6.4 Detection and Alignment Algorithms
Spike detection and alignment (D&A) clips the signal around a suspected spike before it is sorted. Accurate D&A is essential for successful spike sorting, as sorting is sensitive to spike position in the frame (as are all the algorithms described above).
We verify several D&A algorithms [104, 110] with respect to their impact on sorting: a good algorithm aligns spikes so that only a small number of clas- sification errors are caused at the subsequent sorter. Again, we compare our algorithms to the state-of-the-art commercial algorithm described in [109]. Figure 6.9 describes the validation scheme. All algorithms detect spikes by
Evaluated Algorithm rate Reference Compare Sorter Reference D&A Training Reference D&A signal Recorded Error Sorter
Fig. 6.9.D&A algorithms validation scheme
threshold crossing. The initial frame ofM samples is generated, withKsam- ples preceeding andN samples succeeding the threshold crossing event. The alignment is to determine the offseti0 ∈ {1..K} so that N samples starting fromi0 are passed to spike sorting.
6.4.1 Algorithms Verified
The reference algorithm (denoted asPCA D&A) computes principal compo- nent representation of theN-point frame for everyi∈ {0..K}, based on the first two principal components. The offset selected is the one that yields the smallest energy of error between the signal and its representation by the first two principal components. The required computation is lengthy: for every in- spected offset, one must compute projections on the two PCs (2N additions and 2N multiplications). Then compute the representation in PC space: 2N multiplications andN additions. Then subtract it from the signal (N addi- tions). Then calculate the energy of the difference, which is anotherN addi- tions andN multiplications. The whole computation takes 5N multiplications and 5N additions for every offset, giving complexity index ofK·55N.
80 6 Algorithms for Neuroprocessor Spike Sorting
To reduce the computation burden, we have tried to align spikes with respect to the maximum correlation point of the incoming signal with the first principal component (Maximum Projection Alignment, MPA). We take advantage of the observation that this correlation typically exhibits a sin- gle maximum near a spike. The calculation is much simpler: for every offset inspected, one must compute only a projection of the signal on the first princi- pal component, requiringN additions andN multiplications. The complexity index is thereforeK·11N.
As in spike sorting PCA, we also tried to simplify PCA D&A by downsam- pling the signal and the principal components (i.e. Segmented PCA D&A). Downsampling the signal costs N additions. Assuming we use S segments, the computation with downsampled signal requires 5Sadditions and 5Smul- tiplications, similarly to the regular PCA. The complexity index is therefore K·(55S+N).
Similarly to sorting algorithms, we tried to replace principal component shape-space generation (that requires heavy computation of PC projections) by a much lighter integral transform. Its major advantage is the lack of multi- plications. In the same way MPA D&A seeks the maximal correlation with the first principal component,Maximum Integral Transform Alignment searches for the maximum correlation with the rectangular window over the first time interval. As in spike sorting MITA can be viewed as MPA with the first prin- ciple component degenerated to a rectangular window. The computation in- volves summation of samples in a moving window. When implemented effi- ciently, it can be done with 2N+K additions.
6.4.2 Validation Results
Error rates of the software sorter under various D&A algorithms are summa- rized in Table 6.2. We have also examined the performance of the sorter when no alignment is done, i.e. spikes are aligned to the point of threshold crossing. Simulations were performed withNof 200 andKof 50, in accordance with the reference algorithm. As with sorting, integral transform gives small accuracy
Table 6.2.Validation results summary
Algorithm Additions Multiplications Complexity Error rate (%)
Threshold 50 0 50 9.4
MITA 450 0 450 1.2
PC7 12,000 1750 30,000 0.7
MPA 10,000 10,000 110,000 0.3
PCA 50,000 50,000 550,000 0.0
penalty with a very strong reduction of computation complexity, constituting the knee point of the accuracy-complexity graph.
7
MEA on Chip: In-Vitro Neuronal Interfaces
Multielectrode arrays (MEAs) are the principal instruments for non-invasive interfaces with biological neural networks (Chap. 2). MEAs allow multichan- nel recording and stimulation with neuronal networks cultured for several months. Planar arrangement of electrodes upon the substrate defined by pho- tolitographic methods potentially enables high spatial recording resolution with very large numbers of electrodes. Unlike penetrating probes, electrodes of MEAs need not be manually positioned inside the brain tissue one-by-one. Similarly to penetrating probes, MEA must provide bio-compatible elec- trodes for tissue interfacing. To allow sensing of microvolt signal levels, it must be coupled to a low-noise signal conditioning front-end. A processing unit can acquire the signal and originate stimuli back to the tissue. A temper- ature controller must be included within a cultured network recording setup, to maintain the neurons at a/the constant temperature of 36◦.
MEAs on glass substrate typically integrate recording electrodes connected by wires to contact pads on MEA perimeter Fig. 7.1. Contact pads are typ-
Wires
Contact sites Recording sites
82 7 MEA on Chip: In-Vitro Neuronal Interfaces
ically much larger than the recording sites, as they are clipped to recording front-end equipment. The breakout from the compact 2D structure of small recording sites into 1D structure of contact pads limits the number of channels the MEA can provide in practice.
Silicon multielectrode arrays, orMultielectrode Chips (MECs) allow inte- gration of electronic circuits on the same substrate with electrodes (Fig. 7.2). The breakout towards the perimeter is relaxed, potentially allowing for a larger number of electrodes. In addition MEC provides a better system integration
Frontend Frontend Neural network Recording Stimulation Si substrate Frontend Frontend Frontend
Electrode Electrode Electrode Electrode
Processing Unit Electrode
Fig. 7.2.Multielectrode chip concept
and enables on-die processing for data compression and stimulation feedback. Integrated circuits typically use aluminum or copper for metal intercon- nects. Both are subject to fast corrosion when put into biological medium. Re- ported integrated circuits for multielectrode recording fabricated in standard CMOS processes [47, 11, 48, 50] involve various proprietary post-fabrication steps for electrode definition:
• [50]: gold deposited on top of aluminum contacts.
• [48]: areas of field oxide are etched to expose polysilicon electrodes.
• [11]: stack of Ti/Pt and dielectric layer deposited on top of the electrodes.
• [47]: Pt deposited on top of recording sites.
Such processing steps are hardly a commodity: they require special facilities and complicate MEC fabrication. Lithography is probably the most problem- atic, as it requires expensive mask sets.
In our work [111] we have addressed the development of standard CMOS MEC, involving no or only simple post-fabrication processing. The following summarizes the work:
• Design of a prototype sensor circuit
• Fabrication in standard CMOS process