order to increase theability to reach many areas of the body in complex anatomy,the design trend has been to maximize the needle’s curvaturecapability [5]. However with an increase in curvature, moreforce is exerted upon the surrounding tissue during needledeployment. With large tissue forces perpendicular to theneedle come an increased risk of a shearing event in whichthe needle shaft cuts sideways through the surrounding tissue,causing severe damage [4] (see Fig. 2). The force exerted
This research was supported in part by the U.S. National Science Foun-dation (NSF) under Award IIS-1652588 (CAREER) and by the Ministry ofScience & Technology, Israel. Robotics Center and School of Computing, University of Utah, Salt LakeCity, UT 84112, USA [email protected] and [email protected] The Department of Mechanical, Aerospace, and Biomedical Engi-neering, University of Tennessee, Knoxville, TN 37996, USA [email protected] Huntsman Cancer Institute and School of Medicine, University of Utah,Salt Lake City, UT 84112, USA [email protected] Department of Computer Science, Technion - Israel Institute of Technol-ogy, Technion City, Haifa, 3200003, Israel [email protected]
Fig. 1. Force heat maps along the needle path. Darker colors indicatesmall values, lighter colors indicate large values. (a)
Internal force n ( s ) carried by the needle from insertion to tip piercing force, (b) magnitude ofnormal force exerted from the needle on the tissue f t ( s ) for the same pathfollowed in (a), and (c) two paths from start to goal of the same length andof the same two straight segments and one arced segment. It demonstratesthat high curvature at the beginning results in much higher tissue normalforces than high curvature near the end. The maximum tissue normal forceof the right path is 81% higher than the maximum tissue normal force ofthe left path. by the needle on the surrounding tissue is a function ofthe puncture force at the needle’s tip, the needle’s shapethrough the tissue, and the friction between the needle’sshaft and the surrounding tissue. In this work, we developa force model describing the forces from the needle’s shafton surrounding tissue. This force model is integrated into amotion planning framework, and enables us to plan motionsthat reach clinically-relevant targets while minimizing thenormal force exerted upon the tissue by the needle shaftduring insertion (see Fig. 1).Motion planning methods for steerable needles producetrajectories that avoid sensitive anatomical structures whiletargeting a desired location and considering some cost func-tion [6], [7], [8], [9] such as minimizing path length ormaximizing clearance from obstacles. These cost functionsare frequently intended to encourage planned motions thatminimize some notion of tissue damage, by damaging lesstotal tissue or steering far from the most sensitive anatomicalstructures. These cost functions however do not consider theforce being applied by the needle shaft to the surroundingtissue, and as such do not explicitly consider the plannedpath’s potential for shearing.Instead, this work models the forces exerted on the tissueby the needle shaft as it is inserted with a constant piercingforce at the tip. Using this force model, our method generates1 ig. 2. Shearing occurs when the force applied by the needle’s shaft to thesurrounding tissue is larger than the tissue can support without fracturing.Shearing can cause significant damage to patients. We demonstrate thisconcept here in a gel-based tissue simulant, in which the initial and intendedneedle shape can be seen as the bottom edge of the red volume. Shearingoccurred, causing the needle shaft to cut through the tissue simulant,eventually settling at the top edge of the red volume. The red volume, whichhas dye injected into the resulting channel cut by the needle, representstissue damage due to shearing. motion plans that minimize the forces exerted on the tissuewhile still reaching the target, thus significantly reducing thepossibility of shearing during insertion.We model the needle as a Cosserat string [10] and incor-porate friction models to derive tissue forces as a functionof the needle’s planned path in the tissue. The Cosseratstring needle model is an idealization that becomes moreaccurate as the bending stiffness of the needle decreases.This is a particularly relevant assumption in light of recentadvances in needle designs with decreased stiffness [4]. Inaddition, this approach admits an analytical solution for thetissue normal force that depends only on path geometryand frictional properties. Thus, while this idealized stringmodel is an approximation of the true physics of needle-tissue interaction, it provides a physically motivated andcomputationally efficient estimate of tissue normal force.The tissue normal force estimate can be used in a planningalgorithm to generate safety-informed needle trajectories.Notably, with this model, the tissue normal forces are depen-dent on the entire needle trajectory and cannot be determinedlocally in isolation (see Fig. 1). But with a specified tippiercing force we can compute the tissue normal forces as asingle pass analytically backwards starting at the tip. As canbe seen in Fig. 1, high curvature near the beginning causessignificantly larger tissue normal forces than high curvaturenear the path’s end, even for paths of identical length. Thishighlights a key result, namely that neither path length normaximum curvature along a path can accurately serve as aproxy metric for the tissue normal forces of a path.We assume that the magnitude of the tissue normal forceis correlated to the probability of tissue failure that results inthe needle shearing through the tissue. Thus, we incorporatethe maximum tissue force along the shaft as a cost functionduring motion planning. Utilizing this force model costfunction, we present an anytime asymptotically near-optimalmotion-planning algorithm that produces plans which havebetter and better cost as computation time allows, convergingon paths whose cost is a constant factor of the cost of theglobally-optimal path. We demonstrate the results of usingthis cost function in planning in a 3D geometric environment as well as in a lung tumor biopsy scenario.By incorporating a cost function that explicitly modelsthe interaction forces between the needle shaft and thesurrounding tissue, motions can be planned for steerableneedles that reduce the risk of tissue shearing. This has thepotential to reduce the risk of damage to sensitive anatomicalstructures and improve patient outcomes.II. R ELATED W ORK
Due to their potential to reduce the invasiveness of manytypes of therapeutic and biopsy-based procedures, steerableneedles have been proposed for use in the kidneys [11],liver [11], prostate [12], brain [13], and lung [14]. A largeclass of steerable needle designs leverage asymmetric tips,including bevelled [3], pre-bent [13], [15], passive flex-ure, [4], [16], variable-length flexure [17], active flexure [18],[19], and a programmable bevel [20]. See [5] for a reviewon steerable needle designs.Measuring and understanding the force interaction be-tween the needle and tissue is important to minimizing tissuedamage. Force sensors have been placed on needle tipsto more accurately measure the needle’s piercing force tobetter understand the tip’s interaction with different types oftissue [21]. High needle insertion force has been associatedwith excessive tissue damage [22]. Techniques have beenused to decrease needle insertion force with barbs [22],vibrations [22], and slower insertion speeds [23].Many have attempted to model the force interaction be-tween the needle shaft and surrounding tissue, modelinginsertion forces, tissue deformation, needle deflection, andcutting forces [1], [24], [25]. These works primarily focuson finite-element simulations based on the full Cosserat Rodmodel and tissue mechanics. Our modeling simplification us-ing the Cosserat String model enables a simpler analyticallytractable model that can be incorporated into existing motionplanners. This work is further differentiated by utilizing theforce model as the cost function in motion planning tominimize the probability of tissue damage via shearing.Motion planning enables robots to plan trajectories thatavoid obstacles while moving from some start state to a goalstate. Sampling-based motion planning is a popular paradigmwhich leverages random sampling of configurations or con-trols to produce collision-free motion. These include theRapidly-exploring Random Trees (RRT) [26] and Proba-bilistic Roadmap (PRM) [27] methods which incrementallyconstruct a collision-free tree or graph. These methodsprovide a probabilistic-completeness guarantee which statesthat the likelihood of finding a path, if one exists, trendstoward one as the number of samples approaches infinity.Extensions of these methods provide asymptotic optimality,which guarantees convergence to a globally-optimal path.Such methods include PRM* [28], RRT* [28], Fast MarchingTrees (FMT*) [29], and Batch Informed Trees (BIT*) [30].Following the exposition of the first asymptotically-optimal motion-planning algorithms [31], several asymptot-ically near-optimal motion planning algorithms were intro-duced. Here, an algorithm is said to be asymptotically near-2ptimal if, given any user-provided ε > , the solutionobtained by the algorithm converges to a solution whose costis at most ε times the cost of the optimal solution as thenumber of samples tends to infinity. Typically, the extra flex-ibility obtained by relaxing (asymptotic) optimality to nearoptimality reduces computational efforts. This allows, givena finite amount of computation, to find higher-quality so-lution faster than asymptotically-optimal algorithms makingthese algorithms appealing for real-world applications [32].Asymptotic near optimality can be achieved by modifyingthe connection scheme of existing algorithms [33], [34] lazyedge evaluation [35] or by removing roadmap edges [36],[37]. For a survey of asymptotically optimal and near-optimalmotion-planning methods, see [38].Motion planning for steerable needles has been ap-proached in a variety of ways. Pinzi et al present the AdaptiveHermite Fractal Tree (AHFT) algorithm [9], which leveragesoptimized geometric Hermite curves [39] combined with afractal tree. In [40], Favaro et al adapt BIT* [30] combinedwith a path smoothing method in order to plan motionsfor a programmable bevel-tip needle. Patil et al built uponRRT to develop the Reachability-Guided RRT (RG-RRT)method for steerable needles [6], [41]. RG-RRT has beenadapted in other work to plan motions for a three stagelung tumor biopsy robot [7] and to plan in pulmonary costmaps automatically generated from medical imaging [8]. Wefurther adapt RG-RRT in this work to plan motions thatreduce needle-shaft-to-tissue interaction forces to improvethe safety of needle insertion.III. M ETHOD
A. Force Model Derivation
As needles become thinner and more flexible, the bendingstiffness vanishes and the forces required to keep the needlein a static curved shape become negligible. As the needleis pushed through tissue at a constant rate, the piercingforce must be transmitted from the base of the needlealong the shaft and finally at the needle’s tip. We assumethat the dominant forces along the shaft come from thecombination of tangential friction and normal forces due tothe compression force in the needle along the path curvature.The friction and normal forces are coupled in a way similar tothe well-known capstan equation [42]. Therefore, we modelthe needle inside the tissue as an ideal Cosserat string, whichassumes that (1) the flexural rigidity is negligible, and (2)the internal force vector is always tangent to the string’spath in space [43], [10]. Conventionally, a Cosserat stringis assumed to only carry tension force (since an ideal stringwill buckle under any compressive force), but we assume thatcompressive force can be carried without buckling becausethe surrounding tissue will constrain the needle and preventbuckling, even for very low stiffness needles. The modelpresented is otherwise identical to a classical Cosserat string.A Cosserat string is characterized by its centerline curvein space p ( s ) ∈ R as a function of the parameter s ∈ [0 , L ] .In the following derivation, we assume s is the arc lengthalong the needle path of length L . The derivative of p ( s ) Fig. 3. An example piecewise circular arc path with endpoints s i and curvatures κ i . A small segment of length ds is shown with forces.Friction f f ( s ) , tissue normal force f t ( s ) , internal needle tension n ( s ) ,insertion force F i , and piercing force F p are labeled. with respect to s , denoted as ˙ p ( s ) , is a unit vector tangentto p ( s ) .Along the needle’s path, the tissue exerts a distributedforce on the needle shaft that can be decomposed intotwo components as seen in Fig. 3, one parallel to theneedle f f ( s ) = − f f ( s ) ˙ p ( s ) representing friction, and oneperpendicular to the needle f t ( s ) representing the net normalforce from tissue. The force balance on an infinitesimalsection of string is then n ( s + ds ) − n ( s ) + f t ( s ) ds − f f ( s ) ˙ p ( s ) ds = 0 where n ( s ) is the internal force vector carried by the string,defined as the force that the distal string material exerts onthe proximal material. Dividing by ds and allowing ds → ,we get ˙ n ( s ) − f f ( s ) ˙ p ( s ) + f t ( s ) = 0 (1)where the dot represents the derivative with respect to s . Thisis the conventional Cosserat string equilibrium equation asgiven in [43], [10], with the distributed force separated intotwo orthogonal components. The internal force vector n ( s ) isassumed to be parallel to the tangent vector ˙ p ( s ) , implyingthat the string cannot carry internal shear loads. Thus wehave n ( s ) = − n ( s ) ˙ p ( s )˙ n ( s ) = − ˙ n ( s ) ˙ p ( s ) − n ( s ) ¨ p ( s ) where the scalar n ( s ) represents the compressive force car-ried by the needle shaft at s . Substituting these into (1) and3ecomposing into the parallel and perpendicular components,we get ˙ n ( s ) = − f f ( s ) (2) f t ( s ) = n ( s ) ¨ p ( s ) . For any path-length parameterized curve p ( s ) , the magnitudeof ¨ p ( s ) is the curvature κ ( s ) , thus f t ( s ) = κ ( s ) n ( s ) (3)where f t ( s ) is the magnitude of f t ( s ) .To calculate n ( s ) , the magnitude at one point must begiven. Typical points are either at the beginning (the insertionforce n (0) = F i ) or the end (the piercing force n ( L ) = F p )as depicted in Fig. 3. Here, we consider a given piercing force F p since insertion happens at a constant speed and exerts thenecessary insertion force to pierce through the tissue at thetip.We assume a kinetic friction model for f f ( s ) of the form f f ( s ) = C ( s ) + µ ( s ) f t ( s ) where C ( s ) is the nominal distributed frictional force thatwould be present even if the needle was in a straight path, dueto normal forces from the tissue squeezing the needle’s outerwall on all sides, and µ ( s ) is the conventional coefficient ofkinetic friction, which is multiplied by f t ( s ) , the additionalnormal force due to the path curvature. Substituting thisfriction model into (2), we arrive at the following first orderlinear differential equation ˙ n ( s ) = − C ( s ) − µ ( s ) κ ( s ) n ( s ) . (4)Solving this, subject to an initial or final condition yieldsthe internal compression force in the needle, from which thetissue normal force can be calculated via (3). In general, C ( s ) and µ ( s ) could vary along s as the needle passes throughheterogeneous tissues. We can numerically integrate (4)backwards from the tip to the base starting with n ( L ) = F p ,and substitute the solution into into (3) to calculate thetissue normal force distribution across the needle’s path.Alternatively, we can also express the general solution for n ( s ) as n ( s ) = Ae − B ( s ) − e − B ( s ) Z C ( s ) e B ( s ) dsB ( s ) = Z µ ( s ) κ ( s ) ds where A is a constant of integration that can be determinedby applying the tip condition n ( L ) = F p , and where, depend-ing on the nature of the functions C ( s ) , µ ( s ) , and κ ( s ) , theintegrals can either be evaluated analytically or numerically.If C ( s ) , µ ( s ) , and κ ( s ) are piecewise constant (say C i , µ i ,and κ i on s ∈ ( s i − , s i ) as in Fig. 3), then for s ∈ ( s i − , s i ) ,the solution reduces to n ( s ) = − C i µ i κ i + (cid:18) n ( s i ) + C i µ i κ i (cid:19) exp (cid:16) µ i κ i ( s i − s ) (cid:17) (5)with (3) becoming f t ( s ) = κ i n ( s ) . This solution can be iteratively evaluated section by section,starting at s i = L and proceeding backwards to the base.Note that the n ( s ) solution is continuous across the entireneedle trajectory, while f t ( s ) is discontinuous due to possiblecurvature discontinuities at each s i , as illustrated in Fig. 1.For zero-curvature sections, the tissue normal force iszero. If we set friction to zero (by setting both µ = 0 and C = 0 ), we get f t ( s ) = κ ( s ) F p which results in a tissuenormal force directly proportional to the curvature. It maybe intuitive to assume curvature would be a good proxy forthe probability of shearing, but we find that to be equivalentto assuming zero friction. If we ignore the proportionalfriction component (by setting µ = 0 ), we get a simple linearinternal force model for (4). If we consider the full frictionmodel, even for a small friction coefficient µ i , the requiredinsertion force for a given piercing force grows exponentiallywith the friction coefficient times length times curvature. Asthe path gets longer, the internal needle force n ( s ) growsexponentially as seen in (4), very quickly increasing theprobability of shearing. B. Motion Planning
We propose a motion-planning framework that enablesplanning of needle trajectories that minimize the risk of tissueshearing by minimizing the normal forces being applied bythe needle to the tissue during insertion. Specifically, wedefine the cost of a path as the maximal tissue normal forceapplied along the path. This is an example of a bottleneckcost of a path, a concept that has been extensively stud-ied in the motion-planning community (see, e.g., [44] andreferences within) with diverse applications such as Fr´echetmatching [45] and following manipulator and surgical tra-jectories [46], [47]. Due to the nature of our application,we wish to provide (asymptotic) guarantees on the qualityof the solution. Unfortunately, existing planners with suchguarantees either require (i) solving the two-point boundaryvalue problem (see, e.g., [31], [35], [44]) or (ii) cannot beeasily adapted to use a bottleneck cost.As we are not aware of any method to efficiently solvethe two-point boundary value problem for steerable needles,we introduce a general simple-yet-effective framework that isasymptotically near-optimal (ANO). Our approach, summa-rized in Alg. 1, takes as input any probabilistically-completeroadmap-based motion planner ALG and an approximationfactor ε and returns a solution whose cost asymptoticallyconverges to within ε times the cost of the optimalsolution. We run ALG augmented with a maximal costvalue c max (initialized to infinity) such that every roadmapedge whose cost is more than c max is considered invalid.Once a solution is obtained, the maximal cost value c max isupdated to be c/ (1 + ε ) where c is the cost of the solutionreturned by ALG. It is worth noting that our framework baresresemblance to recent approaches [48], [49] to compute anasymptotically-optimal path when path cost is additive (andnot the bottleneck cost). In using Alg. 1, we give the goalposition and orientation in the body as the planner’s starting4 lgorithm 1: ANO Bottleneck-Cost Planner
Input:
ALG: Probabilistically-Complete Planner q origin : start configuration Q target : target configuration set O : obstacle set ε : approximation parameter Output: π : best motion plan found c max ← ∞ while time allows do c, π ← ALG(q start , Q target , O , c max ) c max ← c/ (1 + ε ) report π state q origin , and the needle insertion position, unconstrainedin orientation, as the target state set Q target .While a complete proof that our algorithmic framework isindeed ANO for the bottleneck cost is out of the scope of thispaper, we provide a proof sketch: Let π ∗ be the path with theminimal bottleneck cost and let c ∗ be this cost. This impliesthat for every cost c > c ∗ , there exists some path π c whosebottleneck cost is smaller or equal than c . This, togetherwith the fact that ALG is probabilistically complete impliesthat for every c ≥ c ∗ , ALG will be able to (asymptotically)compute a path whose bottleneck cost is smaller or equalthan c . This process repeats until c < c ∗ . Thus, the last pathreturned will have a maximal bottleneck cost of (1 + ε ) · c ∗ .To apply this framework to our needle-steering domain,we use the RG-RRT algorithm [41]. Roughly speaking,RG-RRT runs an RRT-like algorithm but it extends robotconfigurations in the search tree towards a configuration-space region (where needle orientation is unconstrained) and not a randomly sampled configuration (that includes both theneedle’s position and orientation). While there is no formalproof that the algorithm is probabilistically-complete, we caneasily turn it into a probabilistically-complete algorithm byinterleaving the connections considered by RG-RRT withthose used by kinodynamic RRT which is known to beprobabilistically-complete [50].For our setting we make an additional change to RG-RRT—instead of planning from the needle insertion site tothe target in the body, we instead perform a backward searchand plan from the target in the body to a specified insertionsite. We do so because the derived force model describestissue normal forces which grow from our constant piercingforce of the needle backwards along the path, as in (5). Sincethe piercing force is constant, we evaluate the forces fromthe tip backwards. Every time the tip moves further in thetissue, we would be required to recalculate the forces alongthe entire trajectory using (5). Since the internal needle force n ( s ) increases exponentially with every appended segment,we can consider only the final shape as having the largestforces along the insertion trajectory. This may not be the casefor non-constant piercing force F p ; planning would need toconsider intermediate shapes. But, for constant F p planing (a)(b)(c) Fig. 4. Utilizing our force model during motion planning produces pathswhich reduce the normal force on the surrounding tissue when comparedwith utilizing length as cost during planning. (a)
The first path found byboth planners, which has a maximum tissue normal force of . N/m. (b)
A path found by the planner that is minimizing path length, whichhas a maximum tissue normal force of . N/m. (c)
A path found bythe planner that is minimizing tissue normal forces, which has a maximumtissue normal force of . N/m. from the goal, we can propagate n ( s ) along our trajectoryand use it to solve for the tissue normal force f t ( s ) , takingthe maximum as we do so. The planned path is then executedas normal, from the insertion site to the target in the body.Planning the path as if it were reversed in direction enablesefficient and accurate computation of the maximum normalforces during forward insertion.IV. R ESULTS
For our evaluation we use a fixed friction constant of C =83 . N/m, a friction coefficient of µ = 0 . , and a piercingforce of F p = 0 . N for the entire trajectory. These valueswere estimated by fitting our force model to experimentally-measured insertion forces in a phantom at a constant rateof cm/s from [23]. The fit has an adjusted R = 0 . which represents the model’s explained variation over thetotal variation and indicates that the model fits very closely tothe experimental results. The approximation parameter usedin Alg. 1 is ε = 0 . .We evaluate our method in two scenarios. In the first,shown in Fig. 4, we task the planner with finding a pathfrom the start to the goal, where the planner must avoid twospherical obstacles located between the start and goal. Wetake the median of the results over runs. Our methodstarts from a median . N/m force cost and convergesto . N/m after seconds, as shown in Fig. 5. Wecompare against a version of the motion planner that isminimizing path length—a metric frequently utilized inthe literature. In contrast to our planner that is explicitlyconsidering tissue normal forces during planning, the lengthminimizing planner converged to a median of . N/mafter about seconds with much higher variance than theforce optimizer. The difference between the converged forcevalues of each optimizer is statistically significant with aone-sided Z-statistic value of . resulting in a p -value of . × − . We also compare the path lengths over time foreach of the planners. Notably, the planner that is optimizingfor tissue forces produces paths of comparable length tothe planner that is optimizing for path length directly, but5 ig. 5. The length optimizer (red) and the force optimizer (blue) minimizepath length and maximal tissue normal force over the path, respectively. Thetop and bottom plots depict the path length and maximum tissue normalforce cost over the trajectory for both optimizers, respectively. Of 20 runs,the median cost is shown as the bold line with the upper and lower quartilesshaded around it. does so while significantly improving the tissue forces of thepaths. Although Fig. 5 appears to have the force optimizerdoing better than the length optimizer for the length cost,the converged values do not exhibit a statistically significantdifference with a Z-statistic of . resulting in a p -value of . . However, the ability of the force optimizer to produceshort paths is interesting and worth future study.It is an intuitive result that a planner optimizing for tissuenormal forces would produce plans that have lower tissuenormal forces than one that was not, however we present thisanalysis to demonstrate that path length is not a sufficientproxy metric for tissue normal forces, even though pathlength has an impact on tissue normal forces as shown in (5).The intuition for this is shown in Fig. 1c. Trajectories thatare identical both in length and maximum curvature can havedramatically different maximum tissue normal forces. Thishighlights the need for considering the tissue normal forcesexplicitly during the motion-planning process.We next demonstrate initial feasibility of using the motion-planning method that considers tissue normal forces in ananatomical environment in a clinically-relevant task. We taskthe motion planner with planning a path for a needle froma patient’s chest wall to a target deep in the lung, as inpercutaneous lung tumor biopsy. We utilize a CT scan fromthe 2017 lung CT segmentation challenge [51], [52] in thecancer imaging archive [53]. Using the segmentation methodof Fu et al [8] we segment the large vasculature and bronchialtrees in the lung. These are used as obstacles for the motion Fig. 6. We demonstrate the feasibility of utilizing the tissue normal forcecost function in motion planning for a steerable needle in an anatomicallyrelevant scenario. We show a plan generated by our motion planner for aneedle insertion site at the boundary of a patient’s lung near the chest wall,to reach a target deep in the lung. The plan must curve around the obstacle inthe lung while minimizing tissue normal forces. The plan (green) is shownin three CT scan slices. Slice 1 shows the start and goal locations, as wellas the beginning and end of the planned path. The path curves in 3D, andas such takes multiple slices to show. Slice 2 and 3 are posterior slices thatshow the rest of the planned needle path. planner that must be avoided. As shown in Fig. 6, the motionplanner is able to successfully find a path from the start tothe goal while avoiding the obstacles, and doing so whileminimizing tissue normal forces.V. C
ONCLUSION
In this work we utilized physical tissue friction propertiesderived from experiments in the literature. In future work weintend to experimentally derive these constants for our spe-cific intended clinical applications and evaluate the efficacyof our method in real tissue on a physical steerable needle.Further, we motivate the consideration of tissue normalforces to reduce the likelihood of a shearing event, but weintend to investigate the use of this model and extensionsin reducing the forces being applied to surrounding tissuesin general, which has clinical implications in tissue damagedue to undesired compression, such as in the case of nerves,and ischemia due to compression.This work provides the following contributions: (i) a forceand friction model of the tissue interacting with the needlebased on the Cosserat string, (ii) an asymptotically near-optimal motion-planning framework using the tissue normalforce as a bottleneck cost function, (iii) an evaluation of thisforce bottleneck motion planner in a synthetic environmentdemonstrating that length as a proxy for force is inadequate,and (iv) a feasibility demonstration of using our method in ananatomical and clinically-relevant environment. Minimizingthe tissue normal forces during needle steering has thepotential to significantly reduce the risk of tissue shearing,improving patient outcomes.ACKNOWLEDGMENTThe authors would like to thank the group of Ron Al-terovitz for their insights and assistance with segmentationand the group of Robert J. Webster III, for insights andimages of tissue shearing.6
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