ORIGINAL ARTICLE
A Computational Model of Velopharyngeal Closure for Simulating Cleft Palate Repair Joshua M. Inouye, PhD, Catherine M. Pelland,y Kant Y. Lin, MD,z Kathleen C. Borowitz, CCC-SLP,§ and Silvia S. Blemker, PhDyjj Abstract: The levator veli palatini (LVP) muscle has long been recognized as the muscle that contributes most to velopharyngeal (VP) closure and is therefore of principal importance for restoring normal speech in patients with a cleft palate. Different surgical reconstructive procedures can utilize varying degrees of LVP overlap, and this study developed a new finite-element model of VP closure designed to understand the biomechanical effects of LVP overlap. A three-dimensional finite-element model was created from adult anatomical dimensions and parameters taken from the literature. Velopharyngeal function was simulated and compared with experimental measurements of VP closure force from a previous study. Varying degrees of overlap and separation of the LVP were simulated, and the corresponding closure force was calculated. The computational model compares favorably with the experimental measurements of closure force from the literature. Furthermore, the model predicts that there is an optimal level of overlap that maximizes the potential for the LVP to generate closure force. The model predicts that achieving optimal overlap can increase closure force up to roughly 100% when compared with too little or too much overlap. The results of using this new model of VP closure suggest that optimizing LVP overlap may produce improved surgical outcomes due to the intrinsic properties of muscle. Future work will compare these model predictions with clinical observations and provide further insights into optimal cleft palate repair and other craniofacial surgeries. Key Words: Levator veli palatini, finite-element modelling, cleft palate repair (J Craniofac Surg 2015;26: 658–662)
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he levator veli palatini (LVP) muscle has long been recognized as the muscle that contributes most to velopharyngeal (VP) closure.1,2 Complete VP closure is necessary for producing normal speech. Insufficient VP closure (ie, VP insufficiency [VPI]) can be seen in individuals with repaired cleft palates, resulting in hypernasal From the Departments of Biomedical Engineering; yMechanical and Aerospace Engineering, University of Virginia; Departments of zPlastic rgery; §Therapy Service, Speech-Language Pathology, University of Virginia Health System; and jjDepartment of Orthopaedic Surgery, University of Virginia, Charlottesville, VA. Received May 28, 2014. Accepted for publication November 3, 2014. Address correspondence and reprint requests to Silvia S. Blemker, PhD, 415 Lane Rd, MR5 Room 2231, Box 800759, University of Virginia, Charlottesville, VA 22902; E-mail:
[email protected] This work was supported by a grant from The Hartwell Foundation to S.S.B. The authors report no conflicts of interest. Copyright # 2015 by Mutaz B. Habal, MD ISSN: 1049-2275 DOI: 10.1097/SCS.0000000000001441
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and unintelligible speech. Therefore, the LVP is of principal importance for producing normal speech in cleft palate patients.3–8 Different techniques of cleft palate repair can use varying degrees of overlap of the LVP muscle.5,6,8 –10 For the purposes of this article, we define overlap as the distance that the 2 LVP bundles overlap with each other when sutured together at the midline. The double-opposing Z-plasty5 inherently overlaps the LVP, and intravelar veloplasty11,12 allows for varying degrees of overlap. However, it has also been suggested that separation of the levator ends may also be possible in cleft palate patients after surgery and that the amount of separation may be dependent on the type of surgery.13 A more recent procedure that emphasizes aggressive LVP overlap has shown very promising results in prevention of VPI.14 The extent of muscle overlap has been thought to contribute significantly to speech outcomes owing to the reconstruction of the LVP sling,10 yet the mechanism and extent of this contribution are poorly understood. Is there an optimal amount of overlap to achieve maximum capacity for VP closure? The answer to this question is currently unknown as there have been no studies that provide a mechanistic understanding of the relationship between the amount of overlap and the capacity to produce VP closure. Computational models have enormous potential to increase the mechanistic understanding of VP function. Models can integrate the wealth of literature describing the anatomy, physical properties, and in vivo function of the VP mechanism15–25 and then be used to systematically investigate cause-and-effect relationships that would be either impossible to accomplish in vivo or take decades of clinical trials to uncover. For example, models have the ability to quantify the effect of varying surgical parameters, like the extent of LVP overlap. Finite-element models have been used previously in 2 exploratory studies of VP closure.15,26 One study simulated soft palate configurations during closure movement and speech.15 The other study investigated the effects of LVP angle, a submucous cleft, and the contribution of the palatopharyngeus on VP closure.26 Both studies were two-dimensional simulations and did not incorporate the physical mechanics of muscle force generation, limiting their ability to provide insights related to LVP muscle function. The goals of this work were to (i) create a three-dimensional (3D) finite-element model of the palate based on the wealth of anatomical information in the literature, (ii) validate the model by comparisons with experimental measurements of VP closure force, and (iii) demonstrate the utility of the model by simulating the effects of overlap on VP closure capacity. We created a model and found that it corresponded well with experimental data. Furthermore, we found that overlap can be adjusted to optimize the closure force produced by the LVP due to the mechanics of muscle force generation (ie, the force-length curve of active muscle).
MATERIALS AND METHODS Finite-Element Model We created a biomechanical finite-element model to simulate the LVP function. A hexahedral (cube-like) mesh (Fig. 1A) was
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Model of Velopharyngeal Closure
FIGURE 2. The force-length curve describes the nonlinear relationship between muscle length and force generating capacity. FIGURE 1. A, We use a 3D finite-element model to simulate VP closure. B, We measure the total closure force produced between the velum and the posterior pharyngeal wall at the contact area as the levator is activated. This is a midsagittal cutaway view. C, We simulate varying degrees of levator separation and overlap in our model.
created in TrueGrid software (XYZ Scientific Applications, Livermore, CA). The models included 3D descriptions of the LVP muscle, the passive soft tissue of the palate including the uvula, and the posterior pharyngeal wall. The dimensions LVP muscle and the soft palate were determined from published measurements collected from adult magnetic resonance (MR) images (Table 1).13,18,20,21,27,28 The curve that describes the shape of the posterior pharyngeal wall was defined based on outlines defined on midplane sagittal MR images of the soft palate Osirix software (Pixmeo, Geneva, Switzerland).27 The initial distance between the soft palate and posterior wall was defined based on a straight-line measurement, in the relaxed position. Muscle material properties from a previous study29 were implemented, containing both passive (related to passive muscle stretch) and active (related to muscle activation and muscle stretch) nonlinear tensile components.29 The active tensile component incorporates the known force-length behavior of skeletal muscle,30 where the peak muscle force occurs when the muscle reaches its optimal length (Fig. 2), represented by the optimal fiber stretch parameter, lofl. The material properties of the soft palate were model based on previous work: an isotropic, hyperelastic, quasi-incompressible, neo-Hookean material with a Poisson ratio of 0.499515 and a Young modulus of 25 kPa.31–34 The posterior pharyngeal wall was modeled as a rigid body that had frictionless contact with the soft palate. The input to the model was levator activation, ranging from 0% to 100%, and the output quantities of interest were the magnitude of the total force exerted on the posterior pharyngeal wall (ie, VP closure force) and the deformations of the soft palate (Fig. 1B). Simulations were run on the implicit FE solver Nike3D35 (Lawrence Livermore National Lab).
measured using a silastic bulb device placed in the velopharynx. Electromyography (EMG) activity of the LVP was measured using fine-wire EMG and was normalized within each subject. The subjects uttered either sustained vowels or sequences of vowels, nonnasal consonants, and nasal consonants. We compared the model data with the published data of closure force versus LVP activation, using all the sounds from both sexes from the published data.
Modeling Surgical Overlap Previous literature has shown that the LVP in infants with a cleft is similar to the length in normal infants.24 Therefore, we assume that suturing the LVP halves end-to-end will result in a normal-length LVP sling. We modeled various amounts of overlap and separation of the LVP (Fig. 1C). In order to model these surgical differences in overlap, we change the optimal fiber length parameter lofl29 in the model. This affects the starting point on the active force-length curve.30 We assumed that the muscle fibers are resting at their optimal fiber length in the nominal (healthy palate) model. We tested models with varying amounts of overlap and separation in increments of 10% of the total LVP length ranging from 20% separation to 30% overlap at 50% muscle activation and measured the corresponding closure force. We use closure force as our metric of probability of surgical success in the prevention of VPI. All of our models obtained closure at 50% activation, and the quality of VP closure was measured using the closure force. We reason that higher closure force is more desirable for obtaining a tighter, more complete VP closure and that a lower closure force may lead to hypernasality.
RESULTS
Comparison With Experimental Data
Comparison of Healthy Model With Experimental Data
We compared the model predictions of VP closure with a study published by Kuehn and Moon.36 In that study, VP closure force was
The model predictions of closure force (Fig. 3) correspond well with experimental data reported by Kuehn and Moon.36 The model
TABLE 1. Model Dimensions and Associated Literature Sources Model Feature Major axis of levator cross section Minor axis of levator cross section Levator curve Soft palate thickness Soft palate length Distance between points of origin of LVP Reference angle of LVP Width of soft palate tissue Uvula width (male/female average)
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Measurement 8.8 mm 3.9 mm 4th-Order polynomial 10.3 mm 31.8 mm 55 mm 122.4 degrees 22 mm 10.7 mm
Source Perry et al,13 2013 Inouye et al,27 2013 Tian and Redett,28 2009 Perlman et al,20 2002 Ettema and Kuehn,18 1994 Kuehn and Kahane,21 1990
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FIGURE 3. The normal palate model predictions of closure force compare favorably with experimental data. Each point of the experimental data is one sound from either the male or female mean, and the error bars are 1 SD for both activation and closure force.36
data lies within 96% of the experimental data mean 1 SD. The scatter of the data around the model predictions can come from a variety of sources including the variability of measuring experimental data, contributions of other muscles to VP closure, dynamic features of sound production, and differences among subjects.
Effects of LVP Overlap on Closure Force The models predicted that the closure force is sensitive to overlap (Fig. 4) and that the maximum closure force is achieved when the muscle is overlapped by 15%. Furthermore, we see a 21% reduction in closure force from optimal if the overlap is decreased to 0% and even higher reductions for negative overlap (ie, separation of the LVP bundles). As overlap is increased from 15% to 30%, closure force decreases by 41%. These variations can be explained by the force-length curves (Fig. 4). As the LVP contracts, the muscle length becomes shorter (ie, decreases on the x axis). The 15% overlap case causes the force to peak at the end of the contraction, giving the highest closure force. Thirty percent of overlap significantly decreases closure force because the muscle is not able to get to a high point on the force-length curve.
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Hypothetical overlap ranges differ among current surgeries owing to the nature of the LVP repair technique (Fig. 5). The radical intravelar veloplasty (RIVV) has a wide range of possible overlap distances because of the radical dissection of the LVP. One technique6 uses RIVV and does not overlap, whereas another technique14 uses RIVV and an aggressive amount of overlap. The Kriens-style8 intravelar veloplasty does not dissect the muscle as far laterally and therefore cannot overlap as much as an RIVV. The double-opposing Z-plasty technique5 inherently harnesses some overlap of the LVP bundles, but this amount cannot be adjusted because of the geometry of the repair. Without specific LVP reconstruction via intravelar veloplasty or Z-plasty, there is no overlap. Each of these procedures involves varying amounts of retrodisplacement as well, which can also help explain the differences in success rates. However, we propose that despite other variables that affect surgical success (such as retrodisplacement and scar tissue formation), the amount of overlap alone can have a large effect on closure force and therefore can be harnessed to improve patient outcomes. This idea is supported by success of the doubleopposing Z-plasty technique being attributed to LVP tightening38 and the recently reported high success rates of aggressive overlapping combined with the RIVV technique.14 The model prediction that LVP overlap can be beneficial is a result of the physics of skeletal muscle force generation (Fig. 2). The muscle contractile proteins (sarcomeres) have the highest force-generating potential at an intermediate amount of stretch (at the peak of the force-length curve, 100% normal resting position). Further shortening or stretch will cause the rest position to be altered, and the force-generating capacity will be reduced. However, an initial stretch provided by overlapping the muscle
DISCUSSION In this study, we created a novel 3D computational model of the soft palate and used the model to simulate how varying the amount of LVP overlap influences closure force. The model compares favorably with experimental data and predicts that varying LVP overlap has a large effect on VP closure force—a potentially significant factor that may prevent VPI during speech. This work highlights how computational models can provide new insights that in vivo experiments and surgical trial-and-error cannot provide. Specifically, the model presented in this article revealed the significant effects of overlap on muscle mechanics and palate function, suggesting that it should be considered as an important parameter in cleft repair. One of our central working assumptions was that a higher closure force is a predictor of better VP function, all other variables being equal. One could argue that as long as closure is achieved, the closure force is irrelevant. However, if closure force is higher for a given activation (which our study shows is accomplished by optimizing overlap), then less muscle activation would be needed to produce the same amount of closure force. This is important for fatigue avoidance in patients with borderline VPI.37 Furthermore, higher closure force in general should ensure a tighter, more complete VP closure.
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FIGURE 4. Closure force is highly dependent on overlap. Exact amounts of overlap are affected by modeling assumptions. See Discussion for further explanation.
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FIGURE 5. Possible overlap ranges vary based on surgical procedure.
allows the LVP sarcomeres to initially be longer than 100% normal resting position and contract back to 100% normal resting position, at the peak of the force-length curve at closure (as is the case in the force-length curve for optimal overlap in Fig. 4). Our model was built on dimensions taken from normal adults because the experimental closure force data are not available for children or infants. The LVP of infants is approximately two-thirds of the length of the LVP of adults.13,20,24,25 This suggests that scaling down the simulated overlap distances for surgeries on infants and children would produce the same mechanical effects on closure force. Estimated overlap amounts for adults and infants based on the overlap percentages from this study are shown in Table 2. However, as mentioned earlier, the limitations of this study preclude its ability to prescribe exact amounts of overlap that will be assuredly optimal for any given patient. Our results for the normal model compare favorably with previously published data, validating our model. One point of comparison was the previously published experimental VP closure force data.36 Placement and measurement variability of the EMG and closure force sensors, sex differences, and minor contributions of other palatal muscles to closure are factors that could contribute to the scatter of the data in that study. The other study measured the stretch of the velum rather than the closure force.28 The correlation of our model with force36 and stretch28 data from 2 different studies suggests consistency between our model and physiological reality. One of the most critical assumptions of our study is that the LVP at resting length is at the peak of the force-length curve (ie, that the muscle sarcomeres are at their optimal length for force production).39 Currently, the resting sarcomere lengths of this muscle are unknown. As the optimal sarcomere length in human skeletal muscle is approximately 2.7 mm,30 let us consider the situation that resting sarcomere length in a normal individual’s LVP was 2.7 mm. If the preoperative, resting sarcomere length in a cleft patient were also 2.7 mm, then our assumptions about resting sarcomere length would be validated. However, in the situation where the cleft patient’s preoperative sarcomere length were 10% shorter at 2.43 mm, then an overlap of approximately 10% would be required to restore normal sarcomere length (assuming the LVP total length is the same) and get to the 0% overlap amount in this study using our assumptions. Therefore, the 10% would need to be added to the overlap percentages in this study to obtain similar effects (ie, the ‘‘optimal’’ amount of overlap would be 25% instead of 15%). Techniques for noninvasively measuring sarcomere lengths40,41 have been developed. Future research using these or other techniques would elucidate the sarcomere lengths of the LVP in normal and cleft individuals and to what extent sarcomere lengths vary across the cleft patient population. We also assumed that the total LVP length in cleft and normal infants is the same.24 One could argue that there should be a wide range of total LVP lengths due to a wide range of cleft severities and anatomies. For example, in a case with a very wide cleft, the LVP may be attached more anteriorly within the mouth, so that the origin and insertion of muscle would be farther apart, making the muscle longer. #
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Model of Velopharyngeal Closure
Another example is with a submucous cleft, where the course of the LVP may not be as straight if it comes together in the midline before attaching to the hard palate. A longer overall LVP would tend to benefit from more overlap, as this would be necessary to achieve the same result as a patient whose LVP length is more anatomically normal. If data from future studies refine either of the above assumptions, then the peak of the closure force (Fig. 4) would be shifted left or right, but the same nonlinear relationship would still hold. Regardless of these 2 model assumptions, we can still conclude that the amount of overlap can be optimized. Other factors that may influence our predictions in this modeling study include the properties of the soft palate tissue. We used 25 kPa as the Young modulus for the soft palate tissue, which has been used in several previous finite-element modeling studies of the normal soft palate.31– 34 Other studies have found a wide range of palate stiffness (from approximately 0.5 to 100 kPa, depending on the location in the soft palate).15,42,43 The use of 25kPa in our model results in predictions that correspond well with experimental data. Furthermore, perturbing the stiffness up and down by 50% did not affect closure force more than 10%. Viscoelasticity of muscle and soft tissue is not considered in this study and would reveal dynamic time-varying closure forces; this is an area deserving of further research. Our conclusions that overlap can be optimized are based on the advantageous sarcomere length changes associated with overlap and not on the specific viscoelastic properties or stiffness of the soft palate tissue. The unmodeled factors preclude this model’s ability to prescribe exact amounts of overlap that will be assuredly optimal for any given patient. However, our quantitative results from the computational model, built by many observational and experimental data, support the general conclusion that the degree of LVP overlap strongly influences VP function. Future research will incorporate more features of the soft palate and enable investigation of other aspects of palate function that were unexplored in this study. These features include contributions of other palate muscles (eg, the musculus uvulae, the palatopharyngeus, and the tensor veli palatini), viscoelasticity, inertial forces, scar tissue, LVP volumes, and other surrounding soft tissue structures. These are just a few of the ways that demonstrate the enormous potential of finite-element modeling to provide information that in vivo experiments and surgical trial-and-error cannot provide. While this study explores the acute consequences of overlap on LVP muscle mechanics and its effects on VP closure, future studies will also take into account chronic changes in muscle (eg, fiber-type TABLE 2. Overlap Percentages Calculated for Both Adults and Infants Adult, mm Infant, mm Overlap, % 20y 15y 10y 5y 0 5 10 15 20 25 30
18.1 13.6 9.0 4.5 0.0 4.5 9.0 13.6 18.1 22.6 27.1
12.1 9.0 6.0 3.0 0.0 3.0 6.0 9.0 12.1 15.1 18.1
Overlap percentages are based on 90-mm total LVP length for adults and 60-mm total LVP length for infants. y Negative overlap percentages and distances indicate amount of LVP bundle separation. Exact amounts of overlap are affected by modeling assumptions. See Discussion for further explanation.
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transformation, sarcomere remodeling, fibrosis, and changes in muscle cross-sectional area) due to development, surgery, and remodeling. In summary, we created a novel finite-element model to simulate VP closure with varying amounts of LVP overlap. Overlap has never been investigated from a mechanistic standpoint, even though the most successful modern techniques already utilize some amount of LVP overlap. The results suggest that overlap of the LVP may produce more favorable surgical outcomes for VP closure and therefore normal speech production. This is due to the improved mechanical benefit of the LVP with certain amounts of overlap. Future development of novel cleft repair surgeries and evaluation of current surgeries should consider the principle of overlap presented in this study in order to optimize cleft repair procedures. Further modeling studies will incorporate additional anatomical details and will be validated with dynamic MR imaging scans. In addition, future studies will be able to provide additional mechanistic explanations for other aspects of palate function (such as swallowing) and aid surgeons in making treatment decisions.
ACKNOWLEDGMENT The authors gratefully acknowledge useful discussions with Geoffrey Handsfield and Dr Albert Woo.
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