System and Method for Hierarchical Referencing for Biopotential Measurements

Abstract

The present invention relates to a method of taking biopotential measurements, with the ability to perform in high-density sensing applications. The invention is a hierarchical referencing method for the electrodes in the biopotential measurement system that is able to recover potential at each location with respect to a global reference with smaller requirements on ADC resolution, and thus with lower power and area requirements as compared to current systems.

Claims

1. A system for measuring biopotentials, comprising: a plurality of electrodes, arranged on a surface in a multi-level, hierarchal tree structure with respect to a global reference electrode; a plurality of analog to digital converters to convert the difference in potential between pairs of said electrodes, one electrode of each pair being a parent to the other electrode in said tree structure; wherein each pair of electrodes is spatially correlated with each other.

2. The system of claim 1 further comprising a plurality of differential amplifiers, one for each pair of electrodes, said differential amplifiers taking as inputs the biopotentials measured at each electrode of its respective pair of electrodes and outputting the difference in biopotentials between said electrodes.

3. The system of claim 1 wherein each electrode at a particular level in said tree structure can serve as a parent to one or more nodes at the next lowest level in said tree structure.

4. The system of claim 2 further comprising a means for storing said differences in biopotentials for each of said pairs of electrodes.

5. The system of claim 1 wherein said electrodes are held in spatial relationships with respect to each other by a medium.

6. The system of claim 5 wherein said medium can be worn on the body of a subject.

7. A method for measuring biopotentials, comprising: arranging a plurality of electrodes in a multi-level, hierarchal tree structure with respect to a global reference electrode as the root of said tree, such that each electrode has exactly one parent electrode in said tree structure; measuring the potential at each electrode; taking the difference in potential between each electrode and its parent electrode; converting each difference in potential to a digital value; and storing said digital values on a digital storage medium.

8. The method of claim 7 wherein each electrode is spatially correlated with its parent electrode.

9. The method of claim 7 wherein each electrode has as its parent the physically closest electrode which is in the next higher level of said tree structure.

10. The method of claim 7 further comprising the step of taking the sum of the differences in potential between an electrode and each parent in the path between said electrode and said global reference electrode to obtain the difference in potential between said electrode and said global reference electrode.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 shows the brain-surface to scalp transfer function (in spherical harmonics basis, increasing spherical harmonic index l corresponds to increasing spatial frequencies) using the 4-sphere model of the head with parameters r.sub.1=7.8 cm, r.sub.2=7.9 cm, r.sub.3=8.6 cm, and r.sub.4=9.5 cm, and conductivities of cerebrospinal fluid (CSF) layer 5 times, the skull 1/80 times, and the scalp the same, as the conductivity of the brain.

[0013] FIG. 2 illustrates direct global referencing, and the associated tree, where every electrode is referenced directly against a global electrode.

[0014] FIG. 3 presents sequential bipolar biopotential referencing and the associated tree.

[0015] FIG. 4 shows the new hierarchical referencing strategy. For clarity, the differences of voltages being measured are indicated on the top.

[0016] FIG. 5 shows an example of the use of the device on a human head, forming a neural web

[0017] FIG. 6 shows a physical embodiment of a single set of probes held in place by a customized holder.

DETAILED DESCRIPTION OF THE INVENTION

[0018] For a variety of reasons, spatially dense biopotentials tend to be highly correlated. As an example, the spatial power-spectral-density of EEG as it passes through the CSF, the skull and the scalp is shown in FIG. 1. As such, there is important information buried in the least significant bits of each observation. Because of the decay of high spatial frequencies, as shown in FIG. 1, the least significant bits are precisely the bits in which high resolution information is buried. As a result, small difference between recordings of sensors in close physical proximity to each other capture events that generate small fields either due to their depth or spatial extent.

[0019] This invention is a hierarchical referencing strategy designed to exploit the high spatial correlations to reveal information at lower order bits of the recordings from electrodes. The strategy reduces noise accumulation significantly over sequential differential measurements while allowing low precision ADCs for the same overall noise as direct global referencing. In addition, there is a savings in both power and component expense, as less expensive analog to digital converters, having a smaller number of bits of resolution, can be used to detect the small differences between spatially close sensors.

[0020] Every referencing mechanism can be represented as an associated tree. Each electrode corresponds to one node in the tree. The global reference electrode is the root node; all nodes referenced directly against the global root node are nodes at level 1. All nodes referenced directly against level 1 nodes are level 2 nodes, and so on. In the tree, a node's parent is the node the corresponding node is referenced against. Because each node has exactly one parent, the graph of the topology of the nodes is a tree.

[0021] The mechanism proposed in this invention is illustrated in FIG. 4. Instead of using sequential bipolar referencing, the electrodes are arranged in a tree pattern with a number of levels that can be optimized based on spatial correlations. For placement of electrodes along a grid, one can envision the grid as a hierarchical subdivision of squares. In case of placement of electrodes on a spherical surface, commonly used techniques are inherently recursive (e.g. icosahedron bisections used in EEG grids) and lend themselves naturally to hierarchical constructions of unequal but roughly constant degree per level.

[0022] To show the improvements of this invention over current methods, a comparison of this invention is first done with the sequential bipolar strategy. Input-referred noise variance for all electrodes is assumed to be the same regardless of strategy. To recover potential V.sub.iV.sub.0 from measurements Y.sub.1=V.sub.1V.sub.0+Z.sub.1, Y.sub.2=V.sub.2V.sub.1+Z.sub.2, . . . , Y.sub.i=V.sub.iV.sub.i1+Z.sub.i, one can simply add these potentials:

[00001]$\underset{j=1}{\overset{i}{.Math.}}.Math.Y_j=\underset{j=1}{\overset{i}{.Math.}}.Math.\left(V_j-V_{j-1}+Z_j\right)=V_i-V_0+\underset{j=1}{\overset{i}{.Math.}}.Math.Z_j,$

and thus noise variance increases linearly with the number of electrodes.

[0023] On the other hand, the hierarchical referencing strategy has a slower increase in noise. For instance, consider a tree where every node has D children. Then, to reach every node, one only requires to sum of O(log(n)) terms, and the noise also grows only logarithmically.

[0024] Alternatively, in sequential bipolar referencing, one could allocate different levels of resolution to different electrodes, for e.g., by allocating increasing number of bits of ADCs as the electrode gets farther from the reference electrode. To compare with hierarchical referencing, let us assume that the noise in the worst case is log(n) as well. In that case, one could use

[00002]${}_{\mathrm{zi}}^2={}_{z.Math..Math.0}^2/i,$

because

[00003]$\underset{i=1}{\overset{n}{.Math.}}.Math.\frac{1}{i}.Math..Math.\log \left(n\right).$

However, this requires at least half the electrodes to have noise variance

[00004]${}_{\mathrm{zi}}^{2}2.Math..Math.{}_{z.Math..Math.0}^2/n,$

which reduces to zero as n increases. This noise variance can be kept constant in the hierarchical strategy for log(n) increase in overall noise).

[0025] The hierarchical strategy also makes it easier to ensure good contact. As long as the fewer electrodes in the higher layers have good contact, the larger number of electrodes in the lower layers will be sensed accurately. Having poor contact in the lowest layer hurts only the particular electrode with poor contact because there are no further electrodes that reference against the lowest layer.

[0026] We also note that the hierarchical strategy's tree structure provides an additional benefit: it reduces wiring requirements over the conventional global referencing strategy. This is because the local reference electrodes are nearby in the tree architecture. This lowering of wiring requirements can help with reducing inter-wire coupling, reducing shielding requirements, reducing requirements on amplifier's gain and noise (thus also lowering amplifier energy), and also directly reduce the cost and weight.

[0027] To compare this invention with the direct global referencing strategy, the savings are in energy and area because of savings in ADC bit resolution. The required ADC resolution for the hierarchical topology can be calculated by

[00005]$\frac{1}{2}.Math.\log .Math.\frac{2.Math..Math.{}^2\left(1-\right)}{q_e^2},$

where .sup.2 is the variance of the signal being sensed, q.sub.e.sup.2 is the ADC quantization noise, and p is the correlation between the two signals (where p>0.5, due to sensor spacing and location).

[0028] A specific embodiment of the invention was modeled and analyzed for ultra high density EEG sensing, using up to 9331 electrodes, much greater than conventional systems with up to 512 electrodes. As a byproduct of being able to reduce the ADC bit resolution of this system, energy savings of greater than a factor of 2.7 were achieved. The hierarchical technique goes a step further, and instead of viewing the decay of high spatial frequencies simply as a detriment to signal quality, it exploits it reducing energy and area requirements, enabling the user to dig deeper into the resolution of each sensor, as well as enabling higher sensor density.

[0029] Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limiting to the details shown. Rather, various modifications may be made in the details without departing from the invention.

[0030] FIGS. 5 and 6 show various ways in which the electrodes can be held in place to ensure that they are spatially correlated when in use. Preferably, the electrodes will be embedded in a flexible material or medium that can be worn or placed on the body part where the biopotentials are being measured. FIG. 5 shows such an arrangement wherein the electrodes are held in place in the material of a cap that is worn on the head of the subject. FIG. 6 shows a plurality of the electrodes held in place by a bracket.

[0031] It should also be noted that the invention, to be operational, requires circuitry to read the biopotential differences and to store the differences in digital form for later analysis.