Article

# A growth-accommodating implant for paediatric applications

• Nature Biomedical Engineering 1818825 (2017)
• doi:10.1038/s41551-017-0142-5
Accepted:
Published online:

## Abstract

Medical implants of fixed size cannot accommodate normal tissue growth in children and often require eventual replacement or—in some cases—removal, leading to repeated interventions, increased complication rates and worse outcomes. Implants that can correct anatomical deformities and accommodate tissue growth remain an unmet need. Here, we report the design and use of a growth-accommodating device for paediatric applications that consists of a biodegradable core and a tubular braided sleeve, with inversely related sleeve length and diameter. The biodegradable core constrains the diameter of the sleeve, and gradual core degradation following implantation enables sleeve and overall device elongation to accommodate tissue growth. By means of mathematical modelling and ex vivo experiments using harvested swine hearts, we demonstrate the predictability and tunability of the behaviour of the device for disease- and patient-specific needs. We also used the rat tibia and the piglet heart valve as two models of tissue growth to demonstrate that polymer degradation enables device expansion and growth accommodation in vivo.

Thousands of surgeries are performed annually on children in the United States, and frequently these procedures involve implantation of a medical device to repair anatomical and morphological defects1. Existing surgical implants are extremely effective in many cases2; however, the inability of fixed-size implants to accommodate growth remains a challenge. In paediatric heart surgery, over 1,000 mitral and tricuspid heart valve procedures are performed in the United States each year1. In many cases regurgitant heart valves are pathologically dilated and must be tightened to restore normal size and function. This is true across a range of paediatric heart conditions, including endocardial cushion defects, hypoplastic left heart syndrome, congenital mitral regurgitation and Ebstein’s anomaly3,4,5,6. In adults with dilated heart valves, repair is accomplished by implanting a prosthetic ring on the dilated heart valve annulus7. Prosthetic annuloplasty rings have significantly improved valve repair durability and outcomes in adults8,9. In paediatrics, however, prosthetic rings cannot be used since their fixed size would restrict valve growth following implantation10. Paediatric heart surgeons must therefore use less durable, suture-based annuloplasty techniques11. Sutures are placed around the dilated valve annulus to cinch it down; however, these sutures break or pull through the tissue over time, resulting in pathological re-dilation of the valve and recurrent valve dysfunction. Although a biodegradable annuloplasty ring that fully degrades over several months was recently developed for use in children, the long-term outcomes are still questionable since the biodegradable ring loses mechanical integrity over time and may be subject to mechanical failure12,13. The lack of a suitable prosthetic ring that can reduce and stabilize the dilated paediatric heart valve but then allow for controlled, physiological growth is a major reason for the limited success of valve repair in children. Successful tricuspid valve repair is achieved in only 50% of children with single-ventricle anatomy, and failed repair is an independent risk factor for mortality4,14.

Disorders of long-bone growth, including limb length discrepancy and angular limb deformities, are among the most commonly treated non-traumatic conditions in paediatric orthopaedics15. They can be managed surgically by compression-based growth plate modulation, whereby fixed-size devices (for example, staples and plated systems) are implanted across the long-bone growth plate to temporarily slow bone growth and gradually correct angular limb deformities and limb length discrepancies16. Unfortunately, children require additional surgeries for device removal to avoid premature physeal closure, growth arrest and overcorrection since these devices are fixed in size17. Additionally, following implant removal, children are at risk for rebound growth, which is unpredictable and can require repeat surgical interventions to re-correct recurrent limb deformities18. Similar strategies of growth plate modulation are used to treat scoliosis—another of the most common paediatric orthopaedic conditions requiring surgery, with several thousand surgeries performed each year. An estimated 17,000 surgeries are performed annually to treat scoliosis in the United States1,19. Staples and vertebral body tethering systems are implanted along the convex side of the spine to asymmetrically restrict growth and allow the concave side to ‘catch up’20. However, with these fixed-size implants, overcorrection of the spine can occur requiring repeat surgical interventions for device revision and/or lengthening21,22. An implantable device with autonomous elongation potential could obviate the need for some re-interventions in children by accommodating physiological growth after skeletal deformity correction.

Here, we demonstrate a growth-accommodating device that employs a tubular braided sleeve and a biodegradable core. Sleeve length and diameter are inversely related due to the intrinsic geometry of the braid, so that thinning out of the sleeve results in elongation. This phenomenon has been exploited for pneumatic muscle actuators in soft robotics, where pneumatic expansion or contraction of an elastic bladder effects the shortening or lengthening of a surrounding braided mesh to mimic muscle contraction or elongation23. In the current concept, sleeve diameter is instead controlled by an inner biodegradable core, so that polymer core degradation is coupled to braid length and overall device elongation (Fig. 1a). The device is designed to initially constrict pathologically dilated tissue and correct the contours of malformed structures, as is needed during heart valve repair and correction of skeletal deformities. As the core degrades following implantation, the braided sleeve can thin out and elongate in response to surrounding tissue growth without requiring additional interventions. Importantly, the device design comprises only two principle elements, which helps promote device durability.

We demonstrate tunability and predictability of device behaviour based on the structural and chemical parameters of the braided sleeve and biodegradable core. By altering the braid geometry and polymer degradation rate, we could modify the device elongation profile to target a range of paediatric applications. To maintain the device’s mechanical strength throughout polymer core degradation and ensure conformability around different tissue and organ contours, we used the surface-eroding, biodegradable, biocompatible polymer poly(glycerol sebacate) (PGS), which can possess the requisite mechanical properties to resist compressive forces from the braided sleeve24. The mechanical strength of the device was sufficient to withstand physiological stresses in two distinct in vivo environments. Using two animal models, we demonstrate that the device concept can initially constrict tissue following implantation but then accommodate native growth without requiring additional interventions.

## Autonomous growth accommodation

The ideal growth-accommodating device should: (1) achieve tissue/organ repair like current fixed-size devices, (2) gradually and continuously elongate in concert with native tissue growth in children, (3) possess a tunable and predictable elongation profile to enable disease- and patient-specific application, (4) be mechanically strong enough to withstand physiological stresses throughout growth after implantation, (5) possess a non-degradable element that remains implanted to provide long-term tissue support once the organ has completed growth and (6) be simple in design to facilitate rapid translation to clinical application. We chose a biaxial braid as the outer sleeve construct because the transformation of diameter change into length change can be precisely tailored to generate distinct elongation profiles, enabling better design flexibility. Braided sleeves enable the coupling of inner core degradation to overall device elongation: they are porous enough to allow access of body fluids to the biodegradable polymer core for hydrolytic degradation, but strong enough to stably contain the core.

To demonstrate how degradation of a surface-eroding core could be coupled to braid elongation to achieve gradual autonomous device elongation, we performed expedited ex vivo experiments in a water tank setup. One- and two-dimensional device expansions were studied since they resemble long-bone and heart valve growth, respectively. For the one-dimensional experiments, a biaxial nitinol braided sleeve (Creganna Medical) was tied down on either side of a spherical sucrose core. The sucrose core was used as an expedited alternative to surface-eroding polymers with significantly slower degradation rates. The braid and core device was exposed to a 2N tensile force to mimic the external forces of tissue growth and then submerged in room temperature water. The core diameter gradually decreased over 55 min as the sugar core dissolved underwater, which enabled gradual elongation of the braided sleeve in response to the tensile force (Fig. 1b,c). This mimicked an orthopaedic device implanted along a growing long-bone that could initially limit and guide bone growth following implantation, but then could elongate to accommodate normal growth.

As a two-dimensional growth model, a device prototype was implanted around the tricuspid valve annulus in an ex vivo isolated swine heart preparation, in which physiological cardiac pressures were generated (Supplementary Fig. 1). A rudimentary annuloplasty ring, comprising an ethylene chlorotrifluorethyelene co-polymer biaxially braided sleeve and heat-moulded spherical sugar cores, immediately reduced the tricuspid valve annular area by approximately 25%, analogous to existing annuloplasty ring repairs (Fig. 1d). Placing the heart and device in room temperature water enabled dissolution of the inner spherical cores. Degradation of the core allowed braided sleeve elongation and re-expansion of the tricuspid valve annulus in a gradual and predictable manner akin to native heart valve growth in children (Fig. 1e and Supplementary Video 1). In both ex vivo experiments, core degradation was coupled to braided sleeve diameter and overall device length, thus creating a mechanism of autonomous device elongation and obviating the need for additional interventions to enlarge, elongate or replace the device. Importantly, device elongation, and thus surrounding tissue growth, could be controlled solely by degradation of the core.

## Analytical model for fine-tuning braid behaviour

To fine-tune the growth-accommodating device for paediatric use, a mathematical model describing braided sleeve behaviour was employed25. Braid parameters affecting the elongation profile include: initial sleeve length (Li), initial sleeve diameter (Di), instantaneous sleeve diameter (D) and pitch (that is, the number of fibre turns, c, per unit length). With these inputs, sleeve length (L) was defined as a function of sleeve diameter (equation(1)).

$L ( D )=√( ( π c D i ) 2 + L i 2 −( π c D 2 ))$
(1)

Adjusting braid pitch (c) created a range of unique elongation profiles, with higher pitch enabling greater length change for a given change in the degradable core diameter. Based on the model, devices assembled using a 2 mm core with braid pitches of 46, 54 and 60 picks inch–1 could elongate by 38.4, 50.6 and 62.8%, respectively. Experimentally measured sleeve lengths correlated well with predicted elongation curves (﻿r > 0.99) (Fig. 2a). This demonstrated how the use of a braid as the outer element imparts tunability and predictability on the device concept.

## Polymer development and device characterization

To assess the mechanical strength of a fully assembled device, ESPGS was inserted into an ultra-high-molecular-weight polyethylene (UHMWPE) braided sleeve and tested using a universal mechanical tester. ESPGS dramatically increased device modulus. Figure 2c demonstrates the relationship between the polymer curing time (at 155 °C) and device modulus. Lengthening the curing time significantly enhanced device stiffness. When ESPGS was cured for 86 h, the overall device modulus reached 173 MPa, exceeding the compressive modulus of conventional PGS and surpassing the Young’s modulus of commercially available surgical sutures (for example, PTFE and polydioxanone)30. To evaluate device fatigue, cyclic fatigue testing was performed. This showed that there was no fatigue related to the braided sleeve or the ESPGS core, which was critical for ensuring that controlled polymer core degradation, rather than polymer deformation, was responsible for device elongation (Fig. 2d).

Ex vivo testing was also performed to determine the effect of compressive stress on polymer core degradation. Device prototypes comprising a 1.8 mm ESPGS core and an outer UHMWPE braid sleeve were placed in a 0.1 M NaOH solution and exposed to varying magnitudes of tensile stress (applied to the ends of the braid) (Supplementary Fig. 2). Given the nature of the braid, a tensile stress applied to the braid translated to a compressive stress on the polymer core. Importantly, the amounts of stress applied to the devices were similar to those experienced at the growth plate28. The rate of polymer erosion was determined by measuring the polymer core diameter at various time points after initiating the experiment. Tensile stress on the braid had no impact on the core degradation rate, which is an important feature since it means core degradation is predictable regardless of how much stress is applied (Fig. 2e).

## In vivo bone-growth model

To demonstrate proof-of-principle of autonomous device elongation and tissue growth accommodation in an in vivo environment, a rat tibial bone growth model was developed. Young, growing male Wistar rats (150–200 g) underwent surgical implantation of a device prototype along the left tibia, analogous to conventional implants used to guide bone growth in children, and were studied for an eight-week period (Supplementary Fig. 3). Three animals received a growth-accommodating device with a degradable ESPGS core and three received a fixed-size device with a non-degradable PTFE core akin to existing implants (Fig. 3a). The right tibia served as a control. All animals underwent interval micro-computed tomography (CT) imaging to evaluate tibial growth.

Micro-CT images of the tibia and device in axial and sagittal cross-sections demonstrated the contrasting behaviour of the elongating and fixed-size devices over eight weeks. In animals receiving a device with a non-degradable core, the overall device length remained fixed (Fig. 3b), which was confirmed on direct examination at the time of the explant (Fig. 3c). In animals receiving a device with a degradable ESPGS core, the core became progressively thinner with degradation and the overall device length increased (Fig. 3d). Examination at the time of the explant confirmed this device elongation (Fig. 3e).

Importantly, device behaviour translated to distinct tibial growth profiles for the two animal groups when compared with the contralateral (right) limb (Fig. 3f). PTFE animals experienced significant and progressive growth restriction. Overall growth was only 20.0% over eight weeks compared with 32.0% growth in the unrestricted, right tibia (P = 0.006). There was near arrest of left tibial growth in the final four weeks of the study: 2.6% left tibial growth versus 7.1% right tibial growth (P = 0.01). By the end of the study, the left tibial length in PTFE animals was significantly shorter than the right tibial length (P = 0.004). The distinct growth trends in the final four weeks suggest that further growth differential would have occurred had the animals been studied for longer. The latter four weeks of the study, in principle, represent a time when device removal or exchange would be necessary in a growing child to avoid excessive growth restriction. ESPGS animals, in contrast, experienced continued, guided bone growth, following a more physiological growth pattern that was nearly identical to right tibial growth in the final four weeks (7.3 versus 7.1%; P = 0.98) (Fig. 3f). Arrest of bone growth was avoided because of autonomous device elongation, suggesting that this would prevent the need for device removal or exchange in a growing child.

Based on the device diameter change as measured by micro-CT, the device elongation profile was predicted using the braid elongation model (equation (1)) and compared with the actual device elongation profile (Fig. 3g). The observed device elongation closely correlated with predicted elongation (19% observed elongation over eight weeks versus 22.5% predicted elongation). This demonstrated that predictability could be achieved with the braided device concept in an in vivo environment.

## Proof-of-principle heart valve growth model

We further explored the use of the device on tissues in a more dynamic environment, namely, the heart valve in a growing piglet model. In this preliminary study, four growing female Yorkshire piglets (mean age: 7.3 ± 0.9 weeks) underwent surgical implantation of a growth-accommodating annuloplasty ring prototype on the tricuspid valve and were studied for 5, 12, 16 and 20 weeks to assess device behaviour and valve growth. We performed tricuspid valve annuloplasy rather than mitral valve annuloplasty because tricuspid valve surgery can be performed with the heart still beating and with a lower risk of systemic embolism. It was therefore felt that tricuspid surgery would be better tolerated by the piglets. We fabricated the growth-accommodating annuloplasty device to have a similar geometry to commercially available, fixed-size annuloplasty rings (Fig. 4a). The novel ring prototype was meant to reduce the valve size at implantation akin to existing rings and then expand to accommodate valve growth.

Valve size was measured with epicardial three-dimensional echocardiography immediately before and after ring implantation and at the time of euthanasia. Figure 4b shows the growth-accommodating ring prototype comprising an UHMWPE braided sleeve over a curved cylindrical ESPGS core. Figure 4c shows a magnified view of the sleeve’s biaxial braid configuration. The ring was implanted using the standard technique for ring implantation in adults: the ends of the braided sleeve were anchored to the valve annulus with sutures, and additional sutures were placed through the valve annulus and around the ring along its length (Fig. 4d). This enabled downsizing of the annulus and apposition of the ring to the annulus, as is typically achieved in heart surgery. At the time of euthanasia, the hearts were explanted to assess device fixation and ESPGS degradation.

In all cases, the ring remained well affixed to the valve annulus throughout the survival periods without evidence of dehiscence (Fig. 4e). This was probably promoted by the development of a collagen tissue layer over the device following implantation (Fig. 4f). ESPGS degradation was observed on direct inspection of explanted core segments (Fig. 4g). Cross-sections through explanted ring segments demonstrated areas of significant polymer core erosion following implantation (Fig. 4h, top), although there was regional variation with some segments experiencing less extensive core erosion (Fig. 4h, bottom). Echocardiographic evaluation showed that the tricuspid valve in each animal was effectively downsized by the growth-accommodating ring prototype at the time of surgery (Fig. 4i, pre-implant to post-implant). This demonstrated that the ring could withstand intra-cardiac forces and effectively constrain the valve, as is necessary in heart valve repair surgeries. Valve reduction was then followed by valve growth after device implantation (Fig. 4i, post-implant to euthanasia), although the growth rate varied among the animals. Valve function was assessed with two-dimensional colour Doppler and continuous wave Doppler epicardial echocardiography before and after ring implantation and at the time of euthanasia, looking specifically for evidence of tricuspid valve stenosis, regurgitation and peri-prosthetic leak. In all animals, valve function remained well-preserved with low velocity, laminar blood flow across the valve and no significant transvalvular gradient to suggest the development of tricuspid valve stenosis (Fig. 4j). Additionally, there was no evidence of significant leaflet regurgitation or peri-prosthetic leaking around the rings. This initial proof-of-concept study demonstrates the potential for controlling heart valve growth with core degradation using the growth-accommodating device concept.

## Discussion

Many existing fixed-sized surgical implants suffer limitations for paediatric use due to their inability to accommodate growth. In paediatric orthopaedics, fixed-size implants often require repeated interventions for implant removal or replacement to avoid excessive growth restriction. In paediatric heart valve surgery, fixed-size annuloplasty rings are avoided altogether given the risk of causing valve stenosis.

We demonstrate a concept for autonomous device elongation utilizing a biodegradable core that gradually decreases its diameter via surface erosion and an outer biaxially braided sleeve that transforms core diameter reduction into gradual, longitudinal device expansion to accommodate native tissue growth. Ex vivo and in vivo experimentation validated the concept of coupling polymer degradation to braided sleeve behaviour to achieve autonomous device elongation. In the presence of polymer core degradation, normal tissue growth was observed, whereas the absence of core degradation was associated with significant growth restriction. This demonstrated the link between device core degradation and growth accommodation.

The development of ESPGS was important for creating a device strong enough to withstand in vivo forces in humans. The human tibia generates approximately 1 MPa of compressive stress at the growth plate31. As in the rat, this amount of stress would cause minimal device strain (~ 3%), suggesting that the ESPGS device would be sufficiently strong for orthopaedic applications. The in vivo tensile stress on a prosthetic annuloplasty ring reaches approximately 5 MPa (ref. 32). This higher-magnitude stress is caused by the dynamic, beating heart; it can be inferred that slow and gradual cardiac tissue growth would generate much smaller stresses on a prosthetic ring that would not be sufficient to cause significant device strain. The braid/ESPGS ring would therefore only elongate in response to polymer degradation and would enable predictable, guided tissue growth. Importantly, in vitro studies also showed preservation of device strength after partial degradation, so even as the polymer core degraded the device would remain strong enough to withstand in vivo forces (Supplementary Fig. 2c).

Testing the device in two distinct in vivo models demonstrated how the surrounding microenvironment impacts device behaviour. In the orthopaedic rat model, device elongation correlated with ongoing bone growth throughout the study period. Notably, even with a fixed-size implant there was some bone growth in the first four weeks of the study. This is explained by two factors: (1) despite aiming to implant the device under tension, there was inevitably some slack in the implant that allowed for some degree of initial unrestricted growth, and (2) the tibia has two growth plates (proximal and distal) and the device only crossed the proximal growth plate, thus allowing for some growth at the distal growth plate.

In the swine heart model, polymer erosion and ring diameter decrease were observed, albeit to variable degrees (Fig. 4h). Some segments experienced more dramatic erosion and diameter decrease than others. This is in contrast with the rat bone growth model, in which polymer erosion and device elongation were fairly uniform along the device (Fig. 3d,e). The ideal device should undergo uniform core degradation and device elongation, and this will be a focus of future work. However, it is important to recognize that valve growth was accommodated in all animals despite core degradation not being perfectly uniform. Moreover, valve function was preserved without the development of valve stenosis, leaflet regurgitation or peri-prosthetic leak. This variability in polymer erosion may be partly explained by the growth of a collagen layer on the ring, which may have reduced access of water molecules and/or enzymes to the device, therefore slowing ESPGS degradation. Any variability in collagen overgrowth could have caused regional differences in core degradation and device expansion. Notably, in previous studies of subcutaneous PGS implantation, formation of a thin fibrotic capsule was observed, but PGS still fully degraded over weeks to months27,33. This suggests that our growth-accommodating device concept, despite inducing collagen overgrowth, would continue to experience core degradation, albeit at a slower rate.

There are several ways to modify the sleeve and polymer to encourage ongoing core degradation and device elongation. The number and thickness of braid fibres could be reduced to create a looser braid that would allow greater access of water molecules to the polymer core and facilitate continued polymer degradation. The required overall device strength would have to be considered when making any modifications to the braid fibre number or thickness since reducing the number and/or thickness of braid fibres would also reduce the tensile strength of the overall device. Fibre materials with a higher tensile modulus could be considered for this to maintain the device’s tensile strength. The use of a different braid material that induced a less pronounced fibrous tissue response could also facilitate ongoing polymer degradation and long-term device elongation. The wide range of available braid materials with unique tissue responses could permit the design of devices with distinct elongation behaviours. ESPGS can also be engineered to adjust the degradation profile without compromising the device’s overall mechanical strength. Alternative core geometries (for example, a row of spheres) would increase the polymer’s surface area-to-volume ratio and could enhance degradation. Future work is required to further characterize in vivo device behaviour, focusing on how polymer core degradation is impacted by changes in core geometry and sleeve porosity. This will be important when adjusting the device to target specific clinical applications.

This device concept is somewhat predicated on the ability to predict and approximate the growth rate of a child. In paediatric heart surgery, a Z-scoring system is widely used to normalize heart structures to body surface area. This system is used to appropriately size cardiac implants and help predict future growth34. In paediatric orthopaedics, the spinal growth rate is well characterized throughout childhood35. These growth patterns can be targeted when designing an autonomously elongating device. However, if the predicted growth rate is not accurate for a given patient, mismatches might occur between an implanted device and the patient. Although small mismatches might be well tolerated, larger mismatches could prove problematic for a child. Additionally since the growth rate of many bodily structures, such as the spine, varies throughout childhood, a device with a single, fixed growth rate would be unable to perfectly mirror somatic growth. A potential modification to the device concept involves a core made of several distinct layers, each composed of a unique polymer that possesses a distinct degradation profile. With this type of core, device elongation could be pre-programmed to have different elongation rates at different points following implantation. Even with this modification, the ability to adjust the device following implantation could still help alleviate potential patient–implant mismatches. An additional device modification could include light-triggered cleavable bonds in the ESPGS core, so that accelerated degradation could be triggered by external light. Near-infrared light, which can penetrate soft tissues, could be used so that device elongation could be adjusted without repeated surgical interventions. These proposed modifications to the device concept will be the subject of future work.

Importantly, the device concept comprises only two principle elements (a braided sleeve and a biodegradable core) that work closely in concert to enable growth. Having only two principle components should promote device durability because there are no interlocking or moving parts that are prone to breakdown or failure. Notably, ex vivo studies demonstrated no evidence of device fatigue, and all in vivo devices remained intact throughout the eight week rat study period and the 20 week piglet study period, during which devices were exposed to dynamic biological environments. The flexible nature of the braided sleeve and polymer further contributes to device durability, enabling the device to work in one or more dimensions.

While the braided sleeve and polymer core work in concert to enable growth, they can be independently modified to achieve a range of device elongation profiles that apply to a broad spectrum of clinical applications. In addition to the paediatric cardiac and orthopaedic surgeries already described, potential applications exist for oesophageal and intestinal atresias. The braid could be engineered to have shape memory, such that as the polymer degrades after implantation in the oesophagus or intestine the braid actively elongates to gradually increase the oesophageal or intestinal length. Another potential application is for the surgical treatment of mandibular condylar hyperplasia—a cause of asymmetric facial deformities in the case of unilateral condylar hyperplasia and prognathism (an underbite) in the case of bilateral mandibular condylar hyperplasia. When implanted on the affected condyle this device could limit growth due to condylar hyperplasia but then elongate to allow for normal mandibular growth. This could potentially improve existing surgical techniques, which involve either surgical resection to permanently arrest growth or allowing the disease to burn out and then performing delayed surgical correction36. The ex vivo device characterization and in vivo models presented here demonstrate initial proof-of-principle and form the basis for future work to optimize device design for different clinical needs in paediatrics. In this regard, the present work represents the foundation for a new paradigm of paediatric device development.

## Methods

To make ESPGS, a viscous PGS pre-polymer was synthesized via catalyst-free, solvent-free polycondensation of 0.1 mol each of glycerol and sebacic acid at 120 °C for 8 h in a nitrogen environment and for 16 h in vacuum. The resultant viscous PGS pre-polymer was then injected into thin-walled PTFE tubing (inner diameter = 1.8 mm), which acted as a sacrificial mould, and was then cured in a vacuum oven at 155 °C. Samples were cured up to 86 h to produce 1.8 mm ESPGS cylinders.

For the rat musculoskeletal study, which required a straight device to lie along the tibia, the polymer was cured within the PTFE tubing for 86 h. To create the curved ESPGS samples for the annuloplasty ring of the swine study, straight polymer cylinders were removed from the PTFE tubing after 42 h of curing, placed into an appropriate radius of curvature and cured at 155 °C for an additional 44 h. This division in curing intervals (42 h and 44 h) was chosen because sufficient curing within the straight PTFE tubing was required to produce freestanding polymer cylinders before inducing curvature.

Device manufacturing for the rat study involved insertion of the 1.8 mm diameter cylindrical ESPGS or PTFE core into the biaxially braided UHMWPE sleeve. The UHMWPE braid was manufactured by Biomedical Structures and had a pitch of 60 picks inch–1, with a 1/1 intersecting pattern (Fig. 4c). Twenty-four fibres were used to construct the braided sleeve, with each fibre being composed of 25 12 nm filaments. Two animals received a PTFE (Gore-Tex) braided sleeve for micro-CT imaging. Twelve CV-5 Gore-Tex sutures (W. L. Gore and Associates), each 0.246 mm in diameter, were braided in a 1/1 intersecting pattern around a 2.1 mm mandrel. After inserting the core inside the braided sleeve, a polypropylene (Prolene) suture (Ethicon) was tied to each end of the device; these sutures were used to anchor the device to the bone during surgical implantation.

The production of annuloplasty rings for the swine study involved insertion of a curved ESPGS core into a long segment of UHMWPE braided sleeve (Fig. 4b). The braid/ESPGS composite was then attached to a mounting device for surgical implantation, utilizing polyglactin 910 (Vicryl) sutures (Ethicon) (Supplementary Fig. 4). The mounting device was engineered using SolidWorks design software (2010 Standard Edition, ﻿Service Pack﻿ 0.0)and manufactured with a photoacrylic using an Alaris30 3D printer (Objet). All device implants used for in vivo experimentation underwent a standard ethylene oxide sterilization process before surgical implantation.

Both experimental animal protocols were approved by the Boston Children’s Hospital Institutional Animal Care and Use Committee. All animals received humane care in accordance with the 1996 Guide for the Care and Use of Laboratory Animals recommended by the United States National Institutes of Health. The experiments did not use a method of randomization. The investigators were not blinded to allocation during the experiments and outcome assessment.

### Statistical analyses

To determine the correlation between modelled and experimentally measured braided sleeve lengths (Fig. 2a), the Pearson correlation coefficient was calculated. For multiple comparisons, one-way analysis of variance was performed. If the analysis of variance yielded a statistically significant result (P < 0.05), a post-hoc Tukey’s honest significant difference test was performed at significance levels of 95%. Error bars in all the graphs represent standard deviation. The power calculation (rat tibia growth experiments): it is distinguished as significant with a difference of 60% in the outcome variable between the test and control group; 60% estimated standard deviation; P = 0.05; 90% confidence; n = 3. No statistical methods were used to pre-determine the sample size of the piglet heart valve experiments. All statistical analyses were performed using StatPlus software (Version 2009, AnalystSoft).

### Data availability

The data that support the findings of this study are available within the paper and its Supplementary Information.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

The authors are grateful to the Animal Research Children’s Hospital staff (A. Nedder (head veterinarian) and veterinary technicians) and the Boston Children’s Hospital perfusion team for their overwhelming support and assistance in this project. This work was also supported by the National Institutes of Health (grant GM086433 to J.M.K.) and the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education of Korea (2012R1A6A3A03041166) and the Korea Institute for Advancement of Technology (N0002123) to Y.L.

## Author information

### Author notes

• Eoin D. O’Cearbhaill

Present address: School of Mechanical and Materials Engineering, University College Dublin Centre for Biomedical Engineering, and University College Dublin Conway Institute of Biomolecular and Biomedical Research, University College Dublin, Belfield, Dublin 4, Ireland

1. Eri﻿c N. Feins and Yuhan Lee contributed equally to this work.

### Affiliations

1. #### Department of Cardiac Surgery, Boston Children’s Hospital, Harvard Medical School, 300 Longwood Avenue, Boston, MA, 02115, USA

• Eric N. Feins
• , Nikolay V. Vasilyev
• , Ingeborg Friehs
• , Douglas Perrin
• , Peter E. Hammer
• , Haruo Yamauchi
• , Andrew Gosline
• , Veaceslav Arabagi
•  & Pedro J. del Nido
2. #### Engineering in Medicine Division, Department of Medicine, Center for Regenerative Therapeutics, Brigham and Women’s Hospital, Harvard Medical School, Harvard Stem Cell Institute, Harvard-MIT Division of Health Sciences and Technology, 60 Fenwood Road, Boston, MA, 02115, USA

• Yuhan Lee
• , Eoin D. O’Cearbhaill
•  & Jeffrey M. Karp
3. #### Department of Cardiology, Boston Children’s Hospital, Harvard Medical School, 300 Longwood Avenue, Boston, MA, 02115, USA

• Gerald Marx

### Contributions

E.N.F and Y.L. designed and performed the experiments, analysed the data and wrote the manuscript. E.D.O. contributed to the design of the experiments. N.V.V., S.S. and I.F. contributed to the design and performance of the experiments and to the analysis of the data. D.P., P.E.H., H.Y., A.G. and V.A. contributed to the design of the experiments. G.M. contributed to the analysis of the data. P.J.d.N. and J.M.K. contributed to the experimental design and manuscript preparation and supervised the overall project. All authors read and edited the manuscript.

### Competing interests

E.N.F., Y.L., E.D.O., N.V.V., D.P., P.E.H., H.Y., V.A., J.M.K. and P.J.d.N. have a provisional patent application entitled ‘Autonomously growing implantable device’ (USSN 62/295,768).

### Corresponding authors

Correspondence to Jeffrey M. Karp or Pedro J. del Nido.

## Electronic supplementary material

1. ### Supplementary Information

Supplementary figures, tables and methods.

3. ### Supplementary Video 1

Representative video of a growth-accommodating annuloplasty ring in an ex vivo swine-heart preparation. The video is en face view of the tricuspid valve, with the ring in place. 100× normal speed