Non-Invasive Biomechanical Device for the Club-Foot ...

Proceedings of the 2nd Biennial IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics Scottsdale, AZ, USA, October 19-22, 2008

Non–Invasive Biomechanical Device for the Club–Foot Medical Treatment: A Robotic Rehabilitation Analysis Luis I. Lugo–Villeda, Antonio Frisoli, Fanny Correa Bautista, Vicente Parra–Vega and Massimo Bergamasco Abstract— The analysis, synthesis and mechanical design of a wearable biomechanical device for treating the club– foot children malformation is presented in this paper. This system serves as non-invasive alternative method for correcting this congenital malformation in 0–1 year-old children. Robot kinematics and constrained Euler-Lagrange dynamics tools are employed to analyse this malformation, altogether with a quasi-static computational method, and to asses the normal children feet, in order to design a robotic prototype. The 8-months clinical case presented in this paper establishes a preliminary club–foot correction angle of 90%, without typical patient complains, such as those coming from conventional methods, either because of uneasiness and unrest of long– time cast or invasive clinical surgery. The proposed passive noninvasive robotic prototype allows to analyse and to assess the real progress over time and spatial coordinates, which record real data of the betterment of the club–foot malformation

I. INTRODUCTION Pediatric orthopedics cares for children orthopedic problems as children growth, which is quite different from the orthopedics care of adults, since it is usually preferred to fix malformations and ailments in children at early stages using non–invasive clinical methods, which may avoid mild or severe progressive deformities, disorders, or injuries of the skeleton and associated structures. In particular, the so-called club–foot orthopedic deformity, often refereed as congenital talipes equinus–varus, which is many times confused with other foot congenital deformations such as the calcaneovalgus and metatarsus adductus, [9], have great incidence in children. In many countries like United States of America, United Kingdom, Italy and Mexico, this problem affects approximately 1 of every 1000 births, where this condition prevails twice in males than females. This deformity can be mild or severe and it can affect one foot or both feet, while it occurs 50% in both feet [5]. The main physical characteristics could be defined as an abnormal of feet orientation, classified as equinus adduction, supination and varus, the latest means a inward angulation of the distal segment of a bone or joint, in which the feet are bent towards This manuscript was received on April 23th of 2008. This work was supported by SKILL–IP. Luis I. Lugo Villeda, Antonio Frisoli and Massimo Bergamasco are with Perceptual Robotics, Scuola Superiore Sant’Anna, 56127, Piazza Martiri della libert`a 33, Pisa, Italy. {l.lugovilleda,a.frisoli,

massimo.bergamasco}@sssup.it Fanny Correa Bautista is with Research Center on Technological Innovation , Cerrada de Cecati SN. Col. Santa Catarina Azcapotzalco, 02250, Mexico D.F, Mexico. fanny [email protected] Vicente Parra-Vega is with Robotics and Advanced Manufacturing Division, Research Center for Advanced Studies Saltillo Campus, CINVESTAV Carretera Saltillo-Monterrey Km 13,5 - CP 25000 - Ramos Arizpe, Coahuila, Mexico. [email protected]

978-1-4244-2883-0/08/$25.00 ©2008 IEEE

the interior, as well as rotated affecting all the joints, tendons and ligaments in the foot [8], see figure 1.

Fig. 1.

Club–Foot typical deformation

There are a few clinical studies reported in the literature devoted to this suffering, from etiology point of view. Main research attempts to diagnose it as a neurological problem, muscular, or bony, even when the later is one of the most accepted [2]. Nevertheless, attending this disease is important because it does not affect only to children, but as they growth, to adults, thus there are many implications into medical treatment: the diagnosis stage, the correction phase, and the maintenance phase, that is the stage where the foot takes and maintains its normal position. The full treatment involves advanced orthopedic technology, and nowadays several engineering areas are working synergically for getting better results in a multidisciplinary team work [3]. The treatment is classically divided into invasive and non–invasive, the former concerns with a typical foot surgery to correct the pathology [7], which involves: 1) Perctuneous tenotomy 2) Posterior release 3) Medial release 4) Subtarsal release 5) Complete tendon transfer Results of club foot surgically treatment sometimes are quantitatively below acceptance because it induces rigidity, weakness and early arthritis in the foot. In the other hand, the latter non–invasive treatment does not requires of surgery, and is widely preferred by patients. This is based on the so– called Ponsetti method [2], see figure 21 . A. The Ponsetti Method There is a vast literature dedicated to Ponsetti clinical method application; for completeness, we recall some basic definitions of this method. It begins its application on newborns on the very first days, stimulating with smooth manipulations newborn’s foot during 15 days approximately, 1 Time for applying cast depends on the correction level, in this figure this information is just informative.

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Fig. 2.

Ponsetti method progressively corrects this ailment by using casts

rotating the bones and stretching the tendons. Afterwards a plaster bandage is mounted into child leg from the distal end of his toes foot to the groin, thereafter this cast is changed periodically every 7 or 14 days, according to growth and correction level of the foot. Regularly 5 to 6 cast are required to fully correct the position in a progressive form, there exists a clinical inspection among casts within specific order (adduction, equinus and varus), see figure 2. Nevertheless, this method still has not left totally good results, cause in maintenance phase often might appear relapses of the congenital deformities of the foot, which in some cases pulls the user up to surgery or long incidence when this method is applied. Besides, prolonged use of casts have consequences such as skin dehydration, ulcers’ problems, blood circulation problems when the cast is too tight before the following change, this pronounces with the swelling of the toes, taking a blue coloration or white and other related problems [5]. Therefore, an alternative way to treat club–foot malformation is needed to avoid either surgery or repeated application of the Ponsetti approach. This suggests that advanced passive robots, working synergically with conservative clinical methods, may render an alternative solution to implement analytically and qualitatively the Ponsetti method, see figure 3. To this end, in this paper we design a biomechanical device to facilitate to the specialistic doctor the application of this method, which allows continuous measurement of angle and force application and qualitatively evaluate its correct evolution. B. Contribution This paper reports a biomechanical device for correcting in an acceptable range the equinus, varus and supination malformations, involved with the club–foot pathology. The passive mechanical device is an alternative to both invasive and non–invasive treatments. Our approach requires implementing the conventional clinical process of the Ponsetti method together with our experimental club–foot robotic prototype and the provided analytical tools and methodology, shown in Figure 3. In this way, our passive rehabilitation robot, provides a non–invasive method which corrects the malformation’s foot in children, as it is proved in our 8months old clinical test on a newborn child in southern Mexico2. 2

Notice that this is the first built wearable prototype, we are still working on it. We expect to present in the near future a complete report of its performance, advantages and disadvantages in comparison with Ponsetti’s Methodology.

Fig. 3.

Robotics interaction into medical–treatment

Nevertheless our approach shows a good performance in the trial clinical test, without the typical problems reported in the other approaches, and it is more conservative and easy to handle3. C. Organization Section II shows the advanced robotic rehabilitation analysis, including kinematics and dynamics-based approaches. Based on this, the mechanical design is presented into Section III, while Section IV reports the first clinical case, in which the device has corrected a child club–foot ailment up to 90%. Conclusions are presented in the final Section, whereas exoskeletons philosophy is steaming as a future work for getting fully autonomous passive robotic prototype. II. C LUB –F OOT S IMPLIFIED ROBOTICS A NALYSIS The importance of using the mathematical robotic tools relies on the fact that they allows to analyse qualitatively and quantitatively the temporal and spatial attributes of the motion and force interaction of a given mechanism, in this case the club–foot model in free and non-free (constrained) motion. Since each medical patient has different characteristics on his pathology, kinematics analysis, dynamics analysis, and path planning play an important role in determining accurate data for a passive mechanical adjustable robotic design [12]. In a first attempt to analyse the kinematic model of club–foot patient, rubber silicon anatomic model was designed, its anatomy was taken from a five months-old child, who presented unilateral club–foot, see figure 44 .

Fig. 4.

Silicon rubber model of real 5 months-old club–foot patient

3 This device is protected under Mexican patent No.0231122007. Anyone interested in this patent, just contact the main author for testing trials, within a non–profit policy. 4 With this silicon model we start the robotic analysis and parametric definition.

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A. Forward Kinematic of Child’s foot Assuming a simplified kinematics chain, we define a foot robot–like as open kinematics chain such that it does include the tibial bone, calcaneus, metatarsus and set of phalanges of the foot as four degree of freedom (DOF) kinematic chain, representing a child’s foot.5 The four–link representation is shown in Figure 5, wherein there exists a set of generalized coordinates q ∈ R4 which models the main rotations to be corrected [4].

B. Inverse Kinematic of the Child Foot Consider the toe foot cartesian coordinates X in terms of the set of angles q at which kinematic chain of the child’s foot is positioned. This computation can be made by using the inverse kinematics, i.e.

= d0f − R0f (0, 0, a4)T

T03

f (q)

qi q1 + π2 q2 q3 q4

kinematics is computed using the generalized coordinates q = (q1 , q2 , q3 , q4 )T ∈ R4 , as follows =

D ENAVITH -H ARTENBERG PARAMETERS

X

TABLE I

αi − π2 0 - π2 0

Each link length correspond to the corresponding child’s foot measurements, and therefore the Denavith–Hartenberg parameters can be obtained, see Table I, [4]. The forward

di d1 0 0 0

(5)

Fig. 5. Open kinematic serial chain representing a simplified model of normal foot

ai 0 a2 a3 a4

(4)

Once we found the articular position using the kinematics

link (i) 1 2 3 4

f1 (d03 )

(q1 , q2 , q3 ) =

(3)

Due the kinematics chain has got a position and orientation, it’s quite complex to solve (3), however there is a kinematic decoupling that makes the inverse kinematics solvable [12]. In this way, referring to figure 6, we can set next decoupled equation,

f −1 (X)

=

q

Afterwards, the inverse mapping allows to obtain the path planning strategy to define the progressive correction angle at which our device should be adjusted to correct the misalignment of the club–foot.

(1)

where this mapping can be described in term of general transformation with respect to base frame, defined as the orthogonal fixed system O0 (x0 , y0 , z0 ), and hence,   a1 a2 a3 Px  a4 a5 a6 Py  f  T0 =  (2)  a7 a8 a9 Pz  0 0 0 1

The three–dimensional vector X = (Px , Py , Pz )T ∈ R3 is the position of the toe foot with respect to fixed base frame and it determines the set of relative angles of the abduction, pronation, equinus and varus segments in the club–foot6. 5 A normal foot presents high complexity on its chains in terms of DOF, nevertheless, we are working with at least the principal angular bones rotations for reducing the mathematical complexity but maintaining accuracy. 6 Due to space constrains, full details are omitted.

Fig. 6.

Kinematic decoupling for solving the inverse kinematic problem

decoupling, the Euler angles of the orientation of the toe foot, i.e, last angular position q4 can be computed. Thus, taking into consideration figures in 7, let us find geometrically the first set of generalized coordinates7, q1

= atan2(py , px )

q2

= atan2(pz , r) − atan2(a3 sin(q3 ), a2 + a3 cos(q3 ))(7) p = atan2(± 1 − D2, D); (8) 2 2 2 2 2 px + py +pz − a2 − a3 | {z }

q3

=

(6)

r2

(9) 2a2a3 Finally, for encountering the last angular coordinate, we use the Euler–angles U ∈ SO(3), D

f

R0 (q4 ) = U 7 The

vector (px , py , pz )T stands as decoupled position.


(10)

forces vector and τ ∈ R4 are the control input functions10. The Differential–Algebraic–System (11) is of Index–2, there-

Fig. 7.

Finding q1 ,q2 ,q3 the decoupled position

With this results, some test were conducted with patients who present club–foot to validate and computed the values of these parameters, so as to build the following table for distinguishing the normal angular foot and angular club foot measurements.

TABLE II M AIN ANGULAR DIFFERENCES BETWEEN NORMAL AND CLUB FOOT Fig. 8. Type q1 q2 Normal 0 0 Adduction 17 0 MFP 0 50 MFD 0 15 Adduction* 40 0 MFP* 0 75 MFD* 0 15 Adduction and MFP* 40 75 qi is in deg x,y,z is in cm MFP– Maximal Plantar Flexion MFD– Maximal Dorsal Flexion * – Corresponding data to club foot

q3 0 0 0 0 0 15 15 15

x 0.0000 2.0466 0.0000 0.0000 4.4995 0.0000 0.0000 0.4991

y 7.0000 6.6941 4.4995 6.7615 5.3623 0.7765 6.3619 0.5948

z 0.0000 0.0000 5.3623 1.8117 0.0000 6.8978 2.7765 6.8978

fore it can not be solved by using ordinary differential equations (ODEs), [10], we need to apply some methods like stiff Backward Differentiation Formula of Gear together with the Baumgarte-like constraint stabilizer, in which the DAE system is treated as linear control system reducing the index to 1, see [1] and [6]. Notice that Lagrange multiplier λ is explicitly computed solving the next equation, H(q) −JφT τ − F(q, q) ˙ q¨ = (13) λ φ¨ + 2α φ˙ + β φ JϕT 0 where F(q, q) ˙ = C(q, q) ˙ + B0 q˙ + G(q). In this way, the

C. Dynamic Analysis Including Scleronomic Constraints Once the kinematic mapping are computed, which help us to find the point in the space given the angular coordinates and viceversa, we are going to focus briefly in dynamic analysis that its consequences involving applied forces and torques [12]8. The main goal of subsection is to find out the balance of the antagonistic forces in the correction process, that is, we use next energy balance obtained from the Euler– Lagrange formalism for dynamical serial systems [11], H(q)q¨ + C(q, q) ˙ + B0 q˙ + G(q) = τ + JφT (q)λ (11)

φ (q) = 0

Whole dynamic system indicating applied forces

(12)

where q, q, ˙ q¨ ∈ R4 are the dynamic states, H(q) ∈ R4×4 , stands as inertia mass matrix, C(q, q) ˙ ∈ R4×4 stands as the coriolis matrix, the linear friction matrix between links is given by B0 ∈ R4×4 9 , G(q) ∈ R4 stands as the gravitational 8 Quasi–static analysis and dynamic analysis was made; dynamical analysis was taken in this section because it can approximate with much more accuracy the applied force by the child’s foot and the reaction force while the trajectory of the correction is being done. 9 It’s possible that coriolis matrix as well as viscous friction matrix can be neglected but taking this into account we shall obtain results more accurate and repetitive which are necessary for the mechanical design.

dynamic behavior is taken into account for computing the antagonistic force exerted by the toe foot onto the environment, it means, the force correction exerted by the mechanical device. III. O N THE M ECHANICAL D ESIGN OF THIS D EVICE The biomechanical device consists basically of three mechanisms(the parameters to adjust the device) which are going to carry out the correction: • adjustable flexion–extension fitting on the leg’s length • adduction-abduction corrector, and adjustment of length of the foot • the mechanism of adduction-abduction as well as pronation–supination Figure 9 shows the device structure, indicating with arrows the motions for adjustment and corrections of the foot according to indications of medical doctor. The base of the device is composed by two rectangular plates which are grooved in such a way that are placed perpendicularly to the base to avoid the displacement of the foot outwards, and they are designed mainly to correct the adduction. These plates consequently are adjustable, according to the size of 10 This inputs are controlled on the mechanical device and adjusted by the medical doctor and therapist at each clinical session.


C

A

Fig. 11.

The Club–Foot on two days-old newborn

B

compression problems, toes’ inflammation , as well as severe injuries in the foot and skin problems, see figure 12 At

Fig.14. Estructura del dispositivo en CAD.

(a) A Fig. 9.

(b) B–C

Biomechanical device basic architecture

the foot and particular anatomy of the patient. The device can adjust to leg growth by means of the lateral bars, which can move freely upwards or downwards, according to physicians instructions and patient needs. These same bars have a joint at the bottom which allow to turn them or rotate them, aiming at extending or bending the foot, to correct the equinus malformation. The final prototype is constructed on aluminium alloy for easy machining and handling (weight of 150 gr), commercial availability, lightweight and maintenance, such that the final biomechanical device is shown in figure 10. This mechanical devices is easily adjustable to adapt to the

Fig. 12.

Severe skin injuries because cast uses

the age of 1 month, the patient’s parent suspended the Ponsetti treatment, afterwards in a hospital in Mexico City the proposed passive biomechanical robotic device was implanted. Before this, several clinical studies were conducted to determine the feasibility of implanting our device, that is, it normally consists of a radiological study of the club–foot taking several postures, among them the back–to plant and lateral postures. The figure 13 shows a set of taken x–rays,

(a) A, 47◦ Fig. 13. Fig. 10.

(b) B–C, 50◦

Radiological studies determining the malformations

Final prototype

natural growth of patients. IV. A C LINICAL C ASE : E XPERIMENTAL R ESULTS The first clinical case is reported with a male patient, born on February 15th, 2007, in Xalapa, Mexico, presenting a medical diagnosis of unilateral right club–foot, photos were taken two days later of birth, see figures 11. Clinical archives showed the patient had a conservative Ponsetti treatment at the 13th day, placing the first cast with a lapse of 15 days, however this treatment was interrupted and the patient released cause the child’s foot was presenting and displaying

whereby clearly we can distinguish how the involved bones in the foot are oriented in equinus and varus malformation and how its angles show the projections of the axes onto the bones, according to Table II. In the X-ray back-to plant, see figure 13(a), the foot is oriented 47o approximately with respect to the sagittal plane, which could be seen at sight, whereas figure 13(b) shows the flexion of the foot, for a 50o angle, measured between the bones and the tibio–astragaline joint. After the patient has been diagnosed radiologically and clinically, the club–foot is still a flexible body part and it is a candidate for implementing our proposal, without any


cast, keeping save the physical integrity of the newborn. The biomechanical device was implanted in child foot at the age of 1 month during a 8 month period, see figure 14 and figure 1511. It is clearly visible that exist a normal

Fig. 14.

Biomechanical device treatment–based at 1 month

Fig. 15.

Biomechanical device treatment–based at 8 months

correction of the foot’s malformations cause the adjusted biomechanical device was gradually configured such that a continuous medical visual inspection and smooth massages yields a foot recovering toward its normal posture. Finally the clinical and final diagnosis shows a 90% of correction in a 8 month period, fortunately, there were neither relapses nor other resulting contraindications using our proposed passive biomechanical system.

Fig. 16. Corrected foot at 90% which was diagnosed and approved by a medical institution

V. C ONCLUSIONS The conclusion analysis can be listed as follows 1) A biomechanical device is designed for correcting the club–foot congenital malformation of newborn children. 11 Due to space constrains, full details of the foot measurements at each stage are omitted.

2) Based on advanced robotic fundamentals, an algorithm computes accurate data and precise biomechanical design can be obtained, according to real parameters of a club–foot. This is based on kinematic and dynamic analysis based on Euler Lagrange dynamical systems 3) The mechanical device is adjustable in many of its parts, to be able to easy treat and implement a supervised Ponsetti method on a club–foot, and simultaneously reduce the patient trauma of the surgerybased method or injuries due prolonged use of casts. Its mechanical characteristic let us manipulate easily the device and it to foot length while the patient is growing up and according to his evolution. 4) This biomechanical device is capable to remain statically fixed till it is manipulated by the medical doctor, the therapist or the parents, once they have received accurate medical indications. 5) In spite to have made it in aluminum it turns out a light system and it is comfortable for the newborn, who uses it without complain, because once the foot is perfectly fitted into mechanical device, it will not cause any injuries like those caused by plasters. Finally, the interaction of rehabilitation robotics requires of synergetic interaction among medical doctor, physical therapy, the parents care and advanced technology for creating products for healthy and safe recovery, however, advanced robotic tools are fundamental, as it is presented in this paper. Future work is inherently related with the use of exoskeletons philosophy as well as embedded microprocessor-based prototype instrumented with rated-gyroscopes. R EFERENCES [1] J. Baumgarte, “Stabilization of constraints and integrals of motion in dynamical systems,” Computer Methods in Applied Mechanics and Engineering, vol. 1, pp. 1–16, 1972. [2] Chotel, Parot, Durand, Garnier, Hodgkinson, and Berard, “Initial management of congenital varus equinus clubfoot by ponsetti method,” Rev Chir Orthop Reparatrice Appar Mot, vol. 88, pp. 710–717, 2002. [3] F. Clarire and F. Daniel, “Biomechanics of walking and running: Center of mass movements to muscle action.” Exercise & Sport Sciences Reviews, vol. 26, no. 1, pp. 253–286, January 1998. [4] J. J. Craig, Introduction to Robotics: Mechanics and Control, third edition ed. Pearson Prentice Hall USA, 2005. [5] E. Espinosa-Urrutia and A. Penagos-Paniagua, “Conservative treatment of idiopathic congenital clubfoot. efficiency assessment,” Acta Ortop´edica Mexicana, vol. 18(Suppl. 1), pp. S63–S69, Jul.-Dec 2004. [6] C. W. Gear, “Towards explicit methods for differential algebraic equations,” Computer Methods in Applied Mechanics and Engineering, Springer Netherlands, vol. 46, no. 3, pp. 505–514, 2006. [7] J. T. J. Jerome, M. Varghese, B. Sankaran, R. K. Gupta, S. Thomas, and A. Mittal, “Aberrant tendo-achilles tendon in club foot : A case report,” Podiatry Internet Journal, vol. 2, no. 3, March 2007. [8] K. N. Levin, M. N.and Kuo, C. F. Harris, and D. V. Matesi, “Posteromedial release for idiopathic talipes equinovarus. a long–term follow– up study,” Int Orthop, vol. 242, pp. 265–268, 1989. [9] C. NC, “Preoperative clinical assessment of clubfoot,” In: Simons GW, ed. The Clubfoot: The Present and a View of the Future, pp. 97–98, 1994. [10] L. Petzold, “Differential-algebraic equations are not odes,” SIAM J. Sci. Statist. Comput., vol. 3, pp. 367–384, 1982. [11] M. H. Raibert, Legged Robots That Balance, re-printed edition ed. MIT Press MA USA, 2000. [12] M. W. Spong and M. Vidyasagar, Robot Dynamics and Control, first edition ed. John Wiley and Sons USA, 1989.
