MODELO CAE

The ideal phantom for EIT would accurately reflect the geometric and electrical properties of every tissue in the head, so as to simulate the current distribution in the head as realistically as possible. The irregular geometry of the head and the complexity of the internal tissues dictate that simplifications are often made. Cylindrical, hemispherical and spherical tanks are common as they are quick to achieve and do not require detailed FEMs[70],[127],[141], [142]. However, these shapes differ greatly from the real geometry and thus are of limited use when investigating the feasibility of brain EIT. Geometrically realistic head phantoms have been constructed for both EEG inverse source modelling[143]as well as for EIT specifically [78],[144], shown in fig. 2.4. Some simplifications are still necessary however. As the region of interest is the brain, the facial bones and structures like the ear canal and eyeballs are regularly not considered as they are difficult to model and their effect on EIT measurements still require investigation[78],[127],[141],[144],[145].

Modelling the electrical properties of the head tissues presents a more difficult challenge than mimicking the geometry, with the skull a particular challenge. As described in section 2.1.1 the skull has a high, spatially variable resistivity which cannot be represented with a single concentration of saline or gel[127],[141]. Anisotropy is traditionally considered negligible in EIT for the sake of simplicity, particularly in complex 3D geometry like the head[15],[53]. As the isotropic conductivity of the skull already presents a significant challenge in phantom creation, the anisotropy is commonly ignored. A new approach could be possible based on

the results of Sadleir and Argibay[132], as the skull could be represented as three distinct homogeneous layers. However, the thin shell of the skull already presents a challenge when creating finite element models as there are large changes in voltage over a small volume, necessitating a large number of small elements. Moving to a three layer model would further exacerbate this problem, possibly resulting in a prohibitive number of elements in the FEM. The thinner shells, which in some places are less than a 1 mm thick[131]would also present a difficult challenge in phantom fabrication.

A simple spherical skull phantom, fig. 2.4a, was created by Liston, Bayford, and Holder [127]by casting plaster of Paris and soaking in calcium sulphate CaSO₄. Using this method it was possible to create a realistic conductivity of 0.012 S/m but it was difficult to control across the phantom, as the values were expressed only as a range of 0.008 to 0.013 S/m. A head tank formed of a clay model and employing a real human skull was produced by Tidswell, Bagshaw, Holder,et al.[78], shown in fig. 1.7b, and has been used successfully within the UCL group to image perturbations in time difference and frequency difference, under certain circumstances [54],[58],[68]. This tank was extended to also model the contact impedance with a skin of a marrow or giant zucchini in assessing electrode headnets. However, as described in section 2.1.1, it is the spongey diploe as opposed to the hard compact bone which defines the conductivity, and studies using dead tissue tend to underestimate the conductivity fig. 2.1. Further, the skull required soaking in saline for 48 hours before it was stable long enough to use for an experiment, and the resultant conductivity distribution was unknown[126]. Along with deterioration of the phantom, these are the likely sources of the error in simulated boundary voltages seen in fig. 1.10b.

(a)Liston Spherical Tank (b)Sperandio Four Shell Tank

(c)Collier Mannequin Tank (d)Li Resin Tank

Figure 2.4:3D head phantoms for EIT,(a)spherical tank from Liston, Bayford, and Holder[127],(b)

four shell agar tank from Sperandio, Guermandi, and Guerrieri[141],(c)EEG phantom from Collier,

Subsequently there have been efforts to create an improved head phantom with realistic, known conductivities. A hemispherical phantom was constructed by Sperandio, Guermandi, and Guerrieri[141], consisting of four concentric shells of agar gel thickened saline of differing concentrations. A volume conductive film (VCF) was placed between each shell to prevent diffusion between the differing concentrations in the regions. This material has an electrical conductivity similar to head tissues (0.2 S/m) but is impermeable, and thus prevents ion transfer. Unusually for head phantoms, this tank also included a layer representing CSF as well as those for skin, skull and brain. The phantom showed good agreement with simulated voltages at 100 kHz, accurately modelling the conductivity of the skull. However the VCF introduced a large reactance below 10 kHz, and thus would not be suitable for stroke studies as this is the frequency range of interest. To date, the most detailed work was performed by Li, Tang, Dai,et al.[144], who created an anatomically realistic head phantom, partially using rapid prototyping. The geometry was obtained from a CT segmentation, and resin molds created using selective-laser-sintering (SLS). The skull was divided into separate sections based upon the bone structure and resistivity values from Tang, You, Cheng, et al.[128]. Plaster soaked in calcium sulphate was used to mimic the conductivity of skull, a similar but more methodical technique to that of Liston, Bayford, and Holder[127]. The resistivity variations were replicated by varying the ratio of a mix of distilled water and dental-grade plaster. The problems in resistivity variation experienced by Liston, Bayford, and Holder [127]are not apparent. These were likely overcome through the use of an ultrasonic vibrator during the coagulation process and by allowing the resistivity to stabilise over 12 days during soaking. The results demonstrate the phantom resistivity was within approximately 3 % of the target value when measured directly. However it was difficult to assess the performance of the phantom fully, as only 2D simulations and reconstructions were performed, and only a subset of measurements were compared to simulations. Whilst both the four shell agar tank and the anatomically realistic tank produced accurate results when compared to the corresponding modelling, these methods were not capable of producing a continuously varying conductivity distribution. The resistivity in each section is defined by the plaster mixture, or by the saline concentration, and is uniform across that section[141],[144]. Thus in order for the conductivity to vary smoothly an impractical number of separate sections would be required to create the phantom. These phantoms also have practical disadvantages in that they are not suitable for sporadic use over the long term. The agar phantom created by Sperandio, Guermandi, and Guerrieri[141]required refrigeration between uses as well as thawing of five hours before data collection. The gypsum used in the phantom by Li, Tang, Dai,et al.[144]is moderately water soluble, and the solubility increases with saline concentration[146]. Thus repeated use may cause a drift in the resistivity.

Neonate head phantoms

To the authors knowledge, the only EIT phantoms created explicitly for neonatal brain imaging were manufactured by Tang, Oh, and Sadleir[140]. Initially a spherical design similar to those created by Liston, Bayford, and Holder[127]was built fig. 2.5a before construction of a simplified 3D printed head shaped tank the following year fig. 2.5b. The spherical tank consisted of two polycarbonate hemispheres containing stainless steel electrodes formed the outer layer, and saline of conductivity 1.2 S/m was used to match the CSF. Intraventricular haemorrhages were simulated using agar gel spheres of 0.67 S/m, placed in the centre of the phantom. The geometry used in the head shaped phantom was a smoothed reference model used in previous studies[36]. The model has to be adjusted to fit within the constraints of the printer used. As with the spherical tank, CSF was replicated as saline of conductivity 1.2 S/m. Unlike the models used in simulation in these studies, there was no skull present in either of these phantoms. With increased interest in neonatal applications of EIT, and only simple phantoms available in the literature, there was a clear need for a realistic phantom for neonatal EIT.

(a)Spherical tank (b)Smoothed head tank

Figure 2.5:Neonatal head phantoms.(a)spherical tank by Tang, Oh, and Sadleir[140],(b)smoothed

head shaped tank by Tang and Sadleir[36]