Integrating FEM-Integrating FEM-based deformable based deformable obstacles in PRMobstacles in PRM

Comp768 project presentationComp768 project presentation

Mert SedefMert Sedef

Laparoscopic Surgery & Laparoscopic Surgery & Abdominal RegionAbdominal Region

Abdominal regionAbdominal region Highly dynamic Highly dynamic

environmentenvironment Very little free space - Very little free space -

organs and tissues organs and tissues placed on top of each placed on top of each otherother

In laparoscopic surgery In laparoscopic surgery settings, surgeon has tosettings, surgeon has to Deform and move the Deform and move the

organs on the wayorgans on the way But But implicitlyimplicitly knows how knows how

much force to apply not much force to apply not to harm the tissues!to harm the tissues!

Laparoscopic tool

MotivationMotivation Robotic surgeryRobotic surgery: : Preoperative surgeryPreoperative surgery, , Intraoperative surgeryIntraoperative surgery, ,

Postoperative surgery Postoperative surgery Preoperative surgery Preoperative surgery

before the surgery before the surgery the the flow of surgery is planned based on patient-specific data. flow of surgery is planned based on patient-specific data.

During this part, During this part, a motion planna motion planninging algorithm algorithm can be used to can be used to find find out the ultimate pathout the ultimate path of the surgical tool and of the surgical tool and the most efficient the most efficient and least harmful maneuversand least harmful maneuvers to follow during the Intraoperative to follow during the Intraoperative part, which is the part where actual surgery takes place.part, which is the part where actual surgery takes place.

AssessmentAssessment of performance and training transfer on surgical of performance and training transfer on surgical simulators.simulators. QQuantitative performance measures during a training session uantitative performance measures during a training session

task completion timetask completion time hand motion economyhand motion economy path lengthpath length work done by traineework done by trainee amount of unnecessary tissue damageamount of unnecessary tissue damage

With With a motion planna motion planninging algorithm algorithm designed for a specific virtual designed for a specific virtual surgical task, the surgical task, the optimum valuesoptimum values of measures can be calculated and of measures can be calculated and the values of a traineethe values of a trainee’’s performance can be s performance can be compared with the compared with the optimum onesoptimum ones for a for a realistic and correct assessmentrealistic and correct assessment..

Summary of my projectSummary of my project A simple model of the abdominal area with A simple model of the abdominal area with

rigidrigid obstacles ( obstacles (should not be touchedshould not be touched) and ) and deformabledeformable obstacles ( obstacles (can be touched and can be touched and deformed until some limitdeformed until some limit))

The spherical robot is a The spherical robot is a rigidrigid free-flying free-flying object. It aims to go from start position to a object. It aims to go from start position to a goal position in the abdominal region.goal position in the abdominal region.

A modified motion planning algorithm (PRM) A modified motion planning algorithm (PRM) for the spherical robot to find a path in whichfor the spherical robot to find a path in which The robot The robot cannotcannot collide with the rigid obstacles collide with the rigid obstacles The robot The robot cancan touch and deform the deformable touch and deform the deformable

obstacles (FEM-based organs) until it feels some obstacles (FEM-based organs) until it feels some limit response force from the obstacle.limit response force from the obstacle.

If the limit force is already achieved, the If the limit force is already achieved, the computed path is not acceptable.computed path is not acceptable.

Prior workPrior work

Bayazit, Lien, and Amato (2002). Bayazit, Lien, and Amato (2002). AA motion planning algorithm in a motion planning algorithm in a

geometrically deformablegeometrically deformable environment based environment based on Probabilistic Road Map (PRM) methodon Probabilistic Road Map (PRM) method

Gayle et al. (2005). Gayle et al. (2005). A A constraint basedconstraint based planning algorithm for a planning algorithm for a

deformable robotdeformable robot in complex environments. in complex environments. Rodriguez, Lien, and Amato (2005). Rodriguez, Lien, and Amato (2005).

AA motion planning algorithm based on Rapidly- motion planning algorithm based on Rapidly-Exploring Random Tree technique for a Exploring Random Tree technique for a deformable robotdeformable robot in a completely in a completely deformable deformable environmentenvironment..

ImplementationImplementation

PRM for planning (MPK-PRM PRM for planning (MPK-PRM environment)environment)

Extended with linear elastostatic Extended with linear elastostatic FEM deformationFEM deformation

Implementation details - Implementation details - PRMPRM

start

goal

ExpandTree()

ConnectTree()

TestPath()

TestPathAgainstDeformableObject()

Find out

if response force > limit

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

Fixed here

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

Fixed here

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

Fixed here

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

Fixed here

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

Fixed here

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

Collision !

Fixed here

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRMClosest vertex

Input displacement vector given to closest vertex

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRMKU = Fext

U = Kinv Fext

=

U (dof x 1)

Kinv (dof x dof)

Fext (dof x 1)

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRMKU = Fext

U = Kinv Fext

=

U (dof x 1)

Kinv (dof x dof)

Fext (dof x 1)

known

Unknown response force at closest vertex

000

0000

???

????

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRM

=

Linear set of equations

Solve for the external force on closest vertex

If magnitude of computed force vector > limit

try a different path ( expandTree() )

Else

continue deforming and calculating

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRMKU = Fext

U = Kinv Fext

=

U (dof x 1)

Kinv (dof x dof)

Fext (dof x 1)

Known response force at closest vertex

000

0000

???

????

Solve for the displacements at other vertices

Implementation details – Implementation details – deformable obstacle in deformable obstacle in

PRMPRMKU = Fext

U = Kinv Fext

=

U (dof x 1)

Kinv (dof x dof)

Fext (dof x 1)

Known response force at closest vertex

000

0000

Solve for the displacements at other vertices

DemoDemo