Bite Force Estimation
1 How does MUFIS estimate the bite force?
Bite force estimation is a method to estimate the bite force of an animal based on the cross-sectional area of the muscle fibers by considering the Physiological Cross-Sectional Area (PCSA) of the muscle fibers, the length of the moment arm of the muscle (the lines connecting the temporomandibular joint perpendicularly to the line of action of the muscle), and the distance between the bite point and the temporomandibular joint. This method was proposed by Hartstone-Rose et al. in 2012 (Hartstone-Rose, Perry, and Morrow 2012).
The formula provided by Hartstone-Rose et al. to estimate the bite force is:
\[ \begin{align*} \text{WBF}_{\text{CA}} &= c \left( \frac{(q_{\text{MS}} L_{\text{MS}}) + (q_{\text{TMP}} L_{\text{TMP}}) + (q_{\text{PT}} L_{\text{PT}})}{L_{\text{CA}}} \right) \\ \text{WBF}_{\text{PM}} &= c \left( \frac{(q_{\text{MS}} L_{\text{MS}}) + (q_{\text{TMP}} L_{\text{TMP}}) + (q_{\text{PT}} L_{\text{PT}})}{L_{\text{PM}}} \right) \\ \text{WBF}_{\text{CM}} &= c \left( \frac{(q_{\text{MS}} L_{\text{MS}}) + (q_{\text{TMP}} L_{\text{TMP}}) + (q_{\text{PT}} L_{\text{PT}})}{L_{\text{CM}}} \right) \end{align*} \]
where:
- \(WBF_{CA}\), \(WBF_{PM}\), and \(WBF_{CM}\) are the working-side bite force at the canine, premolar, and molar teeth, respectively.
- \(c\) is the force constant of muscle cross-sectional area (3 Kg/cm²).
- \(q_{MS}\), \(q_{TMP}\), and \(q_{PT}\) are the PCSA of the masseter, temporalis, and pterygoid muscles, respectively.
- \(L_{MS}\), \(L_{TMP}\), and \(L_{PT}\) are the length of the moment arm of the masseter, temporalis, and pterygoid muscles, respectively.
- \(L_{CA}\), \(L_{PM}\), and \(L_{CM}\) are the distance between the bite point and the temporomandibular joint at the canine, premolar, and molar teeth, respectively.
For example if we want to estimate the bite force at the canine teeth, we can use the following values:
- \(q_{MS} = 17\) cm²
- \(q_{TMP} = 23\) cm²
- \(q_{PT} = 2.7\) cm²
- \(L_{MS} = 3.6\) cm
- \(L_{TMP} = 4.4\) cm
- \(L_{PT} = 3.4\) cm
- \(L_{CA} = 17.5\) cm
Substituting these values in the formula we get:
\[ \begin{align*} \text{WBF}_{CA} &= 3 \left( \frac{(17 \times 3.6) + (23 \times 4.4) + (2.7 \times 3.4)}{17.5} \right) \\ &= 3 \left( \frac{61.2 + 101.2 + 9.18}{17.5} \right) \\ &= 3 \left( \frac{171.58}{17.5} \right) \\ &= 3 \times 9.8 \\ &= 29.4 \text{ Kg} \end{align*} \]
Therefore, the bite force at the canine teeth is 29.4 Kg.
In their work Hartstone-Rose et al. estimated the bite force of felids, and in an effort to more fully estimate the bite force, they included the contribution of the balancing-side muscles. For this, they estimated a ratio of the working and balancing-side amplitudes of each muscle using the EMG data of the cat muscles from Gorniak and Gans (1980). The formula to estimate the balancing-side contribution is:
\[ \begin{align*} \text{BBF}_{\text{CA}} &= c \left( \frac{(E_{\text{MS}} q_{\text{MS}} L_{\text{MS}}) + (E_{\text{TMP}} q_{\text{TMP}} L_{\text{TMP}}) + (E_{\text{PT}} q_{\text{PT}} L_{\text{PT}})}{L_{\text{CA}}} \right) \\ \text{BBF}_{\text{PM}} &= c \left( \frac{(E_{\text{MS}} q_{\text{MS}} L_{\text{MS}}) + (E_{\text{TMP}} q_{\text{TMP}} L_{\text{TMP}}) + (E_{\text{PT}} q_{\text{PT}} L_{\text{PT}})}{L_{\text{PM}}} \right) \\ \text{BBF}_{\text{CM}} &= c \left( \frac{(E_{\text{MS}} q_{\text{MS}} L_{\text{MS}}) + (E_{\text{TMP}} q_{\text{TMP}} L_{\text{TMP}}) + (E_{\text{PT}} q_{\text{PT}} L_{\text{PT}})}{L_{\text{CM}}} \right) \end{align*} \]
where:
- \(BBF_{CA}\), \(BBF_{PM}\), and \(BBF_{CM}\) are the balancing-side bite force at the canine, premolar, and molar teeth, respectively.
- \(E_{MS}\), \(E_{TMP}\), and \(E_{PT}\) are the balancing-side amplitude ratios of the masseter, temporalis, and pterygoid muscles, respectively.
The other values are the same as in the working-side formula. The total bite force is the sum of the working-side and balancing-side bite forces:
\[ \begin{align*} \text{Bite Force}_{\text{CA}} &= \text{WBF}_{\text{CA}} + \text{BBF}_{\text{CA}} \\ \text{Bite Force}_{\text{PM}} &= \text{WBF}_{\text{PM}} + \text{BBF}_{\text{PM}} \\ \text{Bite Force}_{\text{CM}} &= \text{WBF}_{\text{CM}} + \text{BBF}_{\text{CM}} \end{align*} \]
However, this approach may be appropriate for felids, since they have relatively fused mandibles and their interdigited symphyses transmit force between the two mandibular rami. For other animals, the balancing-side contribution may be different. For this reason, the balancing-side contribution is not included in the estimation of the bite force in MUFIS.