Autonomous control for mechanically stable navigation of microscale implants in brain tissue to record neural activity

Abstract

Emerging neural prosthetics require precise positional tuning and stable interfaces with single neurons for optimal function over a lifetime. In this study, we report an autonomous control to precisely navigate microscale electrodes in soft, viscoelastic brain tissue without visual feedback. The autonomous control optimizes signal-to-noise ratio (SNR) of single neuronal recordings in viscoelastic brain tissue while maintaining quasi-static mechanical stress conditions to improve stability of the implant-tissue interface. Force-displacement curves from microelectrodes in in vivo rodent experiments are used to estimate viscoelastic parameters of the brain. Using a combination of computational models and experiments, we determined an optimal movement for the microelectrodes with bidirectional displacements of 3:2 ratio between forward and backward displacements and a inter-movement interval of 40 sec for minimizing mechanical stress in the surrounding brain tissue. A regulator with the above optimal bidirectional motion for the microelectrodes in in vivo experiments resulted in significant reduction in the number of microelectrode movements (0.23 movements/min) and longer periods of stable SNR (53% of the time) compared to a regulator using a conventional linear, unidirectional microelectrode movement (with 1.48 movements/min and stable SNR 23% of the time).

1. Introduction

Automated robotic approaches have been successfully used for precise positioning of microelectrodes to isolate and record extra- and intracellular potentials from single neurons in vivo (Chakrabarti et al. 2012; Jackson et al. 2010; Kodandaramaiah et al. 2012). Kodandaramaiah et al. (2012) have successfully demonstrated an automated in vivo patch clamping system. The robot detects a neuron by tracking a temporal sequence of changes in electrical impedance.. Such innovation in neural interfaces promises high fidelity signals, high yield, increased throughput, and adaptability to higher-level integrated systems, decreased need for manual intervention and skill and more importantly lowers barriers for adoption of advanced brain monitoring techniques. The challenge to such precise positioning of microprobes in soft brain tissue or other tissue is the positional inaccuracies induced as a result of tissue drifts given the viscoelastic nature of soft tissue. Hyperelasticities and heterogeneities in brain tissue introduce additional errors in position estimates. The displacement requirements on the microprobes in the case of brain monitoring systems are in the scale of the cell bodies of single neurons (approximately 10 μm diameter spheres) or smaller which adds to the precision requirements of such robotic positioning systems. At the scale of single cells, the dynamics of a pulsating brain and subject behavior (that can cause significant displacements in the brain tissue) can also be failure modes resulting in loss of signal. The challenge is also significantly increased due to lack of any visual feedback on position of the microelectrode within the brain tissue. Feedback is often limited to the electrical signal recorded from the electrode site.

Past approaches in robotic controls for neural activity used stochastic models of neuronal activity patterns to position the microelectrodes to include tissue drifts among other factors that caused non-stationarities in neural recording to isolate and track specific units (Wolf et al. 2009). The autonomous algorithm “SpikeTrack” builds a strong case that autonomous control could in fact isolate single units and maintain signal quality during recording sessions (Chakrabarti et al. 2012). The algorithm is built on a framework of finite state machines that manages the electrode’s movement to optimal depth (Cham et al. 2005). The “SpikeTrack” algorithm was tested on a five channel Eckhorn drive in macaques (Chakrabarti et al. 2012). The algorithm’s performance was compared with passive placement of electrodes and expert human experimenter’s performance in positioning electrodes to obtain stable unit activity in semi-chronic experiments. The algorithm performed significantly better and enhanced signal quality when compared with passive placement of electrodes in recording sessions of 30 min duration. The algorithm’s performance was also comparable to expert human users in maintaining signal quality in experiments that lasted for at most 3 hours. The control algorithm made several small movements of magnitude ~10 μm, with less than 100 sec time interval between movements on an average, in order to maintain the quality of recordings. In an interesting comparison, expert human users employed assorted strategies ranging from frequent, large amplitude movements to rare adjustments with minimal directionality switches. However, stability in neural recordings characterized by the ability of the neural interface to maintain and track a stable signal quality from an identified single neuron still remains a challenge even with the above robotic interfaces. In fact, a recent study (Jackson and Fetz 2007) demonstrated that the act of moving microelectrodes to track single neurons resulted in significant loss of cells immediately after microelectrode movement. The above experience suggests that mechanical stresses induced directly as a result of microelectrode movement might cause instabilities in neural recording due to residual stress built up in the brain tissue.

The approach in this current study involves an automated control that compensates for tissue drifts due to mechanical stresses using a model of brain tissue that can predict stresses in the tissue induced by displacements of microelectrodes in the brain. Such models of brain tissue have been recently reported for porcine (Gefen and Margulies 2004) and rat (Sridharan et al. 2013) brains. However, the above models of brain tissue were developed using indentation techniques that involved measuring relaxation stresses in brain tissue after millimeter scale indentation (subsequent to penetration) of brain tissue. Given the heterogeneities in the cortical gray matter with vasculature and cellular diversity, it is unclear if the above models of brain tissue can scale down and accurately predict stresses in response to microscale displacements of implants in brain tissue that are appropriate for brain monitoring. The first objective of this current study is therefore to develop an empirical model that will estimate the dynamic build-up in mechanical stress in brain tissue in response to microscale movement of implants. The second objective is to test this empirical model in a closed-loop compensator to create quasi-static mechanical stress in the surrounding brain tissue in the specific application of isolating and monitoring single or multiple neurons in the brain. The working hypothesis is that by minimizing mechanical stress build-up in the tissue during microelectrode movement in the brain, the stability of neuronal recordings can be improved resulting in fewer interventions from the automatic controller in the long run.

Steering microscale probes within soft tissue with precision is also important in neurosurgery, in applications involving delivery, manipulation and/or excision of other soft tissues in the body. Applications in neurosurgery and surgery or treatment of other soft tissues usually involve visual feedback in the form of MRI images that are co-registered with the stereotactic coordinates to get an accurate estimation of position and velocity of surgical probes. The objective in these cases generally, is precision delivery of drug or radioactive source for tissue ablation or excision. The challenge to such precise positioning of surgical probes in soft brain tissue or other tissue is the positional inaccuracies induced as a result of tissue drifts given the viscoelastic nature of soft tissue. Tissue hyperelasticities introduce additional errors in position estimates. Therefore, an accurate constitutive model of brain tissue or other soft tissue that can predict stress build-up in response to movement of a microprobe within the tissue will be useful in other neurosurgical applications as well.

2. Methods

Three main challenges exist in developing an autonomous microelectrode positioning system to achieve stable, high-quality neuronal recordings: i) the sources of variability (ranging from immune response, surgical issues, physical displacements or drifts of the brain tissue due to breathing, biological variations in neural activity etc) in a recorded neural signal and their relative contributions are poorly understood. ii) the brain tissue is a hyperelastic and viscoelastic medium and has a time varying strain response to any stressors such as microelectrode displacement and iii) quantitative biomechanical models of stress-strain relationships in microscale brain tissue are complex and cannot be readily applied to in vivo systems. Further, directional anisotropies are present in the microenvironment immediately around the microelectrode. In the first section of this study, we develop an optimized movement protocol for microelectrodes in soft brain tissue that will minimize the residual stresses in the surrounding brain tissue as a result of any movement. Subsequently, we use the optimized movement protocol in a closed-loop control system to minimize the impact of mechanical drift in brain tissue as one of the sources of variability in neural activity. Chakrabarti et al. (2012) proposed an autonomous system where the signal quality metric (SNR) was the only feedback. We propose here a control scheme that has an outer loop that optimizes the SNR of neuronal action potentials as shown in Fig. 1(a). In addition, an inner feedback loop (with a mechanical model) translates the microelectrode displacement commands from the controller to estimated mechanical stress values in the surrounding brain tissue and provides an optimal inter-movement interval that would keep the mechanical stresses at quasi static steady-state conditions to minimize tissue drift. In the first section of this study, we demonstrate that a bidirectional movement pattern with optimized inter-movement interval and step sizes produces quasi static steady-state mechanical stresses in the surrounding brain tissue. In the simplest case, the mechanical model simply reduces to a delay element, where an extended period of wait-time between movement steps of microelectrode shall also maintain steady state stresses in the brain as shown in Fig. 1(b). It should be noted that in the final deployment of the proposed closed-loop control scheme, the optimization of induced stresses is done off-line a-priori and a pre-determined set of movement patterns identified.

Figure 1.

(a) Block diagram of control scheme with the viscoelastic stress relaxation model of brain tissue incorporated for navigation of microelectrode with minimal residual stress in the surrounding brain tissue. Signal to Noise Ratio (SNR) serves as the feedback variable for the outer loop. Stress (σ(t)) and Inter-Movement Interval (IMI) serve as feedback variables for the inner loop (b) Block diagram of the control scheme with a time delay element incorporated for navigation of microelectrode in brain tissue. The mechanical empirical model of the control scheme shown in (a) reduces to a delay element in the simplest case. The time delay input to the controller is represented as Δ that will vary as a function of magnitude of microelectrode displacement.

2.1 Experimental procedure

Microelectrode-tissue interaction forces during micro-scale navigation inside the brain were measured in in vivo experiments in rodents. Stresses on the surrounding brain tissue were estimated from these force measurements.

The experiments were performed in adult Sprague Dawley male rats of weight 300–500g. A total of N=14 animals were used in this study. All animal procedures were carried out with the approval of the Institute of Animal Care and Use Committee (IACUC) of Arizona State University, Tempe. The experiments were performed in accordance with the National Institute of Health (NIH) guide for the care and use of laboratory animals (1996). All efforts were made to minimize animal suffering and to use only the number of animals necessary to produce reliable scientific data.

2.1.1 Surgical procedure

The animals were induced using a mixture of (50 mg/ml) ketamine, (5 mg/ml) xylazine, and (1 mg/ml) acepromazine administered intramuscularly with an initial dosage of 0.1 ml/100 g body weight. The anesthesia state of the animals was monitored closely throughout the procedure using the toe-pinch test. Updates containing a mixture of 50 mg/ml ketamine and 5 mg/ml xylazine were given at a dose of 0.05 ml/100 g body. The rat was attached to a stereotaxic frame (Kopf Instruments, Tujunga, CA, USA). The scalp was reflected by a mid-line incision. A small hole was drilled in the skull with a trephine drill of 3 mm diameter with the center point being 2 mm posterior to bregma and 3 mm lateral of the sagittal suture exposing the cerebral cortex in the barrel cortex area. The dura and pia were carefully removed with a pair of micro scissors and the craniotomy was drained with physiological saline. Phosphate buffered saline was applied to the exposed brain surface periodically to prevent it from becoming dry.

2.1.2 Experimental set-up for force measurements

Polysilicon microelectrodes of dimensions 50 μm width and 4 μm thickness that tapers to a tip over 150 μm as shown in Fig. 2(b) were used. The microelectrodes were dip coated with epoxylite (48–1696 P.D. George Company, St. Louis, MO, USA to insulate the phosphorous doped polysilicon and subsequently epoxylite was etched at the mcroelectrode tip to reveal the recording site. The epoxylite coating added approximately 20 μm of thickness overall. The final dimensions of the probe were approximately 90 μm width and 44 μm thickness. The polysilicon microelectrodes were fabricated at Sandia National Laboratories, Albuquerque, NM. The experimental set-up is as shown in Fig. 2(a). A single microelectrode was attached to a connecting screw post and mounted on a precision 10 g load cell (Futek, LSB210, Irvine, CA). The load cell with the microelectrode set-up was held on a hydraulic micromanipulator (FHC#50-12-1C, Bowdoin, ME). Contact with the brain surface was confirmed by increase in force readings and the microelectrode was lowered into the brain at the rate of 10 μm/s and implanted to a depth of 1 mm below the cortical surface. Once implanted, it was left in place for about 90 mins to allow the forces to settle to steady state and stabilization of the tissue around the microelectrode. The microelectrode was moved according to pre-defined movement patterns in each experiment and the resulting forces recorded. In order to drive the microelectrode in specific step sizes with precise time intervals between steps, defined henceforth as the inter-movement interval (IMI) and control the direction of movement, it was necessary to automate the movement of the microelectrode. The remote control pin in the front panel of the FHC hydraulic manipulator (FHC Inc., Bowdoin, ME) was interfaced the with the TTL ports of a computer that generated voltage pulses according to a programmed movement pattern. A LabVIEW^™ (National Instruments, Austin, TX) program generates TTL pulses that control the step size of movement, IMI and the direction of movement of the microelectrode. Forces experienced by the microelectrode as sensed by the load cell were recorded at the rate of 32 samples per second.

Figure 2.

Experimental setup for measuring forces in vivo during microelectrode navigation inside brain tissue (a) The microelectrode attached to a load cell for force measurement is mounted on a motorized microdrive connected to a stereotactic frame. (b) Micrograph of polysilicon microelectrode 50 μm wide and 4 μm thick with a tip size of 700 nm.

2.1.3 Stress measurements in response to microelectrode movement

Tissue drift in the surrounding brain tissue in response to microelectrode movement can be measured as mechanical stress experienced by the microelectrode during and immediately after movement. The load cell records the force acting on the microelectrode during navigation inside the brain and as the brain tissue relaxes around it. Effective stresses on the microelectrode are estimated as force per contact area. At each time point in the force curve, the total surface area of the microelectrode in contact with the brain tissue is calculated in accordance with the loading rate using the geometry of the microelectrode. The measured force was divided by the calculated contact area to get the total stresses acting on the microelectrode at all time points. Illustrative stresses resulting from typically used unidirectional and bidirectional microelectrode movement patterns are shown in Fig. 3.

Figure 3.

Stress measurements in brain tissue in response to microscale movements. (a) Displacement of microelectrode in an alternate downward and upward movement pattern with increasing step sizes at the rate of 100 μm/s. The microelectrode is held in place for random intervals of time for the tissue to relax before making the next step movement. (b) Corresponding stress measurements show tissue stress relaxation patterns in response to microelectrode movement in both downward and upward directions. (c) Stresses due to unidirectional downward movement of microelectrode in 30 μm steps and 1 min IMI and subsequent upward microelectrode movement with the same step size and IMI. The microelectrode is held in place after 10 steps of 30 μm downward movements immediately followed by relaxation in tissue stresses. Similarly, the microelectrode is held in place after 10 steps of 30 μm upward movements, immediately followed by relaxation in tissue stresses.

The stresses due to a bidirectional movement pattern executed by the microelectrode is shown in Fig. 3(a). Consecutive downward and upward movements of increasing step sizes are executed with random wait times between movements where the tissue is allowed to relax between successive movements. The forces measured are converted to stress values and the characteristic stress recorded for such a movement pattern is shown in Fig. 3(b). Force data is smoothed using a 32-point averaging window. The microelectrode is moved in increasing step sizes, and held in position until recorded forces reach steady-state. Time needed to achieve steady state forces varies with step size and accumulated residual stresses due to prior movements in the surrounding tissue - a phenomenon known as hysteresis due to the time dependent mechanics of brain tissue. Forces acting on the microelectrode represent both shear and compressive forces during downward movement and they register as negative force increments in the load cell. During upward movement of the microelectrode, forces recorded represent both the tensile forces due to tissue adhesion and shear forces. These forces register as positive increments in force in the load cell. It is observed that the resulting stresses in response to both movement directions are proportional to the step-size of movement. Further, the stress relaxation response after a downward movement has slow dynamics varying over a time scale of minutes whereas the stress relaxation response after a upward movement has a fast exponential decrease to steady state.

Figure 3(c) represents the stresses measured in brain tissue after unidirectional movement of microelectrode in steps (n=10 steps) of 30 μm and IMI of 1 min. Such movements are typically used for fine positioning of microelectrodes and are therefore slow and the step sizes are comparable to neuronal soma (cell body) diameters (~ 10 – 20 μm). Each step movement of the microelectrode results in an instantaneous peak stress value that decreases with time to an asymptote over the duration of the IMI producing a time-dependent relaxation. After consecutive step movements, there is a build up of stress possibly because of inadequate time for the tissue to fully relax between steps. Stresses build to a final cumulative stress level of 4 kPa. The microelectrode is left in place for about 10 mins and the brain tissue relaxes in a time-dependent, viscoelastic manner. The stresses relax to only about 50% of its maximum value in 10 mins. A series of 10 upward movements with the same movement parameters are executed and there is a positive increment in stress levels and when the microelectrode movement is stopped, the tissue similarly settles to steady stress values.

2.2 Estimation of viscoelastic parameters

The estimated shear stresses relax in a time-dependent manner once movement is stopped and is characterized using conventional viscoelastic models. The generalized Maxwell model is the most popular in estimating the stress relaxation behavior of viscoelastic materials. The relaxation function G(t) is defined in terms of Prony series parameters. Microscale movements exert small strains, so the stress relaxation response described by a viscoelastic model with a 2nd order Prony series expansion was found to be the best fit (R² >0.90):

$$G(t)=G(0)+{\sum }_{k=1}^N{G}_k(1-e^{-\frac{t}{{\tau }_k}})$$ (1)

where, N=2, G(t) is the relaxation response as a function of time, G(0) is the instantaneous shear modulus which is the maximum peak stress value measured immediately when a microelectrode is moved. G₁ and G₂ are the short-term and long-term shear moduli that characterize the relaxation response of the brain tissue. τ₁ and τ₂ are the corresponding short-term and long-term relaxation time constants. This model to describe stress relaxation is extensively described in previous brain tissue modeling studies (Gefen and Margulies 2004; Sridharan et al. 2013). Subtracting the average value of the steady state response beyond the first 90 sec normalized the individual stress relaxation curves. The normalized stress relaxation curves in response to downward and upward movements are averaged. Estimation of model parameters and simulations were done using least squares error in OriginLab 8.1^® and parameters with the highest R² values (> 0.9) were chosen. The instantaneous shear modulus was calculated as the magnitude of the step change in stress value at each instant of movement. The same analysis procedure was followed for other trials of step sizes and IMIs. While retracting the microelectrode, tensile forces develop as the forces acting on the tip of the probe are released. It was found that a single exponential relaxation model provided the best fit (R²>0.9) to characterize the stress relaxation response to a step movement in the upward direction:

$$G(t)=G(0)+G_1{e}^{-\frac{t}{{\tau }_1}}$$ (2)

2.3 Modeling stress response

The next objective was to simulate the mechanical stress induced in response to consecutive step movements. The asymptotic stress value at the end of the IMI from the previous step was added to the instantaneous shear modulus at the instant of movement of the next step. The same stress relaxation parameters are used to predict the time-course of relaxation at every step. The instantaneous shear modulus had a negative sign for downward movements to denote compression and positive sign for upward movements to denote tension. These simulations produced a stress profile versus time in response to any arbitrary movement pattern and were run in MATLAB^™ (Mathworks Inc., Natick, MA).

2.4 Experimental design

In order to study the effect of different step sizes and IMI values on G(t), the relaxation coefficients in equations 1 and 2 were assessed using a 2-factor ANOVA for different step sizes and IMI. Inter-animal variability for the viscoelastic parameters in equation 1 and 2 was evaluated for a particular step size (30 μm) using 1-factor ANOVA. In order to test the effect of IMI, a 30 μm step size was chosen as this is typically the step size we use to search for neurons in the cortical region. IMI is varied in the following sequence, 30 sec (approximately equal to the secondary relaxation time constant τ₂ for the stress response curve in response to 30 μm movement), 1 min (two times τ₂), 3 min (six times τ₂) and 20 min (forty times τ₂). Ten steps of 30 μm movements were made for each IMI and forces measured during movement and during tissue relaxation after all movements. Stresses were estimated from these force curves and the corresponding model parameters estimated. Step size of 3 μm, with and IMI of 3 min was chosen to test forces experienced by the microelectrode while moving in steps smaller than the diameter of a neuron, movement typically executed while optimizing neural recordings.

2.5 Chronic experiments

Force measurements and stresses were also tested in a 16-week chronically implanted microelectrode in vivo in anesthetized rodent brains. The microelectrode was implanted to a depth of 1 mm in the cortex and left in place for a period of 16 weeks. Sridharan et al. (2013) provide a detailed report of the implantation procedure and maintenance of the implant over 16 weeks. After 16 weeks of implantation, the microelectrode was moved initially over a distance of 500 μm to move through the scar tissue zone seen around chronic implants (Sridharan et al. 2013).

2.6 In vivo validation of control algorithm

Acute in vivo experiments in anesthetized animals were performed to assess neural signal quality using the closed-loop controller shown in Fig. 1 involving models of mechanical properties of brain tissue. Tungsten microelectrodes (FHC^®) with impedances at 1 kHz of approximately of 1 MΩ were implanted in adult, male Sprague Dawley rats in the barrel cortex area using the same surgical procedure described earlier. The neural signals were acquired through the Tucker Davis Technologies® (TDT) signal acquisition system. The raw signal was sampled at 25 kHz and filtered from 500 Hz to 3 kHz. A MATLAB^™ routine was called from the TDT interface that does the signal detection and computes the signal-to-noise ratio (SNR). SNR was computed using the following formula:

$$\mathit{SNR}=10lo{g}_{10}\frac{(\mathit{signal})}{(\mathit{noise})}$$ (3)

where, the “signal” and “noise” represent average of the squares of the amplitudes of signal and noise taken over the length of each time window of 60 sec. In the case of multi-unit activity from the electrodes, signal amplitudes included amplitudes from all the units. The SNR is the feedback variable for the control algorithm, also implemented in MATLAB^™. The movement commands was sent from MATLAB^™ to TDT, which then generated the waveforms necessary for the electrode to move, closing the feedback loop. The microelectrodes were attached to a FHC hydraulic manipulator that was interfaced with the TDT output.

Modes of control algorithm

The closed loop control algorithm presented here has four modes similar to the “SpikeTrak^” algorithm (Chakrabarti et al. 2012). The regulator presented here however maintains quasi-static steady-state mechanical stresses in the surrounding brain tissue while simultaneously optimizing the SNR. The 4 modes are:

1. “Maintain” mode - The microelectrode is held stationary at the site of interest as long as the neural activity recorded is above an arbitrarily set threshold value.

2. “Linear Search” mode - If neural activity is below the set threshold the control algorithm is in the “linear search” phase. A uniform linear search routine searches for neural activity above the set threshold. The microelectrode moves along a linear track with 30 μm step size with the optimal movement strategy determined using methods described earlier such that quasi static steady-state stresses are maintained in brain tissue. Once the microelectrode is positioned at a location where the SNR is above the threshold value the “linear search” routine is terminated and the closed-loop control switches to the “optimization” mode.

3. “Optimization” mode – The SNR is optimized by moving the microelectrode along the gradient of the SNR curve in increments of 10 μm. Quasi static steady-state stresses are maintained using the optimal movement pattern determined using methods described earlier. The SNR as well as peak-to-peak amplitude of the largest spike detected is tracked and the microelectrode position is optimized to maximize the amplitude of the largest spike detected.

4. “Wait” mode - In order to account for events such as an unexpected or abrupt decrease in signal amplitude when a neuron stops firing or when the signal amplitudes diminish suddenly due to possible mechanical shocks, the control algorithm is put on a wait cycle. The “linear search” routine is restarted if neural activity does not recover beyond 3 mins.

Results

Prior studies that fit a non-linear viscoelastic model used the first 90 sec of the stress relaxation response of brain tissue. Similar convention was used in this study, however it was observed that in most cases the estimated model fit the entire duration of the IMI well beyond the 90 sec. The build-up of stresses in brain tissue when the microelectrode is moved downward initially in 10 successive steps of 30 μm each with 3 min IMI and subsequently upward in 10 successive steps also of 30 μm each with 3 min IMI is shown in Fig. 4(a). In order to characterize the individual relaxation curves after each step, the traces were spliced beginning with the instance of movement and lasting for the duration of IMI as shown in Fig. 4(b). Subtracting the average value of the steady state response beyond the first 90 sec normalized the individual stress relaxation curves. The normalized stress relaxation curves in response to downward and upward movements are averaged separately. The short-term and long-term relaxation parameters of the non-linear viscoelastic model were estimated and the model fit is shown in Figs. 4(b) and (c). The instantaneous shear modulus was calculated as the magnitude of the step change in stress value at each instant of movement. Similar analysis procedure was followed for trials of other step sizes and IMIs.

Figure 4.

Modeling the viscoelastic relaxation response of brain tissue due to downward and upward movements of microelectrode. (a) Stress response for 9 steps of 30 μm downward movements with 3 min IMI followed by 10 steps of 30 μm upward movements with 3 min IMI. Data is smoothed using 32 point window averaging. First 90 sec of individual stress relaxation curves for all 30 μm downward movements were averaged after normalizing the individual curves. Normalization was done by subtracting each value in the 90 sec curve by the mean value of the steady state stress beyond 90 sec. Viscoelastic stress relaxation model was fit to the averaged curve. The same procedure was repeated for the upward movements.(b) Average curve and model fit for downward movement (c) Average curve and model fit for upward movement

Small step movements of 3 – 6 μm and arbitrarily long wait times between movements are often used to minimize residual stresses in brain tissue and achieve stable neuronal recordings particularly when the microelectrode approaches the target neuron (Yamamoto and Wilson, 2008). Small step sizes of 3 μm movements with 3 min IMI (movement 1) and 10 movements with step sizes of 30 μm each with long wait times of 20 mins (movement 2) between successive movements were tested in two different animals as a baseline measure of performance without any compensation. The resulting steady-state stress build-up was minimal for both of the above movement patterns and the maximum stress exerted by the brain tissue was approximately 1 kPa. The stress relaxation curves at the end of these experiments were fit to the 2^nd order Prony series and the long-term relaxation constants were 7 sec and 11 sec for movements 1 and 2 respectively. Hence the above conventional, intuitive strategies for moving microelectrodes do indeed result in minimal stress build-up in less than a minute after movement, minimizing the relaxation/tissue-drift effects that could potentially disturb neuronal recordings. However, the time taken to move a distance of 100 μm is 96 mins using movement 1 and 70 mins using movement 2. For brain monitoring applications, it is desirable to minimize the “search/seek” time to find stable and high fidelity neural signals.

3.1 Instantaneous shear modulus

Instantaneous shear modulus is an indicator of the stiffness of the brain tissue. Experimentally derived instantaneous shear modulus for microscale downward movements of the microelectrode show a direct, linear relationship (r²=0.82) with the step-size of movement as shown in Fig. 5(a). The slope of the fit was 33.4 +/− 1.8 Pa and the y-intercept was 371.8 +/− 88.7 Pa. Ideally, the intercept for this linear fit should be zero, however since this data is pooled across different animals and the micro-scale movements were made at different depths and sites encountering heterogeneous cytoarchitecture in the brain, deviations from ideal values are expected. A 95% prediction interval that predicts a range of G(0) values for a given step size is also plotted to account for these variations. The instantaneous shear modulus has a non-linear dependence on the IMI as shown in Fig. 5(b), which is expected due to the viscoelastic (time-dependent stress response) nature of brain tissue. Similarly for upward displacements of the microelectrode, the instantaneous shear modulus has a linear relationship with step-size of the movement as in Fig. 6(a). Modeling results also show that the instantaneous shear moduli for upward movement for a given step size are of the same order of magnitude as the shear moduli for downward movement of the same step-size. For example, for 30 μm downward and upward step, the predicted G(0) from the linear model is 1.3 kPa and 1.1 kPa respectively.

Figure 5.

Instantaneous shear modulus, G(0) for microscale downward movement of microelectrode. (a) Linear dependence of G(0) with step size of movement (b) Variation of G(0) with natural logarithm of IMI. G(0) thus has non-linear dependencies with IMI (c) Box plots of mean G(0) measured for 30 μm step size across n=7 animals (d) Tukey test results for pairwise comparisons of the mean G(0) for 30 μm step size for all animals tested. G(0) was significantly different for 9 out of 21 pairs of animals.

Figure 6.

Instantaneous shear modulus, G(0) for microscale upward movement of microelectrode. (a) Linear dependence of G(0) with step size of movement (b) Variation of G(0) for 30 μm step size with the depth in the cortex at which the movement occurred. Pearson’s correlation coefficient of −0.187 indicates that there is no correlation between G(0) and depth of microelectrode in cortical brain tissue. (c) Box plots of mean G(0) measured for 30 μm step size across n=10 animals (d) Tukey test results for pairwise comparisons of the mean G(0) for 30 μm step size for all animals tested. G(0) was significantly different for 23 out of 45 pairs of animals.

It is important to note that this linear relationship between instantaneous shear modulus and step-size of microelectrode movement holds true only for micro scale movements smaller than 100 μm tested in this study. Sharp et al. (2009), report that the cutting force at which the microelectrode pierces through the tissue is 328 +/− 68 μN for a flat punch probe of 100 μm diameter with a loading rate of 11 μm/s. We observe instantaneous increase in forces larger than 300 μN for displacements above 100 μm and hence we limit the maximum displacements of the microelectrode to 100 μm to stay within the linearity regime. The maximum instantaneous shear modulus observed for downward displacements was 3 kPa. We estimate the elastic modulus of brain tissue assuming a linear viscoelastic model, with Poisson’s ratio of 0.5 (Miller et al. 2000) and with 3 kPa as shear modulus. The elastic modulus value of 4.5 kPa obtained matches well with the value reported widely in literature. This result is significant as it indicates that for microscale indentations within the brain, the stress response of brain tissue is linearly related to the displacement and the brain tissue can be treated as a homogenous isotropic medium for purposes of modeling stress-strain relationships.

However, the structural inhomogeneity of brain cortical tissue at the microscale with laminar organization, blood vessels, cell bodies and process with different mechanical properties is well known. Therefore, we investigated if the values of the instantaneous shear modulus would vary with the location of the microelectrode in the cortex. However, as shown in Fig. 6(b) there seems to be no correlation between depth of microelectrode and instantaneous shear modulus for upward movement (Pearson’s r = −0.187). A Tukey test comparing the mean of experimentally determined instantaneous shear modulus parameters for the same step size (30 μm) across pairs of all animals used in this study was conducted. The test revealed significant difference (p<0.05) in mean instantaneous shear modulus in 9 out of 21 pairs of animals included for downward movement and in 23 out of 45 pairs included for upward movement as shown in Figs. 5(c) & (d) and 6(c) & (d) respectively.

3.2 Stress relaxation model

The values of the long-term and short-term shear modulus G₁ and G₂ and the respective relaxation time constants τ₁ and τ₂ were determined using the bi-exponential model described in equation 1. The sample size consisted of a total of 108 stress relaxation curves for downward movements and 60 stress relaxation curves for upward movements from all the individual trials. For upward movements, the stress relaxation curves were fitted to single exponential model and G₁ and τ₁ were estimated. Two-factor ANOVA was conducted for testing the effect of the two factors - step-size and inter-movement interval (IMI) on the model parameters for both downward and upward movements. Results showed that the shear modulus G₁ and the short-term relaxation time constant τ₁ are not dependent on either of these factors (p>0.4). The relaxation constant τ₂ showed a dependency on step size (p<0.05) and IMI (p<0.05). The shear modulus G₂ also showed a dependency on step size of movement (p<0.05). Statistical power in each of these tests was >0.9. One-way ANOVA was performed for each of the model fitted parameters to test if there was variation across animals. However, this test was not significant (p>0.4) indicating that the model generalizes well across all animals (n=14). Figure 7 shows the spread of the model fitted parameters across all step sizes and IMIs. The variations seen are likely due to the anisotropic and heterogeneous nature of brain tissue and inter-animal variability. Since these model parameters define the constitutive material properties of the brain tissue, average values for all the coefficients were taken and the mean, standard deviation, lower and upper 95% confidence intervals reported in Table 1. The values of the viscoelastic shear moduli fall within these ranges but as discussed earlier they trend with step size as well. It was observed that the overall stress response prediction model for a given movement pattern however, was not sensitive to variations in parameters with IMIs.

Figure 7.

(a) Histogram of short-term and long-term viscoelastic shear moduli (G₁ and G₂) and short-term and long-term relaxation time constants (τ1 and τ2) obtained from fitting 108 stress relaxation curves in response to downward movements of different step sizes across n= 14 animals to a 2^nd order Prony series model. The values of relaxation time constants are consistent across step sizes. The variations of short-term and long-term shear moduli are within the ranges of short-term and long-term shear moduli for brain tissue reported in literature. (b) Histogram of viscoelastic shear modulus (G1) and relaxation time constant (τ1) obtained from fitting 60 stress relaxation curves in response to upward movements of different step sizes across n=14 animals to a single exponential model. The viscoelastic shear modulus for upward movements is consistent and falls in the range of 200–400 Pa across all step sizes.

Table 1.

Estimated parameters of the viscoelastic model for (a) downward and (b) upward movements

a
Parameters	Mean (Pa)	Standard Deviation	Lower 95% CI of Mean	Upper 95% CI of Mean
G1	468.78	185.82	433.34	504.23
G2	559.87	456.27	472.83	646.90
τ1	1.55	1.22	1.31	1.78
τ2	33.64	34.48	26.65	40.62
b
Parameters	Mean (Pa)	Standard Deviation	Lower 95% CI of Mean	Upper 95% CI of Mean
G1	324.17	208.87	270.21	378.13
τ1	2.32	1.96	1.81	2.83

3.3 Validation of model for predicting stresses in real-time unidirectional movements

For a 30 μm step size, stress response model was set up with the following parameters - G₁=460 Pa, G₂=560 Pa, τ₁ =1.5 s, τ₂ =30 sec and G(0) = −1300 Pa for downward movement. The IMI values tested were 30 sec (τ₂), 1 min (2τ₂), 3 mins (6τ₂) and 20 mins (40τ₂). The model simulations fit well with experimental data as shown in Fig. 8 in predicting stresses over a wide range of time scales ranging from 300 sec to 6000 sec. Modeling results indicate that for moving a total distance of 300 μm (10 steps of 30 μm each) at the above movement specifications, the asymptotic value of stress at the end of the 10^th IMI were − 4.8 kPa, −3.5 kPa, −2.78 kPa and −2.71 kPa respectively for the above 4 IMIs that were tested. Increasing the IMI to 20 mins resulted in a stress build up of −2.71 kPa which was not significantly different from the stress build up of −2.78 kPa with IMI of 3 mins. Hence, it can be concluded that longer wait times between step movements while moving towards a target in a viscoelastic soft tissue does not necessarily prevent residual stress build up. Therefore, the stress response model was further explored to determine an optimal movement pattern that will result in quasi static steady-state stresses.

Figure 8.

Validation of model in in vivo experiments with 4 different unidirectional microelectrode movement patterns. Experimental stress measurements are shown in black and simulated stress values are shown in red. The electrode was moved in steps of (a) 30 μm with 30 second IMI (equal to relaxation time constant) (b) 30 μm with 1 min IMI (2 times relaxation time constant) (c) 30 μm with 3 min IMI (6 times the relaxation time constant) and (d) 30 μm with 20 min IMI (40 times the relaxation time constant). The model parameters listed in Table 1 were used in the model for generating the simulated stress curves. It is seen that the model is able to predict the stress profile for different downward movement patterns.

3.4 Bidirectional movement results in quasi static steady-state stresses

Model simulations indicated that a bidirectional movement pattern for the microelectrodes is successful in achieving quasi static steady-state stress conditions in surrounding brain tissue during microelectrode navigation. To compare stresses under the unidirectional movement pattern described earlier involving 30 μm step size and 3 min IMI, we simulated a corresponding bidirectional movement pattern that effectively moves with the same step size and the same overall IMI. For instance, a bidirectional 2-step movement pattern involving 60 μm downward movement, followed by 1 min IMI (IMI1) and subsequently a 30 μm upward movement, followed by a 2 min IMI (IMI2) resulted in an effective movement of 30 μm in 3 mins as illustrated in Fig. 9(a). The simulation results in Fig. 9(b) show that the bidirectional movement pattern produces no significant stress build-up during the microelectrode movement in contrast to the stresses experienced during unidirectional movement of the microelectrode. Experimental results in n=3 rodents shown in Figs. 9(c) and (d) validate the stress build-up predicted by the empirical model in (b) for both bidirectional and unidirectional movement of microelectrodes. In all the trials of bidirectional movement it is seen that even after termination of movement, the stresses remain at steady state with no subsequent evidence of tissue relaxation. We investigated further into the ratio of step sizes for the 2-step bidirectional movement pattern that would result in minimal steady state stresses in the least amount of time.

Figure 9.

Validation of model predicting stress build-up in in vivo experiments with bidirectional microelectrode movement. Bidirectional microelectrode movement result in quasi static steady-state stresses close to baseline values compared to a monotonic build-up of stress with each step during unidirectional movement. (a) Microelectrode displacement profile used for the simulations in (b) and the experimental results in (c) and (d). Bidirectional microelectrode movements involved 60 μm downward movement, an IMI1 of 1 min followed by 30 μm upward movement and an IMI2 of 2 mins. The microelectrode effectively moves 30 μm per step every 3 mins. (b) Simulations of stress build-up during unidirectional downward movements of 30 μm with 3 min IMI (red trace) and bidirectional movements that follow the movement profile shown in (a) (black trace). The parameters listed in Table 1 were used in the models for generating the stress response curves for the two different movement patterns. (c) In vivo measurements of stress build-up during unidirectional 30 μm downward movements with 3 min IMI (red traces) and bidirectional movements that follow the movement profile shown in (a) in n=2 animals (black traces). Quasi static steady-state stresses are observed throughout the bidirectional movement sequence and at the end of all movements. (d) In vivo measurements (from a third animal) of stress build-up during similar bidirectional and unidirectional movements as in (c).

3.5 Optimizing IMI for bidirectional movement pattern

With the bidirectional 2-step movement mechanism, it is possible to have multiple ratios and combinations of pairs of downward and upward steps that result in a net downward movement. Three ratios of step sizes were explored to minimize the IMI such that microelectrode movement is executed in the shortest possible time while still maintaining steady state stresses. The aim of this optimization exercise is to find an IMI that is less than 4 times the long term relaxation time constant (τ2) corresponding to the step movement we execute. The optimization of IMI will enable us to optimize the speed of positioning the microelectrode in a given position while achieving minimal steady-state stresses. Three ratios of step sizes were tested in the simulations: 2:1, 3:2 and 3:1. The step sizes chosen for executing these ratios of movements and the simulation results of IMI are shown in Table 2. IMI1 is the inter-movement interval between the downward and the subsequent upward movement of the current step. IMI2 is the inter-movement interval between the upward movement of the current step and the following downward movement of the next step.

Table 2.

Simulation results for bidirectional microelectrode movement for different ratio of step sizes and the resulting optimal IMIs

Ratio of steps	Step sizes (μm)	Effective downward movement (μm)	IMI1 (s)	IMI2 (s)	Time taken to move 120 μm (s)
2:1	10:5	5	50	10	1440
2:1	60:30	30	60	20	320
2:1	120:60	60	>180	-	-
3:2	30:20	10	15	15	360
3:2	60:40	20	20	20	240
3:1	30:10	20	120	15	810

All of the above movement ratios tested result in quasi-static steady-state stresses in surrounding tissue. Simulation results indicate that movements with 3:2 ratio with effective downward movements of 10 or 20 μm or the 2:1 ratio with an effective downward movement of 30 μm all achieve comparable results in minimizing the time to move 120 μm. The optimization routine is meaningful only for step sizes below 100 μm. For example, the iterations did not converge to steady state stresses for 120 μm step-size downward movement followed by 60 μm step-size upward movement (2:1 ratio in row 3 of Table 2), even after IMI1 was increased to 4 times the relaxation time constant (τ2 = 56 sec) following the 120 μm step downward movement. Bidirectional movements with 3:1 ratio for the downward and upward step sizes also do not optimize the total IMI effectively and result in total IMI > 2 mins. Bidirectional movements of 3:2 ratio for the downward and upward step-sizes with IMI1 = 15s and IMI2 = 15s was validated experimentally with 30 μm downward movement and 20 μm upward movement. Simulated results accurately tracked experimental measurements of stress response to the above movement pattern for n=75 movements in vivo in Fig. 10(a). The microelectrode moved a total of 750 μm and the final stress levels at the end of all movements was approximately −1 kPa. There is some tissue compression as the microelectrode is inserted deeper into the cortical tissue but the resulting stresses are at quasi static steady-state at the end of all movements. When non-optimal IMIs were used in Fig. 10(b) for the bidirectional movement pattern it is possible that the resulting stresses were not at steady state resulting in significant residual stresses build-up. Experimental data shows that the movement pattern with non-optimal IMIs results in approximately −10 kPa of residual stresses (as predicted by the model running with the same movement pattern) resulting in subsequent relaxation of brain tissue.

Figure 10.

Validation of model predicting stress build-up in in vivo experiments using bidirectional microelectrode movements with optimal and non-optimal IMIs. (a) Stress response measured experimentally for 30 μm downward and 20 μm upward movements with IMI1=15 sec and IMI2=15 sec, compared with model simulations for the same movement pattern. The IMIs were optimized as shown in Table 2 through simulation exercises. N=75 movements are made and hence the microelectrode moves a total of 750 μm. There is some compression of brain tissue due to insertion of the microelectrode deeper into the brain however; the stresses at the end of each movement is close to baseline levels. (b) Stress response measured experimentally for 10 μm downward and 5 μm upward movements with non-optimal IMIs of IMI1=15s and IMI2=15s, compared with simulations for the same movement pattern. Stress buildup between and after movements is observed for bidirectional movements with non-optimal IMIs. Model simulations for bidirectional movement with the same downward and upward movement step sizes (10 μm and 5 μm respectively) with optimized IMIs (IMI1=50s and IMI2=10s) show steady state stresses.

Bidirectional movement strategy with the optimal ratio of 3:2 was also tested in a 16 week chronically implanted microelectrode in rat brain tissue. The mechanical properties of brain tissue in chronic implants also change due to the remodeling of tissue around the implant over time (Sridharan et al. 2013). A step movement of 60 μm downward (n=3) was made and the tissue was allowed to relax to steady state. Similarly, 40 μm upward movement (n=3) was made and the tissue was allowed to relax to steady state. The parameters in the viscoelastic stress relaxation model were estimated as described earlier. A bi-exponential model was fit for both downward and upward movements and the following model parameters were determined for the 60 μm downward movement: G(0) = −1280 Pa, G₁ = 459 Pa, G₂ = 239 Pa, τ1 = 5.7 sec and τ2 = 70 sec and for 40 μm upward movement, G(0) = 518 Pa, G₁ = 691 Pa, and τ1 = 1.8 sec. The stress relaxation model was then simulated and the most optimal IMIs for the above step sizes were IMI1 = 60 sec and IMI2 = 60 sec. Therefore, the microelectrode was moved in vivo with the above optimized bidirectional movement parameters and the resulting stresses were plotted in Fig. 11. The microelectrode was moved a total of 140 μm and quasi-static steady-state stresses were more or less maintained at the end of all movements suggesting that the bidirectional movement strategy works also in brain tissue with chronic microscale implants. However, the model parameters needed to be adapted to reflect the change in mechanical properties of the brain tissue around chronic implants. Variations in stresses were observed between consecutive step movements and these could be due to inhomogeneity in brain tissue. The overall magnitude of the stresses seen during bidirectional movements was also significantly larger than that seen during navigation in acute experiments.

Figure 11.

Stress response to bidirectional movement in a 16-week chronic implant. Stress response measured experimentally for optimized movement parameters − 60 μm downward and 40 μm upward movements with IMI1 = 60s and IMI2 = 60s. The IMIs were optimized through modeling and validated experimentally. N=7 movements were made and hence the microelectrode moved a total of 140 μm. The stresses remain at steady state after all movements, validating the bidirectional movement strategy in brain tissue with chronic implants.

3.6 Neural recordings using closed loop control scheme

The closed loop control algorithm was first tested with only SNR of the neural recordings as feedback and the controller is blind to the mechanics of brain tissue (conventional regulator). One of the results is shown in Fig. 12. The controller isolated three single units during the duration of the experiment; however, each unit remained stable only for a span of 6–10 mins. The controller attempted to re-isolate the unit by finding local maxima of the peak of the SNR. One illustration of the performance of the regulator with optimal bidirectional microelectrode movements is shown in Fig. 13. The algorithm isolated a single unit once through the duration of the experiment and maintained a stable unit for nearly 90 mins.

Figure 12.

Performance of the conventional regulator with only SNR as feedback. Microelectrode was moved unidirectionally with no wait time between movements except for a 9 sec window over which SNR was estimated. The microelectrode responds to every change in SNR. From the SNR and peak-peak amplitude plots, it is seen that three units were isolated and lost during a 35-min duration of the experiment.

Figure 13.

Performance of the regulator with optimal bidirectional movements, with SNR as feedback variable and a predetermined optimal bidirectional microelectrode movement strategy that maintains quasi static steady-state stresses in the surrounding tissue. The microelectrode was moved 60 μm downward followed by a 30 μm upward movement, with IMI1 of 1 min and IMI2 of 2 min. The microelectrode isolates a single unit and from the SNR and peak-peak amplitude plots, it is seen that the controller attempts to maximize both these signal quality measures and hold the unit steadily for approximately 90 mins.

Neural activity during the linear search, optimization and maintain modes of the regulator with optimal bidirectional microelectrode movements are shown in Figs. 14, 15 and 16 respectively. During the linear search phase in Fig. 14, the microelectrode was moved in increments of 30 μm in the optimal bidirectional movement pattern with 60 μm forward movement and 30 μm backward movement.

Figure 14.

Isolation of single unit activity during the linear search mode of regulator with optimal bidirectional movements. A single unit (blue waveform) is isolated in three effective step movements of 30 μm each as the microelectrode is moved bidirectionally over a total distance of 90 μm. The threshold for SNR was set to 17 in this experiment to isolate large single unit activity.

Figure 15.

Optimization mode of regulator with optimal bidirectional movements, during which single unit activity obtained from linear search is optimized. The microelectrode is moved in steps of 10 μm bidirectionally around the site of interest in both forward and backward directions to determine the direction of increase in gradient of peak-peak amplitude. The amplitude of unit activity is optimized as long as there is an increasing gradient in peak-peak amplitude.

Figure 16.

Steady unit post-isolation in the maintain mode of regulator with optimal bidirectional microelectrode movements. The unit remains stable for about 90 mins before losing the unit altogether.

Once the microelectrode located unit activity and the SNR was above the set threshold the algorithm switched to the optimization phase. In the optimization phase, the microelectrode was moved bidrectionally with 10 μm effective step size (steps of 20 μm forward and 10 μm backward) as shown in Fig. 15 and IMIs optimized as described earlier.

The algorithm switched to maintain phase once unit activity is optimized and the microelectrode remained stationary. SNR is monitored in windows of 1 min continuously to ensure that the signal quality remains above the desired threshold. The sorted waveforms in Fig. 16 show single unit spike amplitudes recorded during different time intervals in the maintain mode as indexed by the numbers below the waveforms. The amplitude and waveform of these units remained stable for 90 min post isolation.

While the proposed regulator minimizes tissue drifts in response to microelectrode movement and the resulting non-stationarities in neuronal signal amplitude, non-stationarities in the long-term such as those due to behavior and tissue remodeling around the microelectrode still exist and the control algorithm proposed here has to counter for that variability by repositioning the microelectrode. The peak-peak amplitudes of unit activity in 6 different trials (n=3 animals) using the conventional regulator and 3 different trials (n=2 animals) using regulator with optimal bidirectional microelectrode movements are shown in Figs. 17(a) & (b) respectively.

Figure 17.

Figure 17(a). Variation of maximum peak-peak amplitude in neural recordings with conventional regulator and modes of the control algorithm in 6 different trials (n=3 animals). Total time of control from all 6 trials = 216 mins.

Figure 17(b). Variation of maximum peak-peak amplitudes in neural recordings using regulator with optimal bidirectional microelectrode movements and modes of the control algorithm in 3 trials (n=2 animals). Total time of control = 360 mins.

The modes of the control algorithm during the duration of the experiment are also highlighted in Figs. 17(a) & (b). The conventional regulator spends majority of the time in the search phase or waiting to recover activity due to instability in the unit isolated, likely due to tissue drift. The conventional regulator sequentially isolates several units over the duration of the experiment in an effort to keep the SNR above threshold value. In contrast, the units remain relatively stable post-isolation using the regulator with optimal bidirectional microelectrode movement as shown in Fig. 17(b) and the regulator is in maintain mode for a relatively longer duration of the experiment.

The performance of the conventional regulator and the regulator with optimal bidirectional microelectrode movements is compared in Table 3. The duration of experiments using conventional regulator was 216 mins and that using the regulator with optimal bidirectional microelectrode movements 360 mins. It can be concluded that the regulator with optimal bidirectional microelectrode movements decreased the frequency of interventions needed to restore activity resulting in relatively more stable isolation of unit activity.

Table 3.

Comparison of performances of the conventional regulator and the regulator with optimal bidirectional microelectrode movement

	Conventional Regulator	Regulator with optimal bidirectional movement
Number of animals/number of trials	3 animals/6 trials	2 animals/3 trials
Total microelectrode movement during control	7570 μm	2720 μm
Frequency of movement	1.48 movements/min	0.23 movements/min
Average Peak-Peak amplitude	190.11 μV	124.09 μV
Average SNR	14.56 dB	15.55 dB
%Time in Linear Search	25.25	28.01
%Time Optimization	30.14	7.52
%Time Waiting to recover	21.89	7.99
%Time Maintain	22.74	52.89
%Total Time spent in search	77.27	43.52
% Time unit isolated	22.74	52.89

Discussion

We adopted a mechanical model of brain tissue that had been demonstrated by prior porcine and rat studies to estimate relaxation of induced stresses in brain tissue after millimeter scale indentations (Gefen and Margulies 2004; Miller et al. 2000; Sridharan et al. 2013). In this current study, we first estimated the model parameters (from n=14 rodents) by using microscale indentation steps and measuring the induced stresses as the brain tissue relaxed consequent to movement. Given the heterogeneities in brain tissue at microscale due to the presence of vasculature and the diversity of cell shapes and densities, the first goal was to determine a mechanical model that will enable accurate prediction of induced stresses due to microscale displacement of implants. Estimated elastic modulus of 4.5 kPa from micro-scale movements in brain tissue in this study compare well with values derived from large-scale indentation studies in in vivo rat and porcine models (Gefen and Margulies 2004; Miller et al. 2000; Sridharan et al. 2013). The shear moduli values are also similar to previous studies of microelectrode penetration albeit in millimeter scales in rat and mouse brain tissue (Sharp et al. 2009; Sridharan et al. 2013) (Figs. 5–7 and Table 1). Remarkably, the parameters of the model (including G₁, G₂, τ₁ and τ₂) generalize very well from millimeter scale indentations in prior studies (Gefen and Margulies 2004; Sridharan et al. 2013) to microscale displacements in this current study. Since the model parameters reflect the constitutive properties of the brain tissue at the interface they also generalize across other rigid metal (such as tungsten, stainless steel) and silicon microelectrodes of different shapes. We have data using the above electrode systems (not shown in this current study) that confirm the generalizability across different rigid electrodes demonstrating the validity of using such indentation studies to estimate the constitutive properties of surrounding brain tissue.

The proposed mechanical model is validated in both unidirectional and bidirectional microelectrode movement patterns. We defined quasi static steady-state of stresses as a desired end goal where there is minimal build-up of induced stresses during microelectrode movement. The rationale for achieving such quasi static steady-state stresses is multifold. Primarily, it was hypothesized to improve stability of positioning in a viscoelastic medium in the absence of any feedback of position by eliminating or minimizing drifts due to tissue relaxation. The mechanical model developed in this current study for predicting stresses induced in response to microelectrode motion (both downward and upward) demonstrated that a bidirectional microelectrode motion is superior to a unidirectional motion in its ability to minimize build-up of residual stresses (Fig. 9). The model prediction was subsequently validated in a series of experiments with unidirectional and bidirectional microelectrode motions (Figs. 8–11). Validation of the model under different unidirectional microelectrode movements was demonstrated in n=7 cases (n=4 in Fig. 8 and n=3 in Fig. 9(c) & (d)). Validation of the model under different bidirectional microelectrode movements was demonstrated in n=6 cases (n=3 in Fig. 9(c) & (d), n=1 in Fig. 10(a), n=1 in Fig. 10(b) and n=1 in Fig. 11). The model was remarkably robust in predicting stresses under a variety of microelectrode movement conditions. Further, the model does well in predicting stress build-up during repeated movement of microelectrodes without the need to reset or recalibrate (n=75 repeated movements in Fig. 10(a)). By eliminating or minimizing residual stresses in the soft tissue as the microelectrode is advanced, time varying changes (induced by viscoelasticity) in the relative distance between the microelectrode and the target is minimized or eliminated and targeting accuracy increased.

Another important consideration for minimizing the residual stresses created during microscale navigation inside brain tissue is to keep the stresses well within the tissue thresholds for mild traumatic brain injury (El Sayed et al. 2008; Zhang et al. 2004) and minimize inflammation response (Bjornsson et al. 2006; Jensen et al. 2006; Sharp et al. 2006). Limited data is available on the stress magnitudes, rates and durations that cause tissue injury. McConnell et al. (2007) showed that increased peak extraction forces of microelectrodes correlated with GFAP expression in astrocytes. De et al. (2007) found 180 kPa of compressive stress to be the stress threshold for tissue damage and apoptosis due to surgical manipulations in soft viscoelastic porcine liver tissue. Zhang et al. (2004) suggest that the threshold levels of shear stresses at 6 kPa could indicate mild traumatic brain injury with 25% probability through finite element modeling of actual football field accident data. These limits for injury are only representative thresholds, as they may not translate accurately to the case of micro-scale movements with very low strain rates. However, by maintaining quasi static steady-state stresses close to zero with consecutive microelectrode movements, the potential of inducing tissue damage and associated cellular inflammation response is also minimized.

Forces required to move microelectrodes over micron-scale displacements in brain tissue are in the order of a few hundred micro-Newtons. If the tissue is not allowed to relax between consecutive movements, these forces very quickly build-up to the order of milli-Newtons. For bidirectional movements, the maximum cumulative force registered is in the range of 300 μN – 500 μN. Therefore, force requirements reduce by orders of magnitude for penetrating soft viscoelastic materials such as brain tissue using optimal bidirectional movement strategies (Fig. 10). Particularly, for applications using MEMS based microactuators used for navigation in soft tissue (Anand et al. 2012; Muthuswamy et al. 2005a; Muthuswamy et al. 2005b), optimal bidirectional movement parameters reduce the force and power demands on the microactuators. This is of significance in applications where the microactuators are powered by on chip sources such as in chronic microelectrode implants. (Jackson et al. 2010; Sridharan et al. 2013). In the case of chronic implants, our prior work (Sridharan et al., 2013) has documented changes in the constitutive properties of rodent brain tissue around an implanted microelectrode as they change over the first 8 weeks post-implantation before they reach steady-state. Therefore, to achieve quasi-static steady-state stresses in chronic experiments, one will have to just use such a-priori model parameters to determine off-line the optimal movement pattern (optimal IMI1 and IMI2) for a given duration of implant. These optimal bidirectional movement patterns can then be subsequently used in the automated microelectrode positioning system to optimize the SNR. An example of such an exercise is illustrated for a 16-week microelectrode implant that resulted in quasi-static stress conditions in Fig. 11.

The force-displacement curves measured at different regions and depths of the brain had some minor and localized variations but the overall trend was predictable and consistent. In some trials, the viscoelastic model deviated from the measured forces because of noises in the force measurements that could have been caused by the microelectrode severing a micro-capillary or due to changes in intra-cranial pressure, particularly in long duration anesthetized experiments such as the one shown during relaxation after bidirectional movement with non-optimal IMIs in Fig. 10(b). The microelectrode used in the current experiments had a planar structure but it was coated with brain epoxy and had minimal deflection during insertion into the brain. Hence the models developed in this study apply to rigid, incompressible probes and do not take into account the effects of deflection. The data presented here was measured from the cortical regions of adult rats; thus, mechanical properties of the deeper structures of the brain and differences in gray matter and white matter tracts (Green et al. 2008) were not studied. In order to improve model predictions in micro-scale navigation and targeting in a viscoelastic medium, subject-specific characterization of the viscoelastic parameters in vivo would enhance the accuracy of the model (van Gerwen et al. 2012). Although the model has greater tolerance to variations in G₁ and τ₁ values, the values of G₂ and τ₂ are critical to determine response.

With regard to the neural recordings, the performance of the conventional regulator with unidirectional microelectrode movement (30 μm step size and 3 min IMI) in vivo, where the feedback is limited to neural signal activity is shown in Fig. 12 & 17(a). The microelectrode is repositioned more likely to compensate for tissue relaxation effects and re-isolate a drifted neuron. An automated positioning system that adapts to tissue mechanics is able to isolate and maintain a stable single unit recording over a relatively longer period of time without re-positioning as shown in Fig. 17(b) and 18. The neural activity during each stage of positioning using a regulator with optimal bidirectional movement is illustrated in Figs. 14–16. In the isolation phase, as in Fig. 14, the microelectrode searches along the surface normal axis to find target neural activity with SNR above the threshold value. The SNR gradient as a function of depth is known to have valleys and peaks corresponding to positions where the electrode is closest to neurons along the track. There is anecdotal evidence from experimental data to show that these peaks are typically at distances of 50–100 μm apart as reported in the macaque cortex (Branchaud 2006). Once the microelectrode is positioned at a location where the SNR is above the threshold value, the linear search routine is terminated and the microelectrode moves to the optimization phase. The control algorithm in the optimization phases adjusts the position of the microelectrode in order to maximize the peak-peak amplitude of the neuronal signal. The microelectrode moves in smaller increments of 10 μm as shown in Fig. 15. The optimization phase is analogous to the fine-tuning that is routinely employed when manually positioning a microelectrode to record neural activity. The controller advances the microelectrode as long as the gradient of the SNR along the linear track is positive. Once an optimal position is determined, the controller moves to the maintain phase where it is recording neural activity with the desired optimal SNR and stable single unit activity as shown in Fig. 16. If the SNR is still above threshold but is lower than the optimal SNR the controller will move to the optimization phase and re-adjusts the microelectrode. The controller moves back to the linear search mode when the SNR falls below the threshold. The peak-peak amplitudes of the neuronal signal recorded using a conventional regulator and one with optimal bidirectional microelectrode movement are shown in Figs. 17(a) & (b). The data in center and right panels of Figs. 17(b) indicate units with peak-to-peak amplitudes as low as 60 μV. The reason is largely due to the way SNR (feedback variable) is defined in our study and the role played by the user-set SNR threshold (that determines the target SNR) in determining the kind of units isolated. When the SNR is set too high, the microelectrode often ends up in an endless “search” mode moving unsuccessfully up and down the entire 1.5–2 mm column of cortical tissue. In these above instances in Fig. 20(b), the goal was to ensure a quick isolation of a unit, minimize time spent in initial search mode and assess the ability of the regulator with optimized bidirectional microelectrode movements in maintaining the unit. Therefore, the target SNR threshold was set to approximately 12 dB. In addition, SNR is determined in this current study by finding sum of squares of the amplitudes of a single sorted unit and multiply that by its corresponding frequency of occurrence in the window of observation. In the case of multiple units, the signal power is determined by the weighted sum of squares of the amplitudes of each unit (weighted by the corresponding firing rate). So in the event we have a fast firing unit with small amplitude and a sparsely firing unit of large amplitude, the controller could potentially move towards the fast firing unit with smaller amplitude. In other words, the controller does not optimize directly for signal amplitude during the linear search phase but optimizes for SNR.

The regulator with optimal bidirectional microelectrode movement maintains a stable recording 53% of the experimental time compared to 23% of experimental time by the conventional regulator (Table 3). The frequency of interventions to maintain recordings above SNR is minimized for the regulator with optimal bidirectional microelectrode movement at 0.23 movements/min compared to 1.48 movements/min for the conventional regulator (Table 3). With the conventional regulator, the microelectrode is re-positioned close to 220 times with IMIs less than a minute as shown in Fig. 18. Thus the controller adapted to tissue mechanics leads to more stable recordings by a 6-fold reduction in the number of microelectrode movements needed to maintain neural recordings.

Figure 18.

Histogram of inter-movement intervals (IMIs) between microelectrode movements using conventional regulator and a regulator with optimal bidirectional microelectrode movements. Plot on the right is a semi-log rendering of the plot on the left. The y-axis in the plot on the right is in log scale to reveal the points beyond IMI of 500 sec. The two peaks seen at 60 sec and 120 sec are the IMIs of the bidirectional movement pattern during the linear search phase. In the case of conventional regulator (in red), the number of microelectrode movements is large and therefore more frequent and the IMI is <60s as the controller is mostly in linear search phase attempting to isolate the neuron.

One of the primary sources of non-stationarities in neural signal recordings is the dynamic physical change at the neural interface itself (Chestek et al. 2011; Fee et al. 1996; Santhanam et al. 2007; Williams et al. 1999). During initial implantation it is often observed that the brain tissue can dimple over a millimeter as the tissue is pulled along with the microelectrode (Bjornsson et al. 2006). Dynamic physical changes at the interface cause changes in the signal amplitude and shape recorded by the microelectrode (Gold et al. 2006) and in general might account for some of the instabilities seen in signal shapes (Britt and Rossi 1982; Fee 2000). In experiments with awake animals, sporadic but vigorous head movements are typical. In the above experiments, such head movements often result in loss of units. The controller proposed in this study will switch back to search mode in the event of a loss of a unit due to any of the reasons discussed above, and restart the process of seeking and isolating new units. The models proposed here can be useful in predicting induced stresses due to such behavior only if (a) the magnitude of disruptions in the brain tissue are measurable and (b) the relative displacement between the microelectrode and the brain tissue is less than 100 μm beyond which, the linear relationship between G(0) in the model and displacement step size breaks down (Fig. 5(a)) due to high likelihood of fracture in brain tissue.

The performance of the positioning strategy was tested in recording neural activity from single neurons in an anesthetized rodent brain. Further improvement of the algorithm to track individual signal units by using rigorous statistics and regression based algorithms as detailed by Wolf et al. (2009), could be incorporated. Long periods of silence are often observed in the activity of a single neuron being recorded. During such a period if the controller tries to optimize the position of the microelectrode there is a possibility of damaging the neuron and losing the signal altogether. Therefore, a trade-off exists while designing a control scheme for an automated system between consistently good quality recordings versus tolerance for periods of inactivity. Thus along with miniature movable microelectrode array technology, intelligent controls adapted to tissue mechanics would enhance the reliability of the neural recording system and is a promising approach to ensure the stability, consistency, yield, and longevity of neural recordings from implanted micro-electrodes.

While recording extracellular activity in the brain using an array of movable microelectrodes it is often observed that moving one electrode affects the neural activity recorded in the neighboring electrodes. When quasi static steady-state stresses are maintained as proposed here, there is minimal propagation of stresses that integrate with stresses in the neighboring electrodes. Thus, optimal bidirectional positioning technique developed here for minimizing residual stresses in the brain tissue could be extended to multi-channel movable microelectrode systems to ensure that movement of one electrode in the system does not affect the signal quality in the remaining electrodes. We have found that the mechanical stress diminishes exponentially as a function of the radial distance from the lateral surface of the microelectrode into the brain tissue (data not shown). Therefore, when one has more than one microelectrode, models that incorporate the spatial exponential will allow prediction of stresses in the brain tissue due to the movement of any microelectrode in an array of microelectrodes. Future studies with multiple electrodes should investigate the optimal spacing to mechanically isolate electrodes in a multi-electrode movable array.

This proposed technique also has applications to navigation and targeted positioning in robotic surgeries. In clinical procedures with robotic microneedle manipulations such as targeting tumors for ablation and bio-sensing, it is critical to reach the specified anatomical target with minimal error margins. The bidirectional movement strategy proposed here that is adapted to the tissue mechanics can be extended to minimize stresses and hence achieve accuracy in positioning in soft tissue. Currently, the optimal movement strategy is predetermined, but with the integration of a force sensor with microscale probes could potentially lead to online computations of stresses in surrounding tissue and bidirectional navigation to minimize those stresses. The mechanical model parameters could be determined for each individual subject leading to greater prediction accuracy and more accurate positioning.

Conclusion

The goals of the study were (a) to develop and validate a model to predict the magnitude of stress build up in the surrounding brain tissue and the dynamics of tissue relaxation for commonly used microelectrode movement patterns (b) to optimize the microelectrode movement pattern, step size and IMI such that movement of the microelectrode results in quasi static steady-state stresses in the tissue (c) to determine if a controller that is adapted to minimize stress build-up can achieve improved stability of isolated single unit activity. A viscoelastic stress relaxation model was developed that predicts the stress response in brain tissue to a microscale movement pattern. An optimal bidirectional movement strategy was designed that would maintain stress levels in the surrounding tissue close to zero and was subsequently validated in vivo. This results in detailed quantification of the parameters for navigation inside soft viscoelastic brain tissue that would induce minimal stresses in brain tissue and minimize the time taken for movement. The bidirectional movement pattern was validated in rodent experiments and steady state stresses were obtained. Thus, this bidirectional movement technique results in precise targeting and positioning of microelectrode in brain tissue while overcoming tissue drift effects. Finally, the control algorithm that incorporated the bidirectional movement pattern was tested using SNR (of neural recordings) as feedback in vivo to precisely position neural microelectrodes in the brain and showed significant improvement in signal stability. This appears to confirm the central hypothesis of this study that control strategies to minimize mechanical stresses in brain tissue caused by movement of microelectrodes will lead to more stable neural recordings. Further, this positioning scheme adapted to the surrounding tissue mechanics could be applied for positioning any microscale probes and sensors in soft viscoelastic tissue. The optimal navigation strategy of microscale probes could have exciting implications to improve positioning accuracy in medical applications such as tissue biopsy and microscale surgery.