3.4 Discussion
4.3.3 Localisation Accuracy
The mean localisation accuracy in the adult tank was 18.1 and 12.9 mm or 11.7 and 8.4 % with zeroth and first order respectively. Without noise added, the accuracy with first order regularisation was significantly greater than zeroth order (p<0.05). The range of errors was also relatively larger using zeroth order, with a standard deviation of 8.5 mm compared to 5.0
Ant Pos Lat Cen Caud 0 5 10 15 Image Error %
Loc. Shape Noise
(a)0th order
Ant Pos Lat Cen Caud 0 5 10 15 Image Error %
Loc. Shape Noise
(b)1st order
Figure 4.15:Image quantification results in neonatal tank,(a)zeroth order and(b)first order Tikhonov regularisation
mm for first order. For both regularisations, the addition of noise significantly increased the localisation error (p<0.05), to 23.1 mm or 15.0 % for zeroth order and 18.0 mm or 11.72 % with first order.
The location error in the neonatal head was approximately half that of the adult head, with both mean errors less than 5% without noise. Unlike the adult head, the two regularisation algorithms had a similar performance in the neonatal head, with less than 2 % difference. Also contrary to the results in the adult, zeroth order Tikhonov gave the greater accuracy: 3.3 mm or 2.96 % compared to 5.5 mm or 4.95 % with first order. As was found in the adult head, the addition of the noise significantly increases the localisation error (p<0.05), to a mean of 4.87 mm or 4.35 % with zeroth order, and 7.4 mm or 6.6 % with first order.
0th 0th N 1st 1st N 0 10 20 30 40 Loc. Error mm 0 10 20 Loc. Error %
(a)Adult Head
0th 0th N 1st 1st N 0 5 10 15 Loc. Error mm 0 5 10 Loc. Error % (b)Neonatal Head
Figure 4.16:Localisation error (mean±std) of the simulated perturbations in(a)adult and(b)neonatal head, with and without noise present, for both regularisations, expressed as norm of vector distance in mm, and as a percentage of mesh dimensions
The greatest localisation errors with zeroth order regularisation were found towards the edges of the adult tank, particularly in the posterior and coronal regions, where the location error is≈40 mm. The localisation error is lowest in the centre of the head, approximately 10
mm, which correlates with the experimental results in section 4.3.1. The localisation error is more evenly distributed in the simulations with first order Tikhonov, with an accuracy close to 10 mm across the entirety of the adult head. However there is still a significantly higher region of 20-30 mm error in the coronal region of the head closest to the skull. The addition of realistic noise results results in a greater error across the head, with the the largest increases found in the posterior region of the head. The spatial distribution of the error with zeroth order is largely unchanged with the addition of noise, whereas with first order, small region of higher error are now found towards the centre of the skull.
0th
(a)Clean (b)Noise
1st
Figure 4.17: Spatial distribution of localisation error in mm in adult head for both zeroth and first order Tikhonov regularisations, for simulated perturbations with and without realistic noise added
The spatial distribution of the localisation error is more complicated in the neonatal head compared to the adult head, figs. 4.17 and 4.18. Broadly, the localisation error is lower, approximately 5mm, in the upper half of the head above the axial plane compared to the lower region of the skull where the error is approximately 10 mm. There is less variation with depth than was observed in the adult head. The error at the most caudal areas at the base of the mesh, level with the temporal fontanelles is lower than the error in the immediate surroundings. The addition of realistic noise has a similar effect to that observed in the adult skull in that the error is larger and more evenly distributed across the head. Further, for perturbations close to the inion fig. 4.17, the artefacts present in zeroth order reconstructions, e.g. fig. 4.11, were large enough to be incorrectly identified as the perturbation in the image. Thus in this location the localisation error is close to 100 % of the mesh diameter.
0th
(a)Clean (b)Noise
1st
Figure 4.18:Spatial distribution of localisation error in mm in neonatal head for both zeroth and first order Tikhonov regularisations, for simulated perturbations with and without realistic noise added
4.3.4
Signal Size
Adult Head
The spatial distribution of the median voltage change in the adult head in shown in fig. 4.19. The largest changes, approximately 6µV are found in the anterior of the head, close to the ground electrode. The median change decreases as the perturbations move towards the posterior of the skull, to a minimum value of approximately 0.5µV.
(a)Side (b)Top
Figure 4.19: Median voltage change µV for 10 % contrast perturbations across the adult head, (a)
sagittal section and(b)axial section
The potential number of measurable voltages for a given minimum signal is shown in fig. 4.20. The minimum voltage which yields 50 % potential combinations in 50 % of the perturbations is 1.85µV, however this decreases to 0.5 µV to ensure 50 % potential combinations in 95 % of the perturbations.
0 2 4 6 8 10 12 14 16 18 20 0 20 40 60 80 100 Minimum SignalµV P oten tial Com binations % 1st 5th 25th Median 75th 95th 99th
Figure 4.20: Percentage of measurable voltages for a given minimum signal size inµV across all pertur-
bations pi jkin adult head, expressed as percentiles of the perturbation distribution
Neonatal Head
The spatial distribution of the median voltage change in the neonatal head in shown in fig. 4.21. As was found in the adult skull, the largest changes, approximately 8-9µV occur in the anterior of the head, close to the ground electrode. The median change decreases as the perturbations move towards the posterior of the skull, to a minimum value of approximately 0.5µV.
(a)Side (b)Top
Figure 4.21: Median voltage changeµV for 10 % contrast perturbations across the neonatal head,(a)
sagittal section and(b)axial section
The potential number of measurable voltages for a given minimum signal is shown in fig. 4.22. Similar to the adult tank, the minimum voltage which yields 50 % potential combinations in 50 % of the perturbations is approximately 2µV, however this decreases to 0.68µV to ensure 50 % potential combinations in 95 % of the perturbations.
0 2 4 6 8 10 12 14 16 18 20 0 20 40 60 80 100 Minimum SignalµV P oten tial Com binations % 99th 95th 75th Median 25th 5th 1st
Figure 4.22:Percentage of measurable voltages for a given minimum signal size inµV across all pertur-
bations pi jkin neonatal head, expressed as percentiles of the perturbation distribution
4.4
Discussion
4.4.1
Summary of results
In this study, localised impedance changes of approximately 10 % were reconstructed reliably in both an adult and neonatal phantom, using both zeroth and first order regularisation schemes. In the adult tank the global image error was 7.55 and 12.8 % for zeroth and first order respectively. For both regularisations, the localisation of the centre of mass of the perturbation was approximately 5 % or less of the mesh diameter, which equates to approximately 8 mm or less. The reconstructed images in the neonatal head tank were qualitatively better with conductivity changes appearing more localised. The image error in the neonatal tank on average was 8.5 % for all five positions and reconstructions, the centre of mass of the perturbations was reconstructed with 2.5 % or less error, corresponding to 3 mm or less.
The simulation results indicate that 10 % contrast perturbations, such as those arising from focal epilepsy, could be imaged inside the adult head with a mean accuracy of less than 12 % using first order Tikhonov regularisation, 250µA current and the “optimal” protocol. The estimated accuracy in the neonatal head was double that of the adult head with a mean localisation error less than 6 % or 5 mm for both regularisation schemes.
The changes in the standing voltages from these 10 % perturbations were found to range from 0.5 - 6µV on average in the adult head and 0.5 to 8µV in the neonatal head. A noise level of 2µV was shown to provide a measurable change on 50 % of the combinations within each injection protocol for 50 % of the perturbations.
4.4.2
Tank study
The results in this study compare favourably to the previous images reconstructed in a head shaped phantom with skull in section 4.1.1 by Fabrizi, McEwan, Oh, et al.[58], with less than half the localisation error. These images were produced without the post-processing necessary in other studies, including PCA and boundary voltage rejection[58],[79], which is likely due to the increased accuracy of the tank and forward model described in section 2.3.2 and lower noise in the measurements with the ScouseTom system. The three perturbation locations used in the adult tank correspond to the areas with the lowest median signal change as calculated in the simulation study section 4.3.4, and thus do not represent the optimal locations for imaging. Qualitatively, the reconstructions with first order Tikhonove.g.fig. 4.5, are not dissimilar to those obtained in section 3.3.2 with a high contrast plastic perturbation, with the exception of increased artefacts inside the skull cavity.
To the author’s knowledge, these images represent the first reconstructions of a biolog- ically realistic perturbation in a geometrically realistic neonatal head tank with skull. The reconstructions show localised impedance changes across the neonatal head, including the caudal position at the furthest point from the electrodes fig. 4.14. The reconstructed images were both a qualitative and quantitative improvement over the images in the adult head, with clearer localised impedance changes and half the image error. The likely reason for this improvement is the increased sensitivity in the brain due to the increase in skull conductivity and the presence of the fontanelles reducing the shunting of current around the skull. These images suggest that there is a strong cases for clinical success in imaging within the neonatal patients compared to the adult head.
4.4.3
Simulation study
The simulation study shows a clear spatial dependence in the localisation accuracy of pertur- bations across the head, particularly with zeroth order regularisation. The localisation error was greater towards the centre of the skull in the adult tank, which is in agreement with the results from Fabrizi, McEwan, Oh,et al.[58]. The broadness of the perturbation using zeroth order regularisation, figs. 4.4 and 4.5, draws the centre of mass towards the centre of the tank, despite the correctly located maxima. The bias towards the centre of the tank is the likely cause for the counter-intuitive increase in localisation accuracy for perturbations in this region, where the sensitivity is lowest.
The benefits conferred onto the localisation error by the fontanelles is further evinced in the results of the simulation results fig. 4.18. The error is significantly lower in the upper region of the skull where current is injected between electrodes located close to the anterior and posterior fontanelles. The sphenoid and mastoid fontanelles also improve the localisation in the deeper structures, compared to perturbations in the axial plane above the temporal
bone. This dependence upon the fontanelles may prove a challenge in clinical experiments as discrepancies between the actual morphology and the forward model could give rise to greater modelling errors compared to those experienced with the solid skull in the adult skull.
The addition of noise had the greatest influence upon the localisation accuracy in the adult head and in the posterior of the neonatal head, which correlates with the median signal size in figs. 4.19 and 4.21. The less conductive skull in the adult head reduces the signal size by≈2µV, which consequently reduces the SNR in comparison to the neonatal head with
equivalent noise. The change in voltages are substantially greater in the anterior region of the brain
The additive noise added to the simulated voltages was based on scalp recordings from section 3.3.3 which correlates with the sensitivity map of the optimal protocol with the fig. 3.35. This uneven sensitivity and, consequently, signal size, could potentially be alleviated through repositioning of the ground electrode and recalculation of the “optimal” protocol using a ‘seed” electrode placed on the posterior of the head. The noise added to the simulations was equivalent to 1.54µV, when averaged over 20 recordings. The minimum signal size in figs. 4.20 and 4.22, suggests that a median number of perturbations had 55 % of combinations with an SNR above 1, and 99 % of the perturbations had at least 30 % measurable channels. The majority of the perturbations were still localised within 30 mm and 10 mm in the adult and neonatal heads respectively, even without rejection of these noisy channels. Improvements to SNR through improved hardware or higher current, given the sharp increase in the number of percentage channels at 1µV should bring the localisation error closer to the ideal simulated case.