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An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment

An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4308462, 11 pages https://doi.org/10.1155/2019/4308462 Review Article An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment 1 2 2 1 Murtaza Kadhum , Mu-Huan Lee, Jan Czernuszka, and Chris Lavy Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Science, Oxford University, UK Department of Materials, Oxford University, UK Correspondence should be addressed to Murtaza Kadhum; murtaza.kadhum@medsci.ox.ac.uk Received 6 November 2018; Accepted 14 January 2019; Published 25 March 2019 Academic Editor: Jose Merodio Copyright © 2019 Murtaza Kadhum et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Congenital clubfoot is a complex pediatric foot deformity, occurring in approximately 1 in 1000 live births and resulting in significant disability, deformity, and pain if left untreated. The Ponseti method of manipulation is widely recognized as the gold standard treatment for congenital clubfoot; however, its mechanical aspects have not yet been fully explored. During the multiple manipulation-casting cycles, the tendons and ligaments on the medial and posterior aspect of the foot and ankle, which are identified as the rate-limiting tissues, usually undergo weekly sequential stretches, with a plaster of Paris cast applied after the stretch to maintain the length gained. This triggers extracellular matrix remodeling and tissue growth, but due to the viscoelastic properties of tendons and ligaments, the initial strain size, rate, and loading history will affect the relaxation behavior and mechanical strength of the tissue. To increase the efficiency of the Ponseti treatment, we discuss the theoretical possibilities of decreasing the size of the strain step and interval of casting and/or increasing the overall number of casts. This modification may provide more tensile stimuli, allow more time for remodeling, and preserve the mechanical integrity of the soft tissues. Some surgical techniques have been shown to pose a greater 1. Background risk of pain, stiffness, avascular necrosis, infection, overcor- Congenital clubfoot or congenital talipes equinovarus rection, poor long-term ankle range of movement, weakened (CTEV) is a complex pediatric foot deformity (Figure 1). It mechanical strength, and arthritis than if treated conserva- consists of four complex foot abnormalities with varying tively [5–8]. Interestingly, some studies have also reported a correlation between the extent of release surgery and degree degrees of rigidity, namely, midfoot cavus, forefoot adductus, hindfoot varus, and hindfoot equinus [1, 2]. The incidence is of functional impairment [6]. To date, surgical options are widely reported as 1 in 1000 live births in the UK with males mainly employed to manage resistant cases and recurrence being affected about twice as often as females [1, 3]. In almost or if unable to achieve complete correction of the deformity. half of affected infants, both feet are involved. To date, the Currently, the optimal treatment utilizes the Ponseti causes of clubfoot are poorly understood and regarded as idi- method, developed by Ignacio Ponseti in the 1940s [5, 9]. opathic; however, genetic factors and associated conditions This technique consists of two distinct stages of manipula- such as spinal bifida, cerebral palsy, and arthrogryposis have tion and maintenance. The manipulation phase involves been reported [1, 3, 4]. identifying the head of talus to use as a fulcrum, supinating If left untreated, clubfoot inevitably leads to significant the forefoot to eliminate the cavus deformity, and then long-term disability, deformity, and pain [2]. Although vari- abducting the forefoot. This manipulation is then followed ous surgical techniques are used to correct clubfoot, such as up by application of a plaster cast, holding the foot in the cor- soft tissue releases or bony procedures in older children, cur- rected position and providing sufficient time for soft tissue rently, conservative management is the preferred option. remodeling. This manipulation-casting sequence is repeated 2 Applied Bionics and Biomechanics To note, in both of these studies [15, 16], the measurement of soft tissue elasticity was performed on patients undergoing or already treated with the Ponseti method. More informa- tion about the mechanical properties of the soft tissues in untreated clubfeet is needed for comparison. 2.2. Rate-Limiting Tissue: Tendon and Ligament. During the manipulation process of the Ponseti method, the soft tissues responding (or resisting) to stretching include the following: (1) skin, (2) capsule, and (3) tendons and ligaments. To investigate the main tissue that is restricting the foot from reaching the improved position during stretching, the stress values generated from the skin (σ ), capsule (σ ), and skin cap Figure 1: Bilateral clubfeet in a newborn infant. Image taken from tendons and ligaments (σ ) due to the mechanical stretch CURE International with permission. TL are required. To date, the stress values and elastic moduli (E , E , and E ) in these soft tissues in response to on a weekly basis for an average of six weeks, until a 50- skin cap TL degree abduction of the foot around the tibia is achieved. stretching via the Ponseti method have not been studied. An Achilles tenotomy may then be required to eliminate First, consider a simple model simulating hindfoot dorsi- any residual equinus and is followed up by three weeks in a flexion to correct the equinus deformity (Figure 2) in which a cast to aid healing in the lengthened position [1, 5, 9–11]. tendon tissue (red curve) and a skin tissue (blue curve) are The maintenance phase then involves holding the foot in located at distances of d and d , respectively, from tendon−P skin−P an abduction brace for 23 hours per day for 3 months, help- the fulcrum (P). To introduce deformations of the tendon ing to reduce recurrence rates [10, 11]. Zionts et al. [12] (ε ) and skin (ε ) by Ponseti manipulation, an angular TL skin reported that due to the increased use of the Ponseti method, change from θ to θ with respect to P is generated. Examin- 0 1 the estimated percentage of clubfoot treated with surgical ing only the differences in the distance to the manipulation release has dropped from 72% in 1996 to 12%. fulcrum between the two tissues, the forces needed on the tis- sues will be different to create the same angular change (or torque value). Based on the principle of leverage, a larger 2. Main Text force is exerted on the tendon compared to the skin as the 2.1. Clubfoot Abnormalities. Due to the deformities, the tendon is located closer to the fulcrum. dimension, structure, and mechanical properties of most Second, the resistance of the tissues to stretch (stiffness) soft tissues in a clubfoot are different to those of a normal should also be considered. The general constitutive stress- foot. The presence of shortened, thickened, and fibrotic strain relation can be described with the following: tissues at the medial and posterior aspect of the clubfoot has been reported in several studies [13, 14]. This includes σ = E ⋅ ε 1 thickening and shortening of the posterior tibial tendon, Achilles tendon, tibionavicular ligament (deltoid ligament), By calculating the product of Young’s modulus of the tis- and plantar calcaneonavicular ligament. In addition, a sue and the strain value produced by the stretch, the stress value required for manipulation can be acquired. A single fibrous matrix was also seen in the posterior fibulotalar and deltoid ligaments. stretch from a manipulation and casting will generate strain To our knowledge, no work on measuring the mechanical values (ε , ε , and ε ) in each tissue. Typically, ε skin cap TL skin properties of the tendons and ligaments in a clubfoot by and ε will have approximately the same value, while ε TL cap direct mechanical testing has been conducted. Masala et al. will be much smaller than ε and ε in any given stretch; skin TL [15] investigated the difference in mechanical properties of hence, here we consider only tendons and ligaments and skin the Achilles tendon between a clubfoot and a normal foot in our comparison. Young’s moduli of human tendons and by real-time sonoelastography (RTSE). The results show ligaments and human skin at the ankle from existing studies lower mean elasticity values from the Achilles tendons of are listed in Table 1. the clubfeet compared to normal feet (unilateral clubfoot As Young’s moduli of the tendons (lowest: 50 MPa) are patients), demonstrating that the Achilles tendon is stiffer larger than those of the skin (highest: 2 MPa) with almost in a clubfoot. Hattori et al. [16] compared the moduli of soft similar tissue-fulcrum distances, larger stresses (or resis- tissue on the medial, lateral, and posterior aspects of a tance) are generated from the tendons during the Ponseti clubfoot by a scanning acoustic microscope (SAM). They dis- treatment. Tendons and ligaments, therefore, are the rate- covered higher Young’s modulus for the calcaneofibular liga- limiting soft tissues in the treatment of clubfoot. ment compared to the deltoid ligament. This result implies that the lateral soft tissue contracture could also be responsi- 3. Tendon and Ligament Mechanical Properties ble for some of the clubfoot deformities. However, the tissue samples used in this study were fixed in 4% paraformalde- 3.1. Stress-Strain Curve. A typical stress-strain curve for a hyde before measurement, thus leading to excess crosslinking tensile test on a tendon or a ligament is demonstrated in in the ligaments that would result in higher stiffness values. Figure 3. The graph shows three distinct regions [28, 29]. Applied Bionics and Biomechanics 3 skin tendon Fulcrum skin−P P 0 tendon−P (a) Tibia Talus Calcancus Navicular Medial cuneiform Proximal phalanx (b) Figure 2: (a) Illustrative model of the deformations of the two different tissues (tendon and skin) due to a stretch with respect to a common fulcrum to correct equinus. The size of the force exerted to deform individual tissue is inversely proportional to the distance between the tissue and the fulcrum. (b) Diagram of the medial side of a foot with the red line indicating the talus-Achilles length and blue line indicating the talus-skin length. Initially, the collagen crimps are stretched out, and an strain response mainly comes from elongating the aligned increasing number of collagen fibers and fibrils become fibers and fibrils. Further straining induces plastic deforma- aligned to the loading axis. This region is known as the tion by interfibrillar and interfiber sliding, and consequently, “toe” region, and it normally extends to approximately 2% the tissue does not return to the original length and structure elongation [28]. The toe region lies within the elastic limit, after unloading. In the last region (yield and failure region), and thus, the tissue will return to its original length when in which macroscopic defects occur, yielding begins as the unloaded. Further straining brings the tissue into the “linear” slope of the curve decreases, with inevitable tissue failure region which exhibits constant Young’s modulus. The stress- occurring with further load [28, 29]. Achilles tendon 4 Applied Bionics and Biomechanics Table 1: Elastic moduli of different human tendons, ligaments, and skin. Soft tissue type Source Test method Young’s modulus (MPa) Ref. Plantaris tendon In vitro tensile 1 24 × 10 [17] Anterior tibialis tendon Ultrasonography 0 45 − 1 2× 10 [18] 1 − 5× 10 Peroneus longus tendon In vitro tensile [19] Peroneus brevis tendon In vitro tensile 1 − 4× 10 [19] 0 5 − 3 5× 10 Calcaneal tendon In vitro tensile [19] Human ankle tendons & ligaments Calcaneofibular ligament In vitro tensile 0 7 − 4 5× 10 [19] Achilles tendon Ultrasonography 2× 10 [20] 0 45 − 2 7× 10 Deltoid ligaments CT, MRI, and finite element modeling [21] Medial collateral ligaments In vitro tensile 0 99 − 3 2× 10 [22] Lateral collateral ligaments In vitro tensile 2 16 − 5 12 × 10 [22] Neck MRI and finite element modeling ~2 [23] −1 Breast Suction cup method 2 − 4 8×10 [24] −1 Human skin Arm In vivo tensile (extensometer) 3 − 6 57 × 10 [25] −3 Arm In vivo indentation 4 5 − 8×10 [26] −3 ~8 5×10 Arm In vivo indentation [27] excess pain to the patient that may be generated in larger sin- UTS Failure strain gle stretches. 3.2. Ponseti’s Loading: Stress Relaxation. A tendon or a liga- ment displays a time-dependent mechanical behavior known as viscoelasticity, which means it possesses both elastic and viscous properties [30]. Due to the viscoelastic behavior, ten- dons and ligaments display three characteristics: hysteresis, creep, and stress relaxation. Ponseti Creep describes the continuous increase in strain or region deformation under constant loading force. The shape of the deformation-time curve during a creep test is dependent on the loading history (loading force, loading rate, and force Yield & Toe Linear increments) [31, 32]. Wren et al. reported that the time to failure failure decreases with increasing applied stress and increas- 𝜀 ing initial strain [33]. UTS Strain A stress relaxation, demonstrated in Figure 5, describes the continuous decrease in stress over time under constant Figure 3: A typical stress-strain curve of a tendon or a ligament. strain. The relaxation rate of the stress is believed to be faster Ultimate tensile strength (UTS) is the maximum stress that a with a higher initial peak stress [34–36]. Under different material can withstand while being tensile loaded. Arbitrary values. strain rates applied to reach the initial strain, the tendon or ligament will display different relaxation profiles. With a In the Ponseti treatment, the stretch caused by manipula- higher strain rate, the corresponding peak stress will be tion as aimed at producing sufficient plastic deformation of higher, resulting a faster relaxation [31, 37]. the tendons and ligaments to encourage tissue remodeling It is worth highlighting that stress relaxation is an impor- and lengthening. This deformation will normally lie within tant event in the Ponseti method. As the clubfoot is held at an the middle part of the linear region (red bracket in improved position by casting after manipulation, a constant Figure 3), as excess deformation would be painful and risk strain or deformation is applied, and consequently, stress entering the yield and failure region, and insufficient defor- relaxation occurs in the strained soft tissues. The exponential mation would prove ineffective. Notably, the total deforma- relaxation is controlled by two events occurring in the tissues: (1) the microstructure rearrangement and (2) tissue growth. tion needed to correct a clubfoot is greater than the failure strain in a single stretch, as displayed in Figure 4, proving When stress relaxation begins, in response to the constant that multiple stretches and castings are required in the Pon- strain, the collagen fibers and fibrils start to reorganize them- seti method. This factor is also clinically important, avoiding selves through interfiber and interfibrillar sliding controlled Stress (Pa) Applied Bionics and Biomechanics 5 Failure, tissue damage Repeated tissue remodeling Strain Figure 4: Comparison between a single tensile stretch (blue curve) and a Ponseti manipulation-casting sequence (red curve; sequential stress relaxation). Arbitrary values. Peak stress also faster in the higher initial strain group. Therefore, by introducing a smaller strain (smaller correction) or a shorter cast period for each casting phase, the stretched tendons and ligaments should be able to maintain stronger mechanical strength. Since the correction strain in each cast Exponential is smaller, the required number of casts has to increase in decay this modification. In ex vivo studies [36, 39–41], the time to plateau (relaxation time) for tendons is within an hour (2 minutes–1 hour). However, these experiments excluded Plateau the soft tissue remodeling (adaptation) which will occur in vivo during the treatment. In sum, the determination of the optimum cast-maintaining time needs consideration of the initial stain size, strain rate, relaxation time, and suf- ficient tissue remodeling. Time 3.3. Strain Rate Sensitivity. The mechanical response of the tissue is dependent on the strain rate. In general, a faster Figure 5: A typical stress-time curve of a single stress relaxation. loading results in a higher elastic modulus [42–45], as typi- Arbitrary values. cally exhibited by polymers. Pioletti et al. [46] demonstrated that the bovine ACL displayed higher elastic moduli when by the matrix molecules (proteoglycans). At the same time, stretched under higher strain rates (0.1, 1, 5, 10, 20, 30, and -1 recognizing these microstructural deformations, tissue 40% s ); in addition, the corresponding stress at the same remodeling causes subtle tissue growth, which in turn also strain value showed a positive correlation with strain rate as contributes to the stress relaxation. The existing work of well. Woo et al. [47] and Danto and Woo [42] studied this in vitro stress relaxation on tendons and ligaments only effect under wider ranges of strain rates on medial collateral -1 assesses the effect of microstructure rearrangement, without ligaments (0.011-222% s ) and rabbit patellar tendons -1 assessing the effect of tissue growth. It is thus reasonable to (0.016-135% s ), respectively, and both showed the same predict that the in vivo stress relaxation during a Ponseti positive correlation between elastic modulus and strain rate. stretch would be faster than the in vitro tests. According to the results from Bonner et al. [48], by plotting Multiple manipulation-casting cycles are required in the elastic modulus against strain rate, we can see a logarithmic Ponseti method for effective clubfoot treatment, representing relation between them (Figure 6). Hence, when a strain sequential stress relaxations on a stress-strain curve below a critical value of strain rate is applied, the mechan- (Figure 4). To further study or improve the Ponseti method, ical properties of tendons and ligaments show stronger measurements should be made to quantify the amount of the strain rate sensitivity. This critical rate could vary depend- strain generated, the strain rate, and the corresponding peak ing on the specific tendon or ligament tested, patient stress in each casting. Rossetto et al. [38] discovered that both demographics, and comorbidities. (1) a higher initial strain and (2) a longer relaxation duration The increase in ultimate tensile strength (UTS)/failure would result in lower tensile strength (tested right after relax- stress and decrease in strain at UTS (ɛ )/failure strain with UTS ation) in bovine calcaneal tendons. The relaxation rate was increased strain rate were also reported (Table 2) [48–50]. Stress Stress 6 Applied Bionics and Biomechanics 1000 1000 0 2000 4000 6000 8000 10000 12000 14000 Log (𝜀) Strain rate, 𝜀 (%/s) (a) (b) Figure 6: (a) Elastic modulus plotted against strain rate. (b) Elastic modulus plotted against the logarithm of strain rate [48]. These differences in mechanical response according to differ- repairing, and modifying the ECM in tendons and ligaments. ent strain rates can be seen in Figure 7. Fibroblast proliferation, morphology, alignment, and gene An in situ X-ray study on rat tail tendons conducted by expression have been reported to be influenced by mechani- Bailey et al. [51] showed that the deformation of tendon is cal stimuli [58–60]. In terms of ECM synthesis and remodel- always larger than that of the individual fibrils, which sug- ing, studies have shown that cyclic tension on fibroblasts can gests additional deformation in the ground substance increase collagen type I and collagen type III mRNA expres- matrix. In addition, the ratio of fibril deformation to ten- sion [60, 61]. These changes cause the number, diameter, and don deformation increased as the strain rate increased in concentration of collagen fibrils to increase, thus increasing their experiment, i.e., the matrix becomes stiffer under the stiffness of the tissue [62, 63]. By contrast, compression higher strain rates. This phenomenon is believed to be loading is believed to induce the synthesis of proteoglycans caused by the decreased time for effective fluid flow, energy and type II collagen and, in some cases, a decrease in collagen dissipation, and structural matrix rearrangement of the type I [64–66]. This change in composition results in the for- interfibrillar ground substance at higher strain rates [52], mation of fibrocartilaginous matrix [64]. The adaptation of a resulting in a smaller deformation of ground substance tendon or a ligament is dependent on the type of loading, and a higher modulus tendon. Hence, further tension under strain magnitude, strain rate, and number of cycles. It is high loading rates would cause the disruption of matrix- worth mentioning that most existing studies on the effect of fibril bonding and poor transmission of stress between mechanical stretching on tissue adaptation applied short- fibrils, which then lead to uncontrolled interfibrillar sliding term cyclic straining rather than static straining to the tissue and macroscopic failure [48, 51]. [58–61, 67]. On the other hand, under a consistent strain rate These studies on strain rate sensitivity of tendons and lig- or sequential stress relaxations for a longer period of time, the aments may help us understand and predict the stress-strain tissue response and adaptation will be different. response in the biological system. For example, when a club- The Ponseti method utilizes a static stretch to a certain foot is manipulated or stretched under a certain force, the strain value during manipulation, followed by stress relaxa- expected strain or deformation of a tendon or a ligament tion during casting. This stretch-casting sequence is repeated can be designed by altering the strain rate. Furthermore, high several times (sequential stress relaxations), thus generating a -1 strain rates, which are known to cause injuries (>50% s ) and stepwise strain profile (Figure 8). Recent studies [68, 69] have low ɛ (Table 2) [48, 49, 53, 54], should be avoided. shown that clubfeet with more severe deformities can be UTS treated by increasing the number of castings. Nevertheless, 3.4. Mechanical Adaptation. Unlike synthetic materials, bio- the effect of the number of casts on the efficiency and correc- tion rate of Ponseti treatment has not yet been investigated. logical materials including tendons and ligaments are capable of adapting to chemical and physical stimuli. The cells in a In 2008, Screen [70] compared a single stress relaxation with tendon or a ligament, which express a fibroblastic phenotype, sequential stress relaxations to the same amount of strain on rat tail tendons. Higher levels of interfiber relaxation, interfi- are responsible for responding to stimuli by producing growth factors [55], synthesizing collagen and ground sub- brillar relaxation, and stress relaxation were observed in the single-step strained tendon. Lacking previous strain steps to stance of the ECM [56], and remodeling old ECM by releas- ing matrix metalloproteinases (MMPs) [57]. reorganize the collagen structure, these single-step strained Mechanical loading or straining is a key stimulus which tendons are believed to have a higher risk of additional dam- generates a series of signals responsible for maintaining, age or loss of mechanical integrity. Elastic modulus (MPa) Elastic modulus (MPa) Applied Bionics and Biomechanics 7 Table 2: Existing work demonstrating the strain rate sensitivity of tendons and ligaments. -1 Source Strain rate (% s ) Elastic modulus (MPa) UTS (MPa) ɛ (%) Ref. UTS 10 401.1 73.3 25.2 Human Achilles tendon [49, 50] 100 544.7 81.3 21.0 -1 Source Strain rate (% s ) Elastic modulus (MPa) Failure stress (MPa) Failure strain (%) Ref. 1 288 39.9 17 10 364 56.5 18 Porcine lateral collateral ligament 94 656 72.8 14 [48] 1060 763 75.9 11 12990 906 77.4 9 UTS, fast UTS, slow 𝜀 𝜀 UTS, fast UTS, slow Strain Strain Figure 7: Stress-strain curves of a tendon or ligament stretched Figure 9: Illustrative stress-strain profiles of normal Ponseti under a slow strain rate (blue) and a fast strain rate (red). sequential stretches (red), and a modified sequence (blue) with Arbitrary values. smaller strain steps, shorter casting duration, and a higher number of casts. Arbitrary values. a lower strain rate profile. This low strain-rate profile may provide the total correction process a larger ɛ (Figure 7). UTS Furthermore, when more straining steps are applied, the overall stress-time profile shows higher stresses throughout compared with a single straining step [70]. A longer period of higher stresses maintained can be seen as “additional” ten- sile stimuli without overstretching the tissue. These gradual strain steps may also help the cells to “catch up” and remodel the ECM before considerable defects or ruptures occur. Figure 9 compares the stress-strain curves between a normal Ponseti method and a modified version with more castings. In Figure 8, as the number of steps increases, the profile becomes comparable to a constant strain rate stretching. Although this approach would require more attendances by Time patients and shorter intervals between manipulations, it Figure 8: Incremental strain steps over time illustrating the might improve the efficiency of the treatment. Kalson et al. sequential stretches in the Ponseti method performed in 1 step [71] experimented the effect of static stretching on adapta- (red), 2 steps (blue), 10 steps (yellow), and infinite steps (green). tion by slow stretching (0.25%/day) a tendon-like construct Arbitrary values. seeded with embryonic tendon cells for 4 days. The result showed increased collagen fibril diameter, fibril length, fibril number, and mechanical stiffness. The increase in the colla- By decreasing the size of the strain step and increasing the numbers of steps (castings), the overall strain-time profile gen fibril length and number is a promising indication of ten- don growth or lengthening which is expected and desired in shown in Figure 8 appears to display decreasing slopes, i.e., Stress Stress Stress 8 Applied Bionics and Biomechanics additional tolerance of strain is attributed to the tissue adap- tation process during the immobilization by casting. Due to the viscoelastic properties of tendons and liga- ments, the initial strain size, strain rate, and loading history will affect the relaxation behavior and mechanical strength of the tissue. Ideally, the manipulation should be performed as slowly as possible as under a lower strain rate shown in Figures 6 and 7, the tendon or ligament shows lower resis- tance due to lower elastic modulus and higher tolerance of strain (higher ɛ ). To increase the efficiency of the Ponseti UTS treatment, we suggest consideration of decreasing the size of the strain step and interval of casting and/or increasing the overall number of casts. This modification may produce a lower overall strain rate profile (Figure 8), provide more ten- sile stimuli, allow more time for remodeling, and preserve the mechanical integrity of the soft tissues. Time Slow strain rate Standard ponseti Consent Figure 10: Stress-time profile comparing a standard Ponseti stress All authors have consented for submission and publication of relaxation (blue) and a slow straining stress relaxation (red). this paper. Arbitrary values. Disclosure the Ponseti treatment. There are therefore possible potential benefits to treating clubfoot with a larger number of smaller, MK and MHL are considered co-first authors. more frequent corrections. The efficiency of the treatment could also be improved Conflicts of Interest by lowering the strain rate of the stretch before casting (first region before initial stress in Figure 5). As shown The authors declare no conflicting interests. in Figure 10, under a lower strain rate during stretching, a smaller peak stress is generated in response to the same Authors’ Contributions value of strain. Since the peak stress is lowered, the time required for stress relaxation (plateau) is also shortened, The idea for this project was conceived by CL. MHL and MK thus reducing the time interval between each cast. This mod- contributed to the writing of the first draft of this work. JC ification allows the surgeon to produce the same degree of and CL reviewed and critically appraised the work. All correction while reducing the casting period. However, some authors have read and approved the manuscript. limitations do exist in this study. This paper is theoretical in nature and utilises arbitrary values derived from the liter- Acknowledgments ature. Some of these values were extrapolated from work investigating human adults, cadavers, or animal models. 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An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment

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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4308462, 11 pages https://doi.org/10.1155/2019/4308462 Review Article An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment 1 2 2 1 Murtaza Kadhum , Mu-Huan Lee, Jan Czernuszka, and Chris Lavy Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Science, Oxford University, UK Department of Materials, Oxford University, UK Correspondence should be addressed to Murtaza Kadhum; murtaza.kadhum@medsci.ox.ac.uk Received 6 November 2018; Accepted 14 January 2019; Published 25 March 2019 Academic Editor: Jose Merodio Copyright © 2019 Murtaza Kadhum et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Congenital clubfoot is a complex pediatric foot deformity, occurring in approximately 1 in 1000 live births and resulting in significant disability, deformity, and pain if left untreated. The Ponseti method of manipulation is widely recognized as the gold standard treatment for congenital clubfoot; however, its mechanical aspects have not yet been fully explored. During the multiple manipulation-casting cycles, the tendons and ligaments on the medial and posterior aspect of the foot and ankle, which are identified as the rate-limiting tissues, usually undergo weekly sequential stretches, with a plaster of Paris cast applied after the stretch to maintain the length gained. This triggers extracellular matrix remodeling and tissue growth, but due to the viscoelastic properties of tendons and ligaments, the initial strain size, rate, and loading history will affect the relaxation behavior and mechanical strength of the tissue. To increase the efficiency of the Ponseti treatment, we discuss the theoretical possibilities of decreasing the size of the strain step and interval of casting and/or increasing the overall number of casts. This modification may provide more tensile stimuli, allow more time for remodeling, and preserve the mechanical integrity of the soft tissues. Some surgical techniques have been shown to pose a greater 1. Background risk of pain, stiffness, avascular necrosis, infection, overcor- Congenital clubfoot or congenital talipes equinovarus rection, poor long-term ankle range of movement, weakened (CTEV) is a complex pediatric foot deformity (Figure 1). It mechanical strength, and arthritis than if treated conserva- consists of four complex foot abnormalities with varying tively [5–8]. Interestingly, some studies have also reported a correlation between the extent of release surgery and degree degrees of rigidity, namely, midfoot cavus, forefoot adductus, hindfoot varus, and hindfoot equinus [1, 2]. The incidence is of functional impairment [6]. To date, surgical options are widely reported as 1 in 1000 live births in the UK with males mainly employed to manage resistant cases and recurrence being affected about twice as often as females [1, 3]. In almost or if unable to achieve complete correction of the deformity. half of affected infants, both feet are involved. To date, the Currently, the optimal treatment utilizes the Ponseti causes of clubfoot are poorly understood and regarded as idi- method, developed by Ignacio Ponseti in the 1940s [5, 9]. opathic; however, genetic factors and associated conditions This technique consists of two distinct stages of manipula- such as spinal bifida, cerebral palsy, and arthrogryposis have tion and maintenance. The manipulation phase involves been reported [1, 3, 4]. identifying the head of talus to use as a fulcrum, supinating If left untreated, clubfoot inevitably leads to significant the forefoot to eliminate the cavus deformity, and then long-term disability, deformity, and pain [2]. Although vari- abducting the forefoot. This manipulation is then followed ous surgical techniques are used to correct clubfoot, such as up by application of a plaster cast, holding the foot in the cor- soft tissue releases or bony procedures in older children, cur- rected position and providing sufficient time for soft tissue rently, conservative management is the preferred option. remodeling. This manipulation-casting sequence is repeated 2 Applied Bionics and Biomechanics To note, in both of these studies [15, 16], the measurement of soft tissue elasticity was performed on patients undergoing or already treated with the Ponseti method. More informa- tion about the mechanical properties of the soft tissues in untreated clubfeet is needed for comparison. 2.2. Rate-Limiting Tissue: Tendon and Ligament. During the manipulation process of the Ponseti method, the soft tissues responding (or resisting) to stretching include the following: (1) skin, (2) capsule, and (3) tendons and ligaments. To investigate the main tissue that is restricting the foot from reaching the improved position during stretching, the stress values generated from the skin (σ ), capsule (σ ), and skin cap Figure 1: Bilateral clubfeet in a newborn infant. Image taken from tendons and ligaments (σ ) due to the mechanical stretch CURE International with permission. TL are required. To date, the stress values and elastic moduli (E , E , and E ) in these soft tissues in response to on a weekly basis for an average of six weeks, until a 50- skin cap TL degree abduction of the foot around the tibia is achieved. stretching via the Ponseti method have not been studied. An Achilles tenotomy may then be required to eliminate First, consider a simple model simulating hindfoot dorsi- any residual equinus and is followed up by three weeks in a flexion to correct the equinus deformity (Figure 2) in which a cast to aid healing in the lengthened position [1, 5, 9–11]. tendon tissue (red curve) and a skin tissue (blue curve) are The maintenance phase then involves holding the foot in located at distances of d and d , respectively, from tendon−P skin−P an abduction brace for 23 hours per day for 3 months, help- the fulcrum (P). To introduce deformations of the tendon ing to reduce recurrence rates [10, 11]. Zionts et al. [12] (ε ) and skin (ε ) by Ponseti manipulation, an angular TL skin reported that due to the increased use of the Ponseti method, change from θ to θ with respect to P is generated. Examin- 0 1 the estimated percentage of clubfoot treated with surgical ing only the differences in the distance to the manipulation release has dropped from 72% in 1996 to 12%. fulcrum between the two tissues, the forces needed on the tis- sues will be different to create the same angular change (or torque value). Based on the principle of leverage, a larger 2. Main Text force is exerted on the tendon compared to the skin as the 2.1. Clubfoot Abnormalities. Due to the deformities, the tendon is located closer to the fulcrum. dimension, structure, and mechanical properties of most Second, the resistance of the tissues to stretch (stiffness) soft tissues in a clubfoot are different to those of a normal should also be considered. The general constitutive stress- foot. The presence of shortened, thickened, and fibrotic strain relation can be described with the following: tissues at the medial and posterior aspect of the clubfoot has been reported in several studies [13, 14]. This includes σ = E ⋅ ε 1 thickening and shortening of the posterior tibial tendon, Achilles tendon, tibionavicular ligament (deltoid ligament), By calculating the product of Young’s modulus of the tis- and plantar calcaneonavicular ligament. In addition, a sue and the strain value produced by the stretch, the stress value required for manipulation can be acquired. A single fibrous matrix was also seen in the posterior fibulotalar and deltoid ligaments. stretch from a manipulation and casting will generate strain To our knowledge, no work on measuring the mechanical values (ε , ε , and ε ) in each tissue. Typically, ε skin cap TL skin properties of the tendons and ligaments in a clubfoot by and ε will have approximately the same value, while ε TL cap direct mechanical testing has been conducted. Masala et al. will be much smaller than ε and ε in any given stretch; skin TL [15] investigated the difference in mechanical properties of hence, here we consider only tendons and ligaments and skin the Achilles tendon between a clubfoot and a normal foot in our comparison. Young’s moduli of human tendons and by real-time sonoelastography (RTSE). The results show ligaments and human skin at the ankle from existing studies lower mean elasticity values from the Achilles tendons of are listed in Table 1. the clubfeet compared to normal feet (unilateral clubfoot As Young’s moduli of the tendons (lowest: 50 MPa) are patients), demonstrating that the Achilles tendon is stiffer larger than those of the skin (highest: 2 MPa) with almost in a clubfoot. Hattori et al. [16] compared the moduli of soft similar tissue-fulcrum distances, larger stresses (or resis- tissue on the medial, lateral, and posterior aspects of a tance) are generated from the tendons during the Ponseti clubfoot by a scanning acoustic microscope (SAM). They dis- treatment. Tendons and ligaments, therefore, are the rate- covered higher Young’s modulus for the calcaneofibular liga- limiting soft tissues in the treatment of clubfoot. ment compared to the deltoid ligament. This result implies that the lateral soft tissue contracture could also be responsi- 3. Tendon and Ligament Mechanical Properties ble for some of the clubfoot deformities. However, the tissue samples used in this study were fixed in 4% paraformalde- 3.1. Stress-Strain Curve. A typical stress-strain curve for a hyde before measurement, thus leading to excess crosslinking tensile test on a tendon or a ligament is demonstrated in in the ligaments that would result in higher stiffness values. Figure 3. The graph shows three distinct regions [28, 29]. Applied Bionics and Biomechanics 3 skin tendon Fulcrum skin−P P 0 tendon−P (a) Tibia Talus Calcancus Navicular Medial cuneiform Proximal phalanx (b) Figure 2: (a) Illustrative model of the deformations of the two different tissues (tendon and skin) due to a stretch with respect to a common fulcrum to correct equinus. The size of the force exerted to deform individual tissue is inversely proportional to the distance between the tissue and the fulcrum. (b) Diagram of the medial side of a foot with the red line indicating the talus-Achilles length and blue line indicating the talus-skin length. Initially, the collagen crimps are stretched out, and an strain response mainly comes from elongating the aligned increasing number of collagen fibers and fibrils become fibers and fibrils. Further straining induces plastic deforma- aligned to the loading axis. This region is known as the tion by interfibrillar and interfiber sliding, and consequently, “toe” region, and it normally extends to approximately 2% the tissue does not return to the original length and structure elongation [28]. The toe region lies within the elastic limit, after unloading. In the last region (yield and failure region), and thus, the tissue will return to its original length when in which macroscopic defects occur, yielding begins as the unloaded. Further straining brings the tissue into the “linear” slope of the curve decreases, with inevitable tissue failure region which exhibits constant Young’s modulus. The stress- occurring with further load [28, 29]. Achilles tendon 4 Applied Bionics and Biomechanics Table 1: Elastic moduli of different human tendons, ligaments, and skin. Soft tissue type Source Test method Young’s modulus (MPa) Ref. Plantaris tendon In vitro tensile 1 24 × 10 [17] Anterior tibialis tendon Ultrasonography 0 45 − 1 2× 10 [18] 1 − 5× 10 Peroneus longus tendon In vitro tensile [19] Peroneus brevis tendon In vitro tensile 1 − 4× 10 [19] 0 5 − 3 5× 10 Calcaneal tendon In vitro tensile [19] Human ankle tendons & ligaments Calcaneofibular ligament In vitro tensile 0 7 − 4 5× 10 [19] Achilles tendon Ultrasonography 2× 10 [20] 0 45 − 2 7× 10 Deltoid ligaments CT, MRI, and finite element modeling [21] Medial collateral ligaments In vitro tensile 0 99 − 3 2× 10 [22] Lateral collateral ligaments In vitro tensile 2 16 − 5 12 × 10 [22] Neck MRI and finite element modeling ~2 [23] −1 Breast Suction cup method 2 − 4 8×10 [24] −1 Human skin Arm In vivo tensile (extensometer) 3 − 6 57 × 10 [25] −3 Arm In vivo indentation 4 5 − 8×10 [26] −3 ~8 5×10 Arm In vivo indentation [27] excess pain to the patient that may be generated in larger sin- UTS Failure strain gle stretches. 3.2. Ponseti’s Loading: Stress Relaxation. A tendon or a liga- ment displays a time-dependent mechanical behavior known as viscoelasticity, which means it possesses both elastic and viscous properties [30]. Due to the viscoelastic behavior, ten- dons and ligaments display three characteristics: hysteresis, creep, and stress relaxation. Ponseti Creep describes the continuous increase in strain or region deformation under constant loading force. The shape of the deformation-time curve during a creep test is dependent on the loading history (loading force, loading rate, and force Yield & Toe Linear increments) [31, 32]. Wren et al. reported that the time to failure failure decreases with increasing applied stress and increas- 𝜀 ing initial strain [33]. UTS Strain A stress relaxation, demonstrated in Figure 5, describes the continuous decrease in stress over time under constant Figure 3: A typical stress-strain curve of a tendon or a ligament. strain. The relaxation rate of the stress is believed to be faster Ultimate tensile strength (UTS) is the maximum stress that a with a higher initial peak stress [34–36]. Under different material can withstand while being tensile loaded. Arbitrary values. strain rates applied to reach the initial strain, the tendon or ligament will display different relaxation profiles. With a In the Ponseti treatment, the stretch caused by manipula- higher strain rate, the corresponding peak stress will be tion as aimed at producing sufficient plastic deformation of higher, resulting a faster relaxation [31, 37]. the tendons and ligaments to encourage tissue remodeling It is worth highlighting that stress relaxation is an impor- and lengthening. This deformation will normally lie within tant event in the Ponseti method. As the clubfoot is held at an the middle part of the linear region (red bracket in improved position by casting after manipulation, a constant Figure 3), as excess deformation would be painful and risk strain or deformation is applied, and consequently, stress entering the yield and failure region, and insufficient defor- relaxation occurs in the strained soft tissues. The exponential mation would prove ineffective. Notably, the total deforma- relaxation is controlled by two events occurring in the tissues: (1) the microstructure rearrangement and (2) tissue growth. tion needed to correct a clubfoot is greater than the failure strain in a single stretch, as displayed in Figure 4, proving When stress relaxation begins, in response to the constant that multiple stretches and castings are required in the Pon- strain, the collagen fibers and fibrils start to reorganize them- seti method. This factor is also clinically important, avoiding selves through interfiber and interfibrillar sliding controlled Stress (Pa) Applied Bionics and Biomechanics 5 Failure, tissue damage Repeated tissue remodeling Strain Figure 4: Comparison between a single tensile stretch (blue curve) and a Ponseti manipulation-casting sequence (red curve; sequential stress relaxation). Arbitrary values. Peak stress also faster in the higher initial strain group. Therefore, by introducing a smaller strain (smaller correction) or a shorter cast period for each casting phase, the stretched tendons and ligaments should be able to maintain stronger mechanical strength. Since the correction strain in each cast Exponential is smaller, the required number of casts has to increase in decay this modification. In ex vivo studies [36, 39–41], the time to plateau (relaxation time) for tendons is within an hour (2 minutes–1 hour). However, these experiments excluded Plateau the soft tissue remodeling (adaptation) which will occur in vivo during the treatment. In sum, the determination of the optimum cast-maintaining time needs consideration of the initial stain size, strain rate, relaxation time, and suf- ficient tissue remodeling. Time 3.3. Strain Rate Sensitivity. The mechanical response of the tissue is dependent on the strain rate. In general, a faster Figure 5: A typical stress-time curve of a single stress relaxation. loading results in a higher elastic modulus [42–45], as typi- Arbitrary values. cally exhibited by polymers. Pioletti et al. [46] demonstrated that the bovine ACL displayed higher elastic moduli when by the matrix molecules (proteoglycans). At the same time, stretched under higher strain rates (0.1, 1, 5, 10, 20, 30, and -1 recognizing these microstructural deformations, tissue 40% s ); in addition, the corresponding stress at the same remodeling causes subtle tissue growth, which in turn also strain value showed a positive correlation with strain rate as contributes to the stress relaxation. The existing work of well. Woo et al. [47] and Danto and Woo [42] studied this in vitro stress relaxation on tendons and ligaments only effect under wider ranges of strain rates on medial collateral -1 assesses the effect of microstructure rearrangement, without ligaments (0.011-222% s ) and rabbit patellar tendons -1 assessing the effect of tissue growth. It is thus reasonable to (0.016-135% s ), respectively, and both showed the same predict that the in vivo stress relaxation during a Ponseti positive correlation between elastic modulus and strain rate. stretch would be faster than the in vitro tests. According to the results from Bonner et al. [48], by plotting Multiple manipulation-casting cycles are required in the elastic modulus against strain rate, we can see a logarithmic Ponseti method for effective clubfoot treatment, representing relation between them (Figure 6). Hence, when a strain sequential stress relaxations on a stress-strain curve below a critical value of strain rate is applied, the mechan- (Figure 4). To further study or improve the Ponseti method, ical properties of tendons and ligaments show stronger measurements should be made to quantify the amount of the strain rate sensitivity. This critical rate could vary depend- strain generated, the strain rate, and the corresponding peak ing on the specific tendon or ligament tested, patient stress in each casting. Rossetto et al. [38] discovered that both demographics, and comorbidities. (1) a higher initial strain and (2) a longer relaxation duration The increase in ultimate tensile strength (UTS)/failure would result in lower tensile strength (tested right after relax- stress and decrease in strain at UTS (ɛ )/failure strain with UTS ation) in bovine calcaneal tendons. The relaxation rate was increased strain rate were also reported (Table 2) [48–50]. Stress Stress 6 Applied Bionics and Biomechanics 1000 1000 0 2000 4000 6000 8000 10000 12000 14000 Log (𝜀) Strain rate, 𝜀 (%/s) (a) (b) Figure 6: (a) Elastic modulus plotted against strain rate. (b) Elastic modulus plotted against the logarithm of strain rate [48]. These differences in mechanical response according to differ- repairing, and modifying the ECM in tendons and ligaments. ent strain rates can be seen in Figure 7. Fibroblast proliferation, morphology, alignment, and gene An in situ X-ray study on rat tail tendons conducted by expression have been reported to be influenced by mechani- Bailey et al. [51] showed that the deformation of tendon is cal stimuli [58–60]. In terms of ECM synthesis and remodel- always larger than that of the individual fibrils, which sug- ing, studies have shown that cyclic tension on fibroblasts can gests additional deformation in the ground substance increase collagen type I and collagen type III mRNA expres- matrix. In addition, the ratio of fibril deformation to ten- sion [60, 61]. These changes cause the number, diameter, and don deformation increased as the strain rate increased in concentration of collagen fibrils to increase, thus increasing their experiment, i.e., the matrix becomes stiffer under the stiffness of the tissue [62, 63]. By contrast, compression higher strain rates. This phenomenon is believed to be loading is believed to induce the synthesis of proteoglycans caused by the decreased time for effective fluid flow, energy and type II collagen and, in some cases, a decrease in collagen dissipation, and structural matrix rearrangement of the type I [64–66]. This change in composition results in the for- interfibrillar ground substance at higher strain rates [52], mation of fibrocartilaginous matrix [64]. The adaptation of a resulting in a smaller deformation of ground substance tendon or a ligament is dependent on the type of loading, and a higher modulus tendon. Hence, further tension under strain magnitude, strain rate, and number of cycles. It is high loading rates would cause the disruption of matrix- worth mentioning that most existing studies on the effect of fibril bonding and poor transmission of stress between mechanical stretching on tissue adaptation applied short- fibrils, which then lead to uncontrolled interfibrillar sliding term cyclic straining rather than static straining to the tissue and macroscopic failure [48, 51]. [58–61, 67]. On the other hand, under a consistent strain rate These studies on strain rate sensitivity of tendons and lig- or sequential stress relaxations for a longer period of time, the aments may help us understand and predict the stress-strain tissue response and adaptation will be different. response in the biological system. For example, when a club- The Ponseti method utilizes a static stretch to a certain foot is manipulated or stretched under a certain force, the strain value during manipulation, followed by stress relaxa- expected strain or deformation of a tendon or a ligament tion during casting. This stretch-casting sequence is repeated can be designed by altering the strain rate. Furthermore, high several times (sequential stress relaxations), thus generating a -1 strain rates, which are known to cause injuries (>50% s ) and stepwise strain profile (Figure 8). Recent studies [68, 69] have low ɛ (Table 2) [48, 49, 53, 54], should be avoided. shown that clubfeet with more severe deformities can be UTS treated by increasing the number of castings. Nevertheless, 3.4. Mechanical Adaptation. Unlike synthetic materials, bio- the effect of the number of casts on the efficiency and correc- tion rate of Ponseti treatment has not yet been investigated. logical materials including tendons and ligaments are capable of adapting to chemical and physical stimuli. The cells in a In 2008, Screen [70] compared a single stress relaxation with tendon or a ligament, which express a fibroblastic phenotype, sequential stress relaxations to the same amount of strain on rat tail tendons. Higher levels of interfiber relaxation, interfi- are responsible for responding to stimuli by producing growth factors [55], synthesizing collagen and ground sub- brillar relaxation, and stress relaxation were observed in the single-step strained tendon. Lacking previous strain steps to stance of the ECM [56], and remodeling old ECM by releas- ing matrix metalloproteinases (MMPs) [57]. reorganize the collagen structure, these single-step strained Mechanical loading or straining is a key stimulus which tendons are believed to have a higher risk of additional dam- generates a series of signals responsible for maintaining, age or loss of mechanical integrity. Elastic modulus (MPa) Elastic modulus (MPa) Applied Bionics and Biomechanics 7 Table 2: Existing work demonstrating the strain rate sensitivity of tendons and ligaments. -1 Source Strain rate (% s ) Elastic modulus (MPa) UTS (MPa) ɛ (%) Ref. UTS 10 401.1 73.3 25.2 Human Achilles tendon [49, 50] 100 544.7 81.3 21.0 -1 Source Strain rate (% s ) Elastic modulus (MPa) Failure stress (MPa) Failure strain (%) Ref. 1 288 39.9 17 10 364 56.5 18 Porcine lateral collateral ligament 94 656 72.8 14 [48] 1060 763 75.9 11 12990 906 77.4 9 UTS, fast UTS, slow 𝜀 𝜀 UTS, fast UTS, slow Strain Strain Figure 7: Stress-strain curves of a tendon or ligament stretched Figure 9: Illustrative stress-strain profiles of normal Ponseti under a slow strain rate (blue) and a fast strain rate (red). sequential stretches (red), and a modified sequence (blue) with Arbitrary values. smaller strain steps, shorter casting duration, and a higher number of casts. Arbitrary values. a lower strain rate profile. This low strain-rate profile may provide the total correction process a larger ɛ (Figure 7). UTS Furthermore, when more straining steps are applied, the overall stress-time profile shows higher stresses throughout compared with a single straining step [70]. A longer period of higher stresses maintained can be seen as “additional” ten- sile stimuli without overstretching the tissue. These gradual strain steps may also help the cells to “catch up” and remodel the ECM before considerable defects or ruptures occur. Figure 9 compares the stress-strain curves between a normal Ponseti method and a modified version with more castings. In Figure 8, as the number of steps increases, the profile becomes comparable to a constant strain rate stretching. Although this approach would require more attendances by Time patients and shorter intervals between manipulations, it Figure 8: Incremental strain steps over time illustrating the might improve the efficiency of the treatment. Kalson et al. sequential stretches in the Ponseti method performed in 1 step [71] experimented the effect of static stretching on adapta- (red), 2 steps (blue), 10 steps (yellow), and infinite steps (green). tion by slow stretching (0.25%/day) a tendon-like construct Arbitrary values. seeded with embryonic tendon cells for 4 days. The result showed increased collagen fibril diameter, fibril length, fibril number, and mechanical stiffness. The increase in the colla- By decreasing the size of the strain step and increasing the numbers of steps (castings), the overall strain-time profile gen fibril length and number is a promising indication of ten- don growth or lengthening which is expected and desired in shown in Figure 8 appears to display decreasing slopes, i.e., Stress Stress Stress 8 Applied Bionics and Biomechanics additional tolerance of strain is attributed to the tissue adap- tation process during the immobilization by casting. Due to the viscoelastic properties of tendons and liga- ments, the initial strain size, strain rate, and loading history will affect the relaxation behavior and mechanical strength of the tissue. Ideally, the manipulation should be performed as slowly as possible as under a lower strain rate shown in Figures 6 and 7, the tendon or ligament shows lower resis- tance due to lower elastic modulus and higher tolerance of strain (higher ɛ ). To increase the efficiency of the Ponseti UTS treatment, we suggest consideration of decreasing the size of the strain step and interval of casting and/or increasing the overall number of casts. This modification may produce a lower overall strain rate profile (Figure 8), provide more ten- sile stimuli, allow more time for remodeling, and preserve the mechanical integrity of the soft tissues. Time Slow strain rate Standard ponseti Consent Figure 10: Stress-time profile comparing a standard Ponseti stress All authors have consented for submission and publication of relaxation (blue) and a slow straining stress relaxation (red). this paper. Arbitrary values. Disclosure the Ponseti treatment. There are therefore possible potential benefits to treating clubfoot with a larger number of smaller, MK and MHL are considered co-first authors. more frequent corrections. The efficiency of the treatment could also be improved Conflicts of Interest by lowering the strain rate of the stretch before casting (first region before initial stress in Figure 5). As shown The authors declare no conflicting interests. in Figure 10, under a lower strain rate during stretching, a smaller peak stress is generated in response to the same Authors’ Contributions value of strain. Since the peak stress is lowered, the time required for stress relaxation (plateau) is also shortened, The idea for this project was conceived by CL. MHL and MK thus reducing the time interval between each cast. This mod- contributed to the writing of the first draft of this work. JC ification allows the surgeon to produce the same degree of and CL reviewed and critically appraised the work. All correction while reducing the casting period. However, some authors have read and approved the manuscript. limitations do exist in this study. This paper is theoretical in nature and utilises arbitrary values derived from the liter- Acknowledgments ature. Some of these values were extrapolated from work investigating human adults, cadavers, or animal models. 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