The role of hand motion connectivity in the performance of laparoscopic procedures on a virtual reality simulator

Abstract

Assessment of surgical skills based on virtual reality (VR) technology has received major attention in recent years, with special focus placed on experience discrimination via hand motion analysis. Although successful, this approach is restricted from extracting additional important information about the trainee’s hand kinematics. In this study, we investigate the role of hand motion connectivity in the performance of a laparoscopic cholecystectomy on a VR simulator. Two groups were considered: experienced residents and beginners. The connectivity pattern of each subject was evaluated by analyzing their hand motion signals with multivariate autoregressive (MAR) models. Our analysis included the entire as well as key phases of the operation. The results revealed that experienced residents outperformed beginners in terms of the number, magnitude and covariation of the MAR weights. The magnitude of the coherence spectra between different combinations of hand signals was in favor of the experienced group. Yet, the more challenging (in terms of hand movement activity) an operational phase was, the more connections were generated, with experienced subjects performing more coordinated gestures per phase. The proposed approach provides a suitable basis for hand motion analysis of surgical trainees and could be utilized in future VR simulators for skill assessment.

Appendix

The posterior distribution for the MAR coefficients structured in a vectorized form is $p({\mathbf{w}}/{\mathbf{O}}) = N({\mathbf{w}}/\overline{\mathbf{w}} ,\overline{\varvec{\Upsigma}})$ with

$$\overline{{\varvec{\Upsigma}}} = \left( {\overline{{\varvec{\Uplambda}}} \otimes {\mathbf{X}}^{\text{T}} {\mathbf{X}} + \overline{\lambda } {\mathbf{I}}_{{n}} } \right)^{ - 1} $$

(18)

$$\overline{{\mathbf{w}}} = \overline{{\varvec{\Upsigma}}} \left( {\overline{\Uplambda } \otimes {\mathbf{X}}^{\text{T}} {\mathbf{X}}} \right){\mathbf{w}}_{\text{ML}} $$

(19)

Where ⊗ is the Kronecker product and w _ML is the vec() form of the ML solution for the weights given by Eq. (6).

The distribution for the precision on the MAR coefficients is $p({\lambda \mathord{\left/ {\vphantom {\lambda \varvec{O}}} \right. \kern-0pt} \varvec{O}}) = {\text{Gam}}\left( {{\lambda \mathord{\left/ {\vphantom {\lambda {b\prime ,}}} \right. \kern-0pt} {b^{\prime} ,}}c^{\prime} } \right)$ with

$$\frac{1}{b^{\prime} } = 0.5(\overline{{\mathbf{w}}} )^{\rm T} \overline{{\mathbf{w}}} + 0.5{\text{tr}}(\overline{{\varvec{\Upsigma}}} ) + b^{ - 1} $$

(20)

$$c^{\prime} = 0.5n + c $$

(21)

$$\overline{\lambda } = b^{\prime} c^{\prime} $$

(22)

The parameters of Gam are selected so that it is sufficiently uninformative (b = 1,000 and c = 0.001).

The noise precision posterior is a Wishart distribution p(Λ|O) = W _d(Λ |s, S) where

$${\mathbf{S}} = ({\mathbf{Y}} - {\mathbf{X}}\overline{{\mathbf{A}}} )^{\rm T} ({\mathbf{Y}} - {\mathbf{X}}\overline{{\mathbf{A}}} ) + {\varvec{\Upomega}} $$

(23)

$$s = N $$

(24)

$$\overline{{\varvec{\Uplambda}}} = s{\mathbf{S}}^{ - 1} $$

(25)

$${\varvec{\Upomega}} = \Upsigma_{t} \left( {{\mathbf{I}}_{\text {d}} \otimes {\mathbf{x}}_{t} } \right)\overline{{\varvec{\Upsigma}}} \left( {{\mathbf{I}}_{\text {d}} \otimes {\mathbf{x}}_{t} } \right)^{\rm T} $$

(26)

The Gamma and Wishart distributions are given in the Appendix of [18].

The updates are initialized using the maximum likelihood estimates [see Eqs. (6)–(8)]. The Bayesian evidence is computed as:

$$E(r) = - \frac{N}{2}{\text{ln}}|{\mathbf{S}}| - {\text{KL}}\left( {q({{\mathbf{w}} \mathord{\left/ {\vphantom {\varvec{w}}{\mathbf{O}}} \right. \kern-0pt}}),p({{\mathbf{w}} \mathord{\left/ {\vphantom {{\mathbf{w}} \lambda }} \right. \kern-0pt} \lambda })} \right) - {\text{KL}}\left( {q(\lambda ,{\mathbf{O}})} \right) + {\text{const}} $$

(27)

where KL(p, q) denotes the Kullback-Liebler (KL) divergence between the distributions p and q. Iteration terminates when the Bayesian evidence increases by less than a predetermined threshold.