A Computational Model Quantifies the Effect of Anatomical Variability on Velopharyngeal Function

Abstract

Purpose: This study predicted the effects of velopharyngeal (VP) anatomical parameters on VP function to provide a greater understanding of speech mechanics and aid in the treatment of speech disorders.

Method: We created a computational model of the VP mechanism using dimensions obtained from magnetic resonance imaging measurements of 10 healthy adults. The model components included the levator veli palatini (LVP), the velum, and the posterior pharyngeal wall, and the simulations were based on material parameters from the literature. The outcome metrics were the VP closure force and LVP muscle activation required to achieve VP closure.

Results: Our average model compared favorably with experimental data from the literature. Simulations of 1,000 random anatomies reflected the large variability in closure forces observed experimentally. VP distance had the greatest effect on both outcome metrics when considering the observed anatomic variability. Other anatomical parameters were ranked by their predicted influences on the outcome metrics.

Conclusions: Our results support the implication that interventions for VP dysfunction that decrease anterior to posterior VP portal distance, increase velar length, and/or increase LVP cross-sectional area may be very effective. Future modeling studies will help to further our understanding of speech mechanics and optimize treatment of speech disorders.

Figure 1.

Inputs of velopharyngeal anatomical parameters and mechanical properties of muscle and the soft palate were used to create a computational model for assessing velopharyngeal function. MRI = magnetic resonance imaging; LVP = levator veli palatini.

Figure 2.

(a) Magnetic resonance imaging (MRI) measures in the sagittal and oblique-coronal image planes. (b) Line segments represent the velum, levator veli palatini (LVP), and posterior pharyngeal wall (PPW). Width of posterior pharyngeal wall line segment was based on the velopharyngeal (VP) width measurement. The velum line segment extends down to the middle of the LVP, not along the nasal surface. (c) Orientation of the components with the MRI planes. (d) Computational model in the orientation shown in Panel C. (e) Model components reflect anatomical representation (Perry & Kuehn, 2007).

Figure 3.

The force–length properties of skeletal muscle were used to calculate active muscle tension on the basis of the amount of contraction. A higher amount of contraction from a 100% rest position lessens muscle force-generating capacity. LVP = levator veli palatini.

Figure 4.

Line segment model configuration for (a) relaxed levator veli palatini (LVP), (b) LVP during velopharyngeal (VP) closure, and (c) determining closure force calculations using a simple force balance.

Figure 5.

We conducted three sets of computational simulations with our model. The first simulation set comprised 10 image-based simulations, each from the magnetic resonance images of the individual subjects, as well as an averaged simulation. The second set was 1,000 randomized simulations with each parameter drawn independently from a uniform probability distribution varying between the mean ± 1 SD for each anatomy. The third set was parameter isolation simulations that adjusted each parameter up and down 1 SD from the mean while holding other parameters constant to determine sensitivity of velopharyngeal closure to individual parameters.

Figure 6.

Effects of parameter adjustments on model anatomy. Velopharyngeal (VP) distance increased by moving the posterior pharyngeal wall (PPW) posteriorly in the oblique-coronal plane. Extravelar levator veli palatini (LVP) length increased by moving the points of origin posteriorly in the oblique-coronal plane. Intravelar LVP length increased by increasing the width of the intravelar segment while keeping the origin-to-origin distance and extravelar LVP length constant. This moved the points of origin posteriorly in the oblique-coronal plane. Distance between points of origin remained constant. VP width increased by widening the PPW contact area. Distance between points of origin increased while keeping extravelar LVP length constant. Velum–LVP angle increased by rotating the velum anteriorly in the sagittal plane. Velar length increased by extending the point of attachment to the hard palate posteriorly and superiorly while keeping the velum–LVP angle constant.

Figure 7.

(a) The average model agrees well with experimental data, falling within 1 SD of all data points. Individual models from magnetic resonance imaging scans (a) and randomized models (b) show variability similar to that observed experimentally.

Figure 8.

Parameter isolation simulations. (a) Ranked parameter sensitivities measured by percentage increase in closure force when varying parameters up or down 1 SD from the mean and holding other variables constant. (b) Closure force has positive relationships with isolated increases in some variables and negative relationships in others. VP = velopharyngeal; LVP = levator veli palatini; CSA = cross-sectional area.

Figure 9.

Parameter isolation simulations. (a) Ranked parameter sensitivities measured by percentage decrease in minimum activation required. (b) Minimum activation required has positive relationships with isolated increases in some variables and negative relationships in others. VP = velopharyngeal; LVP = levator veli palatini; CSA = cross-sectional area.

Figure 10.

Parameter isolation simulations (see Figures 8 and 9) enable identification of the most influential aspects of velopharyngeal (VP) closure. It is interesting to note that the most influential parameters for closure force (see Figure 8) tended to be those measured in the oblique-coronal plane and related to levator veli palatini (LVP) configuration, whereas the most influential parameters for minimum activation required (see Figure 9) tended to be those measured in the sagittal plane and related to velar configuration. PPW = posterior pharyngeal wall.

Figure 11.

Randomized simulation set, with each data point representing one random anatomy. Higher closure force at full muscle activation, in general, correlates with a lower minimum activation required in our model.

Figure 12.

Effect of velopharyngeal (VP) distance. A large VP distance requires more levator veli palatini contraction, resulting in less force capacity, and vice versa.

Figure 13.

Three plots of randomized simulation set, with each data point representing one random anatomy. Although the above anatomical parameters are the most influential, they cannot be considered in isolation of the other parameters because there is considerable variability of closure force for a given value of each individual parameter. Closure force was measured at 100% muscle activation. VP = velopharyngeal; LVP = levator veli palatini.

Figure 14.

Tissue parameter sensitivity analyses on closure force. Velopharyngeal (VP) distance remains most important in all cases. Increasing velar stiffness by 10 times relative to nominal while keeping specific tension at nominal value (upper right panel) increases the effects of parameter variations about five times. Moreover, velum–levator veli palatini (LVP) angle and velar length increase in relative importance to second and third most influential, respectively. CSA = cross-sectional area.