### Isolation of the spinal cord

Guinea pig spinal cords were isolated using previously specified techniques [22–24]. Ketamine (80 mg/kg), xylazine(12 mg/kg), and acepromazine(0.8 mg/kg) were used to anaesthetize adult guinea (350–500 gms). The guinea pig hearts were then perfused with 500 ml of oxygenated Krebs solution [124 mM NaCl, 5 mM KCl, 1.2 mM KH_{2}PO_{4}, 1.3 mM MgSO_{4}, 2 mM CaCl_{2}, 20 mM dextrose, 26 mM NaHCO_{3} and 10 mM sodium ascorbate], equilibrated with 95% O_{2} and 5% CO_{2} to remove blood and lower the body temperature. The vertebral column was excised, spinal cords quickly removed and immersed in cold Krebs solution. All animal use received prior approval by the Purdue University Animal Care and Use committee, in strict accordance with Federal, State, and University guidelines.

### Vibrating electrodes for the measurement of extracellular current

Measurements were made with non- invasive one dimensional (1 D) and neutating (or 2 D) probes for the measurement of extracellular current [7, 26, 27]. The former gives the density of electric current entering or leaving a biological source normal to its surface with time, while the latter provides this as well as two-dimensional information in the form of current density vectors. Spatial resolution is on the order of 20 μm, and, depending on the resistivity of the bathing media, such probes can detect current densities on the order of picoA/cm^{2} – far below the resolution required here. Current Vectors are displayed as raw data by software and are superimposed over the digital video image and captured by digital image acquisition.

Microelectrodes used for fabricating the vibrating probes were Pt/Ir electrodes (Micro Probe Inc, Gaithersburg, MD) with a 3 – 5 μm exposed tip, while the rest of the electrode was insulated. The tip of the probe was platinum blackened by electroplating to form a 25–30 μm diameter Pt ball. Alternately, the platinum tip can be replaced with one of a calcium specific resin, which then measures only the calcium component of the net current flow. The completed probes were then calibrated in Krebs solution at 37 degrees C as were physiological measurements. A KCl filled glass microelectrode was used as a point source for calibrations (see below). The point source was made using a 1.5 mm internal diameter borosilicate glass capillary tube pulled to a tip diameter of 8–10 μm. This was performed on a David Kopf Vertical puller (David Kopf Instruments, Tujunga, CA). The probe was vibrated at a distance of one tip diameter between its two extreme positions with X and Y frequencies ranging from 250–300 Hz. The probe actually measures the small voltage difference between its extreme positions with a phase/frequency lockin amplifier. This voltage difference together with the known resistivity of the media is used to calculate the bulk current or the current density associated with the sample of interest. The direction of the current vectors shows whether the current is an influx or efflux.

### Temporal and spatial profiles of spinal cord injury currents

Using the vibrating voltage probe to study spinal cord injury we measured a large inwardly-directed injury current at the lesion soon after injury to the spinal cord. This current then decreased rapidly in magnitude to approximately 20% of its original magnitude within 30 minutes (refer to Results above). This decay can be approximated by a 3-parameter exponential decay model:

*y*(*t*) = *y* 0 + *a* exp(-*bt*)

where y(t) = current density drop as a function of time, t = time, and y0, a and b are empirically derived, normalized constants.

This expression is the basis of the model for all time-dependent current density measurements.

In a separate study, the vibrating probe was brought to a starting position 50 μm away from the surface of the injury site of the spinal cord. The vibrating electrode was then sequentially stepped back away from the injury site at fixed intervals with the injury current density measured at each point. This step-back, or fall-off, profile provides a reasonable assessment of the spatial profiles of the external electrical field associated with the injury to the spinal cord. This would not be expected to be the same as that data taken from a point source, given the complex and extended geometry of the tissue surface.

An exponential linear combination current decay model provided the best fit for these step-back experiments. We used the formula:

*y*(*x*) = *y* 0 + *c* exp(-*dx*) + *ex*

where y(x) = current density drop as a function of distance from injury site, x = distance from injury site, and y0, c, d and e are empirically derived normalized constants. This formula does not account for the current decay with respect to time. To correct for this we applied a correction factor which compensates for this loss to yield the following model;

*y*(*x*) + Δ*y* = *y* 0 + *c* exp(-*dx*) + *ex* + |-*ab* exp(-*bt*)Δ*t*|

Finally, it is of interest to know the magnitude of the current entering the spinal cord at the "instant" of injury (time = 0), and to more properly account for the increased magnitude of the current at the surface of the cord from that actually recorded at the standard measurement position. Given the rapid decline in current with time after the acute injury, and the fact that the probe can not be vibrated any closer than 30–50 μm from the cord's surface without damage, this required some separate study and quantitative normalization of the recorded data.

Calculation of the correction for the current "fall off" due to both time and distance is calculated based on the combination of the formulas presented above in Methods, and is as follows:

Δ*Y*(*x*,*t*) = |[-*CD* exp(-*Dx*) + *E*]Δ*x*| + |-*AB* exp(-*Bt*)Δ*t*|

This current when added to the original current (Y) reveals the injury current at the surface instantaneously after injury for any one experiment:

*Y*(*x*,*t*) = *Y* + Δ*Y*(*x*,*t*) and,

*Y*(*x*,*t*) = *Y* + |[-*CD* exp(-*Dx*) + *E*]Δ*x*| + |-*AB* exp(-*Bt*)Δ*t*|

We calculated all of the empirical coefficients using normalized data sets compromising approximately 10 different scans of spinal cord injury current profiles. By using normalized data for this analysis, it was possible to calculate "universal" coefficients. This is necessary since the calculations of constants derived from the raw data can be misleading given the large variations observed when measuring endogenous injury currents, whereas normalized coefficients had less than 1% variability. These coefficients can be used to adjust normalized data sets that then need to be converted back to discrete data.

$Y(x,t)=Y+\left[\begin{array}{l}\left|-(78.818)(0.0065)\mathrm{exp}(-0.0065x)+(-0.0098)]\Delta x\right|+\\ \left|-(95.83)(0.04625)\mathrm{exp}(-0.04625t)\Delta t\right|\end{array}\right]$

This derived current density data should not be considered to provide a perfectly accurate picture of the dynamics of injury current flow in the spinal cord; however, it provides the most accurate data extant for understanding the *immediate* decay in physiological currents at any distance from the injury site. Moreover, this method permitted us to both calculate, then compare, the injury current at t = 0 and x = 0 for raw data measured from both ventral and dorsal portions of the spinal cord.