A numerical study towards shape memory alloys application in orthotic management of pediatric knee lateral deviations

Abstract

Exerting a constant load would likely improve orthosis effectiveness in treating knee lateral deviations during childhood and early adolescence. Shape memory alloys are potential candidates for such applications due to their so called pseudoelastic effect. The present study aims to quantitatively define the applicable mechanical loads, in order to reduce treatment duration while avoiding tissular damage and patient discomfort. This is essential for performing a more efficient design of correction devices. We use a patient-specific finite elements model of a pediatric knee to determine safe loading levels. The achievable correction rates are estimated using a stochastic three-dimensional growth model. Results are compared against those obtained for a mechanical stimulus decreasing in proportion to the achieved correction, emulating the behavior of conventional orthoses. A constant flexor moment of 1.1 Nm is estimated to change femorotibial angle at a rate of (7.4 ± 4.6) deg/year (mean ± std). This rate is similar to the achieved by more invasive growth modulation methods, and represents an improvement in the order of 25% in the necessary time for reducing deformities of (10 ± 5) deg by half, as compared with conventional orthoses.

Figure 1

Finite elements model used in the study. Epiphyseal plates have been colored in green. Geometry was obtained from a left 10 years old female patient MRI. (1) tibia diaphysis (2) tibia epiphysis (3) femur epiphysis (4) femur diaphysis (5) fibula epiphysis (6) fibula diaphysis (7) patella (8) tibia physis (9) femur physis (10) fibula physis (11) lat. colat. ligament (12) med. colat. ligament (13) ant. cruc. ligament (14) post. cruc. ligament(15) patellar tendon (16) lat. meniscus (17) medial meniscus (18) lat. tibial cartilage (19) med. tibial cartilage (20) fem. art. cartilage (21) pat. art. cartilage (22) menisci horns.

Figure 2

Stresses on the epiphyseal plate, for a unitary (1 Nmm) applied moment. Values and arrows in pink indicate the estimated stress peak level and its location, respectively. Maximum normal stress is the more conservative criterion for preventing epiphyseal damage, allowing a maximum applied moment of 1.1 Nm in order to not surpass a stress level of 0.153 MPa, considered to be safe. Global error in the numerical solution was estimated in the order of 2% (Sup. Fig. 3), while material behavior related uncertainty in the computed stresses was estimated to be in the order of 1.5% (Sup. Fig. 4).

Figure 3

Comparison between the knee tissue stress estimators and deformations, for a typical load F occurring during still standing and for an “equally stressing” correcting moment T. •: location of maximum von Mises equivalent stress. × : location of maximum contact pressure. + : location of maximum menisci displacement. Tension in the medial collateral ligament due to the orthotic use was estimated in 77 N for this case.

Figure 4

Typical correction evolution under a constant orthotic load. (a) Dependence of correction speed for the femur and the tibia, as a function of time and applied flexor moment. (b) Evolution of the femur and the tibia correction angle. Notice how the model predicts an initial, more rapid mean correction rate, that stabilizes at around 10 days of treatment in the case of a constant load orthotic, progressively decreasing in the case of a decreasing load orthotic with a goal correction ${\theta }_0$ = 2 deg.

Figure 5

Growth evolution quantifiers in a set of 200 stochastic runs, for an orthotic applying a constant correcting load. (a) Change in the knee deviation angle evolution. (b) Femur versus tibia correction ratio evolution. (c) Correcting speed pdf. as a function of time. (d) Dependence of correction time with growth speed. (e) Dependence of correction time with initial deviation. (f) Dependence of time for correction with the time the patient uses the orthotic.

Figure 6

Time necessary to reduce an initial knee deviation by half. (a) Comparison of the pdf of necessary time, for a constant load and a decreasing load orthotic. (b) Pdf of the difference in wearing time for a constant load and a decreasing load orthotic. With a probability greater than 50%, treatment time for reducing deformity by half is 12 weeks shorter with a constant load orthotic.