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Trends and Challenges in Modeling and Simulation: An Industry Perspective

October 14,2010 • 2:00-3:00 p.m. ET Register today at www.memagazine.org/webinar.html

Modeling and simulation have been core methods in modern engineering for decades. The basic question of whether the tools and techniques of today are sufficient to meet emerging design challenges has engaged the global engineering community in many segments. This webinar offers insights into the key challenges facing modern engineering, and some of the activities that address these challenges.

• What makes modern engineering so different from traditional practice?

• How do we manage system complexity? • What are the leading edge initiatives?

The speakers represent two distinct perspectives. Dr. Butts is an accomplished engineer from the automotive industry and academic research sector. He will discuss some of the key developments from this important industry. Dr. Lee is a veteran of the engineering computing industry and he will offer his observations on the unique computational trends and the core technologies that will make a difference for the modern engineering community in the years to come.

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M Mathematics • Modeling • Simulat i on

of healing A lab studies knees

and machines to help ligament-graft patients get back on their feet.

By Daniel Wiznia

e've all heard of athletes tearing their anterior cruciate ligament, which is

one of the ligaments connecting the tibia to the femur. The tear is usu­

ally caused by a bad maneuver, such as when an athlete comes to a quick

stop by landing on a leg and rotating the knee. For an active individual, the

injury can be hard to live with . Besides the pain and swelling it causes, the

rupture can make the knee unstable.

As many as 200,000 people a year in the United States undergo surgery to repair a torn ACL, in

Daniel Wiznia. a mechanica l engineer. is a medical student at Weill Cornell Medical College and assists with research in the Tissue Engineering. Regeneration. and Repair Program of the Hospital for Special Surgery in New York.

which the native ligament is replaced with a graft, often using part of a tendon from somewhere else in the patient's body. While the reconstruction techniques have been well established over the past 20 years, not much has been established regarding the rehabilita­tive steps a patient should take after surgery. Experts disagree on when a patient should begin to walk after surgery or the exercises that should be included in a physical therapy regimen. This confusion leads to varied long-term outcomes.

At the Hospital for Special Surgery in New York, we are investigating the biological mechanisms ofhow tendon heals to bone, in order to ultimately influence rehabilitative

anterior

fibula

protocols. Our lab, directed by Scott Rodeo and part of the hospital's Tissue Engineering, Regeneration, and Repair Program, has been focusing on how mechani­cal loads placed on tendons affect the healing process by initiating biological signals.

Our current model involves studying rodents that have undergone ACL reconstruction to examine the effect of mechanical loading on tendon biology. By observing the results of different therapies on the rodents, we will develop empirical evidence that will lead to future protocols for therapy-in short, to have people heal and return to their normal lives again as

soon as possible. Our research on rodents will identify the most promising regimens to try farther up the food chain.

After an ACL reconstruction has been conducted on the rodent, we will use a custom-designed computer­controlled system to apply an axial load to the tendon­to-bone repair site. We will then examine the healing process through a variety of mechanical and biological methodologies.

One therapy that has demonstrated some success in patients recovering from ACL surgery has been continu­ous passive motion (CPM). In this therapy, a patient's

leg is placed in a device called a CPM

FOUR FORCES USED TO DESCRIBE LOADS APPLIED TO THE KNEE JOINT machine that guides the knee joint slowly through a controlled range of motion, a period of flexion to exten-Compressive and distractive forces

Compressive I force l t Distractive

1

fme

Ill_ Compressive force

Posterior and anterior forces

Posterior force

I I ~terior L ee

Posterior force

sion (about 90 degrees of motion) that takes about 45 seconds to complete. The therapy is described as passive because the CPM machine applies forces to the leg that effect a slow rate of motion, whereas the muscles remain in a relaxed state and do not apply significant forces.

As the knee passes through its range of motion from flexion to extension, the new ACL tendon graft experiences varied tensile loads. While the CPM machine is regularly used in total knee replacement and hip replacement to increase a patient's range of motion following surgery, protocols have yet to be refined for post-ACL reconstruc­tion therapy. As the role of motion on healing of the ACL reconstruction is unknown, we are investigating the

screw to hold graft in place in tibial tunnel

October 2010 I mechanical engineering 23

mechanical loads that are felt by the graft as the knee bends, as well as how these loads affect healing.

Our laboratory decided to build a miniature CPM machine that we could use with a rodent ACL patient. There are many designs available, however, and so we had to identify which one seemed best for the specific needs of therapy after an ACL graft.

The team working on this project consists of two orthopedic surgeons, Xiang-Hua Deng and Scott Rodeo, and me, a medical student and mechanical engineer. We also had help from mechanical engineer Carl Imhauser, and two research mechanical engi­neers, Dan Choi and Mark Stasiak. We decided to use a four-step process for choosing a design as the basis for our research. First, we created design criteria for a CPM machine that would satisfy our research requirements. Second, we assembled a list of existing CPM designs. Third, we built m athematical models for each design to determine which best fulfilled our criteria. Fourth, we then generated a design of our top candidate in Solid­works, and built a mockup of the device which we are now currently testing.

To describe loads applied to the knee joint, there are traditionally four force vectors oriented in relation to the tibia-compressive/distractive, anterior/posterior, medial/lateral, and internal/external rotation. It is important to note that approximately 85 percent of the anterior forces applied to the knee are transmitted to the ACL graft.

Therefore, our design criteria for the CPM machine included minimizing the load on the ligament graft by reducing anterior forces and anterior displacement of

' CLINICAL CPM DESIGN I HINGE MODEL

Results for the design that best met the lab's criteria.

Fnt =force from plate supporting femur

Wt = weight of femur

Force in the anterior I posterior direction is always zero. Force in the compressive I distractive direction is never greater than w; and is alwayS distractive.

24 mechanical engineering I October 2010

the knee. We were not concerned if forces were applied in the posterior direction, as the ACL is primarily loaded by forces in the anterior direction. In addition, we required a design that would prevent the knee from being placed under excessive compressive loads, which we defined as tw ice the weight of the rodent, and we required a design that would reduce the amount of internal and external rotation of the tibia on the femur. We also included in our criteria that the design ensure that the knee follow a natural physiological motion as it is flexed and extended.

Once we settled on the design criteria, we assembled a list of four existing CPM designs and one internal concept that we felt could be suitable for our rodent model. Designs were included from laboratories that had developed animal model CPM machines, (two of the animal designs were built for rabbits, and two were built for rats) as well as clinical designs. We excluded animal CPM machines that were not designed specifi­cally for the knee joint.

Then, for each of the five designs , we created math­ematical models , which involved deriving a system of equations developed from force body diagrams, and solving for the anterior/posterior and compres­sive/distractive forces at the knee joint as a function of flexion . Within our models, we assumed that the knee behaves like a hinge and the joint surfaces exert negligible friction forces. Because each cycle of the CPM machine takes approximately 45 seconds, we assumed that the leg musculature is passive (the animals will be placed under anesthesia so there is minimal muscle activation), and all structures are in

0.04

0.02

0

Force vs. flexion angle, rodent model

Ul c 0 ~ -0 .02 ~ 20 40

" 60 80 1 00

" "' ~ -Camp/ Dist

~ -0 04 - . -Ant/ Post ~ -0.06

0::

~ -0.08

-0.1 ~

\ -0.12 FLEXION ANGLE Distractive

quasi-static equilibrium. As the systems of the knee will be moving at very slow velocity, their ener-gies can be assumed to be zero. To solve some of the equations, we used measurements taken from rodent anatomy, and we simplified the models to be solved for only the x-y plane. The results of our models were represented in graphs of the compressive/dis­tractive and anterior/ posterior forces vs. angle of knee flexion.

The models helped the team gain a stronger under­standing of the forces applied to the knee by each design and helped us identify which design best fulfilled our criteria. The models clarified the extent and direc­tion of forces, some of which were not as intuitive as one might think, and provided a graphical representa­tion of forces that influenced our understanding of how forces applied to the leg were translated to the knee joint. The models were flexible enough to allow for multiple manipulations and adjustments. Our models demonstrate that while each device accomplishes a similar purpose of moving the knee passively through its range of motion, each device applies a unique set of forces to the knee joint.

Of the five designs we modeled, the CPM design that is currently used in the clinic proved to be the most suitable for our experiments. In the clinical design, the weight of the femur and tibia are each fully supported by separate plates. These plates are attached by a hinge, and provide normal forces which are always aligned with the anterior/posterior vectors. Therefore, the normal forces from the plates are always countering the forces from the weight of the leg in the anterior/ pos­terior direction, and the anterior/ posterior forces were found to be zero. In addition, the force in the com­pressive/distractive direction is never greater than the

The clinical CPM design was rendered in Solidworks (left). The lab built a device and is now testing it on cadaver rats before moving on to live subjects. Above is the first generation of the device, HSS CPM-Version-1.

weight of the tibia, and is always distractive. In addition, our models demonstrated that some CPM

designs created forces at the knee that failed to fulfill our design criteria. For example, one design created unacceptably high compressive loads. Also, our models helped elucidate whether springs could counter anterior forces. It was found that while springs could be helpful, they also induced compressive forces.

Based on the results of our models, we developed with SolidWorks a representative prototype of a miniature CPM similar to the clinical design. We then built the device in our laboratory.

The machine's motion is powered by a Haydon step­per motor which is controlled by a LabJack data acquisi­tion U3 and a US Digital microstepping motor driver. With guidance from software engineer Daniel Fichter, we wrote custom software in Java that allows us to con­trol for displacement, speed, and number of cycles.

Currently, we are in the process of validating the machine with cadaver rats. Once we complete our validation, we will begin live animal studies. With our CPM machine, we hope to gain a better understand­ing ofhow knee motion and mechanical loading of the ACL graft will affect healing. We will investigate the many variables that may influence the mechani­cal signals on healing, such as the duration of the CPM therapy, the onset of the therapy after surgery, the speed of the motion, the number of cycles and the frequency of cycles.

Currently, knee motion is commonly prescribed to a patient recuperating from ACL surgery, but we do not know its effects. ACL graft healing is a slow process, and with our rodent model, we hope to discover the best rehabilitative protocols that will hasten recovery and reduce graft tendon failure rates. •

October 2010 1 mechanical engineering 25