ESPECIFICACIONES TÉCNICAS DE LA PRÓTESIS

The low conductivity of the skull is a problem unique to brain applications of EIT, and has been considered the most important factor limiting successful imaging[30]. Therefore it is essential for accurate simulations and phantoms experiments that the conductivity of the skull is modelled correctly. Saha92 Law93 Compact Law93 Other Akh tari00 Top-Compact Akh tari00 Spongy Akh tari00

Low-Compact_Akhtari00 Bulk Oostendorp00Tidsw ell03 TAO52 Akh tari02 Top-Compact Akh tari02 Spongy Akh tari02

Low-Compact_Akhtari02 Bulk Tang08 Standard tri-la yer Tang08 Quasi-tri-la yer Tang08 Standard compact Tang08 Quasi-compact Tang08 Den tate sutur e Tang08 Squamous suture 0.00 0.01 0.02 0.03 Conductivit y S /m

Dry Tank Live

Figure 2.1: various skull conductivities

The conductivity of the skull is inhomogeneous due to variations in the tissue structure throughout[129]. Despite this, in EIT and other inverse source modelling applications it is common to consider the skull as having uniform conductivity and thickness[78],[127]. There have been numerous investigations into the conductivity of the skull and its variations with position, using either "dry" tissue from cadavers or "live" tissue measured soon after excision. A summary of these studies is shown in fig. 2.1.

The first detailed investigations into the variations of the skull conductivity were performed by Law[129]based on measurements of dry cadaver skull soaked in saline. The results demonstrated that conductivity varied with thickness as well as structure, and suggested a value of 0.006 S/m for the areas of the skull aside from sutures. However, this study and others based on a cadaver skull soaked in saline all suffer from an element of circular reasoning - the saline concentration used is based on assumed values of the conductivity of the interstitial tissue between the hard layers of bone[129],[130]. Studies on living tissue freshly obtained

from patients undergoing surgery give generally lower estimates of the resistivity of the skull, and furthermore demonstrate that the skull could be divided into distinct layers as shown in fig. 2.2. The three primary layers are an inner and outer layer of compact bone and an internal layer of diploe - a spongey structure with its pores and cavities filled with tissues with a high fluid content[128],[131]. The ratio of diploe to compact bone has been shown to be highly correlated with the effective conductivity of skull in that region, and better explains the regional conductivity variations than the thickness, as shown in fig. 2.3[128].

Figure 2.2: Skull samples demonstrating tri-layered structure, with two outer "compact" bone layers and

a inner spongey layer of diploe, from Tang, You, Cheng,et al.[128]

These results from Tang, You, Cheng,et al. [128]represent the most systematic study of skull conductivity to date, and demonstrate a wide range in conductivities across the surface of the skull, from as low as 0.0037 S/m for the most compact bone to 0.0125 S/m for regions with the highest proportion of diploe. The sutures between the bone plates were shown to have a generally higher conductivity than the immediately surrounding bone[128]. The layered anatomy of the skull may also be the cause of the apparent anisotropy in its conductivity. A study by Sadleir and Argibay[132]demonstrated both in simulation and in phantom experiments that a high resolution FEM of three homogeneous layers can explain the anisotropy measured in skull plugs.

(a)Thickness (b)Diploe-skull ratio

Figure 2.3: Scatter plots demonstrating the correlation of skull resistivity with(a)thickness r=−0.596

and(b)percentage of diploe r=−0.917from Tang, You, Cheng,et al.[128]

Previous brain EIT studies have traditionally used a single value of the conductivity[59], [78],[127]which, in the light of the results from Tang, You, Cheng,et al.[128]and Akhtari,

Bryant, Mamelak,et al.[131]is a poor representation of the real tissue conductivity. As the conductivity correlates best with the ratio of diploe, merely representing the thickness of the skull with a material of fixed conductivity will not represent the conductivity distribution accurately. Further, the value commonly used in the UCL group of 0.0048 S/m was based upon the results of Akhtari, Bryant, Mamelak,et al.[130]and Law[129]which, when compared to the literature in general, somewhat underestimates the real conductivity. Thus there was a clear need for a more realistic representation of the skull conductivity, both in simulations and in phantoms.

Neonate Skull conductivity

There has been less focus in the literature upon the conductivity of the neonatal and infant skull, with no in-vivo measurements in humans and the first mammalian conductivity values published as recently as 2011 by Pant, Te, Tucker,et al.[133]. The neonatal skull has a more complex structure than that of an adult skull, comprising of smaller bones connected by thin sutures and large openings known as fontanelles[134]. Moreover these smaller bones fuse together over a period of approximately two years, leaving behind the sutures seen in the adult skull[129]. This complexity and variability of the neonatal skull properties, coupled with the obvious difficulties in obtaining in-vivo measurements from skull plugs as conducted by Tang, You, Cheng, et al. [128], has necessitated the use of a range of conductivities when investigating neonatal brain function. One of the first impedance measurements of the neonatal head was performed by Murray[135]who suggested a range of conductivities between 0.033 to 0.2 S/m. These values present sensible upper limit based on the conductivity of most soft tissues in adults[136]and and a lower limit of the best estimate of adult skull at the time of writing. Despite a range encompassing the conductivities of nearly every human tissue, this estimate has persisted in the literature in the absence of a more detailed study [33],[137]–[140]. Thus it has been necessary for researchers to demonstrate the sensitivity of their chosen method to the potential conductivity of the skull by performing calculations with multiple models with varying conductivity. For example, Gibson, Bayford, and Holder[33] demonstrated that the size of the voltage changes for a realistic perturbation in the neonatal head varies by 15 % across the values suggested by Murray[135]. Tang, Oh, and Sadleir [140]created two separate models: “open skull”, where the fontanelles shared the same conductivity as scalp, and “closed skull” where they were set to the same value as the rest of the skull. The open skull demonstrated a 7-10 % increase in sensitivity in the centre of the brain.

To date the only in vivo estimate of a neonatal mammalian skull conductivity was performed by Pant, Te, Tucker,et al.[133]who measured the conductivity of skull plugs taken from a neonatal piglet model. The methodology was similar to that employed by Tang, You, Cheng, et al.[128], except measurements were only collected at single frequency of 1 kHz. Their

results demonstrated that the conductivity was towards the lowest estimate of Murray[135], finding a value of 0.0358 S/m for frontal bones and 0.025 S/m for parietal bones. Similar to the conclusions of Tang, You, Cheng,et al.[128]it was noted the two bone types were of similar thickness, and the difference in conductivity was ascribed to differing fractions of the inner spongey layer. Pant, Te, Tucker,et al.[133]concluded a single value of 0.03 S/m for the overall conductivity, possibly increasing up to 0.04 S/m with consideration of the increase in conductivity with temperature.

Another factor unique to neonatal applications of head EIT is the changing structure of the developing skull. To date, no studies have investigated the age dependence of skull conductivity. Pant, Te, Tucker,et al.[133]showed there was no significant difference between the conductivity of full term and pre term piglet skulls, however the rate at which the conductivity reaches the adult values found by Tang, You, Cheng,et al.[128]is not descirbed in the literature. Additionally, the fontanelles, approximately 2.1 cm at birth, close over the course of several months, with 96 % closure rate at 24 months[134]. However, the median age of closure is 13.8 months, with 1 % of babies having closed fontanelles by as little as 3 months. This large variability not only in the tissue of the neonatal skull but also the geometry, presents a particularly difficult modelling challenge.