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where d(t), the displacement, is composed of a 1 Hz oscillation of the wrist superim-
posed by a 10 Hz tremor. Using such models, the data may be approximated and the
model can be fitted with the data by adding more signal components of tremor and
noise.
An alternate approach is to extract the model of the motion from the data by identi-
fying the oscillations (a range of frequencies) present in the data. An example is em-
pirical mode decomposition. In Empirical Mode Decomposition [26] the temporal
information is preserved while decomposing the signal into a number of lower fre-
quency components. Unlike the Fourier and Wavelet methods, the original nature of
the signal is maintained and each component can be easily be related to the original
signal. This method can analyze surgical motion data to reveal the physical process of
performing the surgical motion tasks.
In empirical mode decomposition [26] a time based signal D(t) is decomposed into
a number of components Ij(t), known as IMFs (Intrinsic Mode Functions), which are
individual oscillations of a scale. Individual oscillations are zero mean. By iteratively
removing the individual oscillations, a monotonic signal tendency is observed at
which point the decomposition stops. The residual signal that shows the monotonic
signal tendency is called the trend part of the original signal.
Let D(t) be the displacement function of a surgical motion experiment which can
be described as a discrete set of N points at N equally spaced times. Through Empiri-
cal Mode Decomposition [26], D(t) can be decomposed as shown in equation (2).
Rn(t) is the residual signal after extracting IMFs Ij(t) in n iterations.
D(t) = Rn(t) + ∑ Ij(t) for j = 1, …, n
(2)
By decomposing the complex motion data, we aim to identify physical processes
such as oscillation of the measurement device, physiological tremor of the subject,
dexterous movement by the subject, geometry of the path, etc. Since the isolated
components (IMFs) are similar in nature to the original signal, it can be assessed
using the number of movements present in it or the types of movement.
In Hotraphinyo et. al [29] a motion study of a microsurgical task is described, indi-
cating the frequencies of motion components. Three types of involuntary motion were
identified, tremor, jerk and drift in addition to the erroneous hand movement. Howev-
er, it [29] does not decompose the motion data to physical processes, they are instead
assessed using spectral decomposition. Further, a large sample study was not possi-
ble due to the need of consenting patients and surgeons to record surgical motion. Our
study is aimed at removing these limitations.
Although the extraction of certain characteristic parameters such as frequency or
velocity of surgical motion may be readily achieved, the quality of the movement is to
be assessed.
3
Surgery Training System
In Fig. 2, the software architecture of the training system is given. The training system
consists of four parts. The first component is a digital forceps that helps the surgeon
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