Proprioceptive and Cutaneous Representations of the Rat Ventro Posterior Lateral (VPL) Thalamus.

Joseph T. Francis, Shaohua Xu and John K. Chapin. (J Neurophysiol (February 20, 2008). doi:10.1152/jn.01206.2007)

Determining how and where proprioceptive information is represented in the rat VPL is important in allowing us to further investigate how this sense is utilized during motor control and learning. Here we demonstrate using electrophysiological techniques that the rostral portion of the rat VPL nucleus (rVPL -2 mm to -2.5 mm Bregma) carries a large amount of proprioceptive information. Caudal to this region is a zone where the cutaneous receptive fields are focal (mVPL for middle VPL -2.5 mm to -3.2 mm Bregma) with a fine topographic map of the fore and hind limbs. The forepaw is represented with digit 1 medial and each subsequent digit increasingly lateral, all of which are dorsal to the pads. The caudal VPL (cVPL -3.2 mm to -4.0 mm Bregma) has broad receptive fields and is the target of lamina 1 and 2, as well as the dorsal column nucli, and may represent the flow of nociceptive information through the VPL (Gauriau and Bernard, 2004). Thus, we propose that the VPL may be thought of as three subnuclei, the rostral, middle and caudal VPL, each carrying preferentially a different modality of information. This pattern of information flow through the rat VPL is similar, although apparently rotated, to that of many primates, indicating that these regions in the rat (rVPL, mVPL and cVPL) have become further differentiated in primates where they are seen as separate nuclei (VPS, VPL and VPI/VMpo).

Error generalization as a function of velocity and duration: human reaching movements.

Joseph T. Francis (Exp Brain Res (2008) 186:23-37)

Our sensory-motor control system has a remarkable ability to adapt to novel dynamics during reaching movements and generalizes this adaptation to movements made in different directions, positions and even speeds. The degree and pattern of this generalization are of great importance in deducing the underlying mechanisms that govern our motor control. In this report we expand our knowledge on the generalization between movements made at different speeds. We wished to determine the pattern of generalization between different speed and duration movements on a trial-by-trial basis. In addition, we tested three hypotheses for the pattern of generalization. The first hypothesis was that the generalization was maximum for the speed of the movement just made with a linear decrease in generalization as one moves away from that preferred speed. The second was that the generalization is always highest for the fastest speed movements and linearly decreases with speed. The last hypothesis came from our preliminary results, which suggested that the generalization plateaus. Human subjects made targeted reaching movements at four different maximum speeds (15, 35, 55 and 75 cm/s) presented in pseudorandom order to one spatial target (15 cm extent) while holding onto a robotic manipulandum that produced a viscous curl field. Catch trials (trial where the curl field was unexpectedly removed) were used to probe the generalization between the four speed/ durations on a movement-by-movement basis. We found that the pattern of generalization was linear between the first three speed categories (15-55 cm/s), but plateaued after the 55 cm/s category. We compared the subjects' results with a simulated adaptive controller that used a population code by combining the output of basis elements. These basis elements encoded limb velocity and associated this with a force expectation at that velocity. We found that using a basis set of Gaussians the adaptive controller produced movements that generalized in virtually the exact manner as the subjects, as we have previously demonstrated for movements made to different spatial targets. Thus, the human internal model may employ such a population code.

Neural ensemble activity from multiple brain regions predicts kinematic and dynamic variables in a multiple force field reaching task.

Joseph T. Francis and John K. Chapin (IEEE TNSRE Special issue on Brain Computer Interfaces June 2006).

In everyday life we reach, grasp and manipulate a variety of different objects all with their own dynamic properties. This degree of adaptability is essential for a brain controlled prosthetic arm to work in the real world. In this study rats were trained to make reaching movements while holding a torque manipulandum working against two distinct loads. Neural recordings obtained from arrays of 32 micro-electrodes spanning the motor cortex were used to predict several movement related variables. In this paper we demonstrate that a simple linear regression model can translate neural activity into endpoint position of a robotic manipulandum even while the animal controlling it works against different loads. A second regression model can predict, with 100% accuracy, which of the two loads is being manipulated by the animal. Finally, a third model predicts the work needed to move the manipulandum endpoint. This prediction is significantly better than that for position. In each case the regression model uses a single set of weights. Thus, the neural ensemble is capable of providing the information necessary to compensate for at least two distinct load conditions.

Force Field Apparatus For Investigating Movement Control in Small Animals

Joseph T. Francis and John K. Chapin (IEEE Trans Biomed Eng. 2004 Jun;51(6):963-5)

As part of our overall effort to build a closed loop brain-machine interface (BMI), we have developed a simple, low weight, and low inertial torque manipulandum that is ideal for use in motor system investigations with small animals such as rats. It is inexpensive and small but emulates features of large and very expensive systems currently used in monkey and human research. Our device consists of a small programmable torque-motor system that is attached to a manipulandum. Rats are trained to grasp this manipulandum and move it to one or more targets against programmed force field perturbations. Here we report several paradigms that may be used with this device and results from rat's making reaching movements in a variety of force fields. These and other available experimental manipulations allow one to experimentally separate several key variables that are critical for understanding and ultimately emulating the feedforward and feedback mechanisms of motor control.

Sensitivity of Neurons to Weak Electric Fields

Joseph T. Francis, Bruce Gluckman and Steven J. Schiff. (J. Neurosci., Aug 2003; 23: 7255-7261)

Weak electric fields modulate neuronal activity, and knowledge of the interaction threshold is important in the understanding of neuronal synchronization, in neural prosthetic design, and in the public health assessment of environmental extremely low frequency fields. Previous experimental measurements have placed the threshold between 1 and 5mV/mm,although theory predicts that elongated neurons should have submillivolt per millimeter sensitivity near 100 mV/mm. We here provide the first experimental confirmation that neuronal networks are detectably sensitive to submillivolt per millimeter electrical fields [Gaussian pulses 26 msec full width at halfmaximal, 140 mV/mm rootmeansquare (rms), 295 mV/mm peak amplitude], an order of magnitude below previous findings, and further demonstrate that these networks are more sensitive than the average single neuron threshold (185 mV/mm rms, 394 mV/mm peak amplitude) to field modulation.

Quantifying Generalization from Trial-by-Trial Behavior of Adaptive Systems that Learn with Basis Functions: Theory and Experiments in Human Motor Control

Opher Donchin, Joseph T. Francis and Reza Shadmehr. J. Neurosci., Oct 2003; 23: 9032-9045

During reaching movements, the brain's internal models map desired limb motion into predicted forces. When the forces in the task change, these models adapt. Adaptation is guided by generalization: errors in one movement influence prediction in other types of movement. If the mapping is accomplished with population coding, combining basis elements that encode different regions of movement space, then generalization can reveal the encoding of the basis elements.Wepresent a theory that relates encoding to generalization using trial-by-trial changes in behavior during adaptation.Weconsider adaptation during reaching movements in various velocity-dependent force fields and quantify how errors generalize across direction. We find that the measurement of error is critical to the theory. A typical assumption in motor control is that error is the difference between a current trajectory and a desired trajectory (DJ) that does not change during adaptation. Under this assumption, in all force fields that we examined, including one in which force randomly changes from trial to trial, we found a bimodal generalization pattern, perhaps reflecting basis elements that encode direction bimodally. If the DJ was allowed to vary, bimodality was reduced or eliminated, but the generalization function accounted for nearly twice as much variance. We suggest, therefore, that basis elements representing the internal model of dynamics are sensitive to limb velocity with bimodal tuning; however, it is also possible that during adaptation the error metric itself adapts, which affects the implied shape of the basis elements.

Supplementary Information: Quantifying Generalization from Trial-by-Trial behavior

Differentiability implies continuity in neuronal dynamics

Joseph T. Francis, Paul So, Bruce J. Gluckman, Steven J. Schiff (Physica D 148 (2001) 175–181)

Recent work has identified nonlinear deterministic structure in neuronal dynamics using periodic orbit theory. Troublesome in this work were the significant periods of time where no periodic orbits were extracted - "dynamically dark" regions. Tests for periodic orbit structure typically require that the underlying dynamics are differentiable. Since continuity of a mathematical function is a necessary but insufficient condition for differentiability, regions of observed differentiability should be fully contained within regions of continuity. We here verify that this fundamental mathematical principle is reflected in observations from mammalian neuronal activity. First, we introduce a null Jacobian transformation to verify the observation of differentiable dynamics when periodic orbits are extracted. Second, we show that a less restrictive test for deterministic structure requiring only continuity demonstrates widespread nonlinear deterministic structure only partially appreciated with previous approaches.

Early Seizure Detection

Jerger KK, Netoff TI, Francis JT, Sauer T, Pecora L, Weinstein S, Schiff SJ. J Clin Neurophysiol. 2001 May;18(3):259-68.

Periodic Orbits: A New Language for Neuronal Dynamics

Paul So, Joseph T. Francis, Theoden I. Netoff, Bruce J. Gluckman, and Steven J. Schiff (Biophysical Journal Volume 74 June 1998 2776–2785)

A new nonlinear dynamical analysis is applied to complex behavior from neuronal systems. The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs). UPOs are rigorously identified in data sets representative of three different levels of organization in mammalian brain. An analysis based on UPOs affords a novel alternative method of decoding, predicting, and controlling these neuronal systems.

Chemorepellents in Paramecium and Tetrahymena

Joseph T. Francis and Todd M. Hennessey. J Eukaryot Microbiol. 1995 Jan-Feb;42(1):78-83.

Oxidants act as chemorepellents in Paramecium by stimulating an electrogenic plasma membrane reductase activity.

Todd M. Hennessey, Lee Frego and Joseph T. Francis. J Comp Physiol [A]. 1994 Nov;175(5):655-65.

Book Chapter

Comparison of Methods for Seizure Detection.

Jerger KK, Netoff TI, Francis JT, Sauer T, Pecora LM, Weinstein SL, Schiff SJ

In: Epilepsy as a Dynamic Disease. eds. Milton J, Jung P Springer, New York , 2003

 

The neural representation of Kinematics and Dymanics in Multiple Brain Regions: The Use of Force Field Reaching Paradigms in the Primate and Rat.

Joseph T. Francis

In: Springer, New York , 2008

 

Recent Meetings

Error generalization as a function of velocity: human reaching movements

While making reaching movements humans and animals such as rats and non-human primates must plan the direction, distance, speed, and magnitude of the forces needed to achieve a goal. In resent years several researchers have suggested that there is an internal model within the motor control system, and that this internal model is responsible for transforming desired movements, or goals into motor patterns that accomplish the goal by reaching the target position. It has been theorized that our motor system may employ a set of motor primitives that can be summed via different weightings to produce a wide variety of movements. Recently our group has suggested that there exists a hypothetical set of such motor primitives that function by associating a given force with a given velocity (Thoroughman and Shadmehr 2000; Donchin et al. 2003). Consequently when subjects learn to actuate a robotic manipulndum in the presence of a perturbing force field we were able to use a simple time series model Y(n) = D*F(n) - Z(n) with Z(n+1) = Z(n) + B*Y(n) to predict the pattern of errors Y(n) made by the subjects with the added constraint that all movements were about the same speed, duration (500 msec) and distance (10 cm). This model states that the error on the nth movement Y(n) is the difference between the internal models expectation Z(n) and the true force experienced D*F(n), where D is a compliance term that translates force into displacement. In the present study subjects made reaches to a visual target 15 cm away with a maximum velocity of 15, 35, 55 or 75 cm/sec cued in a pseudorandom order via a minimum jerk trajectory viewed before each movement. Subjects experienced a viscous curl field with catch trials (approximately 16% of reaches). We found that a simple simulation that is composed of Gaussian basis elements in velocity space reproduces the same type of generalization seen for the human subjects as we have previously shown for movements made in different directions (Donchin et al. 2003) extending the set of movements that such a model can represent, and that the simple time series model seen above accounts very well for both the simulations results as well as the humans with an r-squared value of 0.92 between the simulations data and the subjects. With the generalization function B being indistinguishable between the simulation data and the subjects' data using Gaussians with sigmas of about 15cm/sec as in our previous work.

Neural ensemble activity from multiple brain regions predicts kinematic and dynamic variables in a multiple force field reaching task in the Rat.

Just what the motor cortex is encoding when we reach and retrieve an object is still under debate. Perhaps insight may be gained by focusing on how it interacts with other cortical regions such as the somatosensory cortex and more rostral areas as well as lower brain regions like the VPL thalamus.In order to gain insight into how these multiple brain regions interact to formulate reaching movements under differing dynamic constraints we trained rats to grasp a manipulandum handle while making multi-joint reaching movements as the manipulandum imposed several different force fields. The two force field paradigms we chouse were a constant force paradigm and a spring paradigm. In both versions the manipulandum randomly switched in a block fashion between large force and small force versions of the fields, which the rats learned to compensate for while maintaining their null field kinematics (Francis et al. IEEE TBME Vol. 51, No. 6 2004). Seven rats were implanted with a 32 channel microwire array that spanned 5 mm covering both the caudal and rostral motor cortex as well as the sensory cortex while a second implant was placed in the rostral VPL, which has been shown to respond to proprioceptive and cutaneous stimuli (Francis et al SFN meeting 2003). We generally obtained 40-60 neurons per animal and recorded 16 LFP channels in the cortex and 8 LFP channels in the rVPL. We used multiple linear regression models to fit the neural data to either kinimatic or dynamic variables such as position, work, velocity and the force produced by manipulandum. In general the best predictions were to the force as well as position (average r = .7). In addition we found that neurons of the sensory-motor cortex of the rat segregate into the same groups of cells seen in the primate that is tonic, phasic-tonic etc… We also found a set of cells that predicted the time of the next self paced movement.

Neuronal ensemble representation of cutaneous stimuli in the somatosensory cortex of awake and anaesthetized macaques

To investigate the mechanisms of population encoding of somatosensory stimuli, simultaneous multi-neuron activity was recorded from arrays of 16-32 electrodes implanted in cortical areas 4, 3a, 3b, 1 and/or 2 of awake and anesthetized bonnet macaques. A mechanical stimulator was used to deliver controlled tactile stimulation to each of up to 15 cutaneous locations on the hand/arm at a range of frequencies: 2Hz, 5Hz, 10Hz, and 50Hz. Spike discharges recorded simultaneously from up to 60 single neurons were then analyzed to determine how sensory information was encoded at the single neuron and population level. In both the awake and anesthetized condition many neurons yielded surround inhibition as well as complex temporal patterns of activity depending on the stimulation site. We found several cells in the anesthetized condition that had a simple phasic response at 13 msec regardless of which area on the hand was stimulated, but no such cells in the population under study were found in the awake condition. Though the shortest latency responses to these stimuli were identical (~13ms) in the two conditions, the anesthetized state yielded a longer sequence of late responses lasting up to 150ms. Multivariate statistical techniques were then used to demonstrate that the simultaneously recorded population of neurons could be used to accurately predict sensory parameters such as the skin location and frequency of the stimulus. Thus, at the neural population level, information processing in the primate somatosensory cortex appears to be fairly similar under both anesthetized and awake conditions with some key differences.

Tracking neural state transitions as rats make reaching movements holding a novel torque manipulandum.

In order to fully integrate a neural-prosthetic arm we must be able to determine if the user is attempting to engage the device or not. One possible solution to this problem is tracking changes in the state of the neural ensemble used to control the device as it transitions between actively moving the prosthetic device and conducting all other activities. In addition it is useful for the user-prosthetic system to control grasped objects with differing dynamical properties. To address these issues we trained rats to grasp the handle of a torque manipulandum (Francis et al. IEEE TBME Vol. 51, No. 6 2004) and make reaching movements to remembered target positions for a water reward. After learning the task rats were anesthetized with pentobarbital 50mg/kg and 40 micro-wire electrodes were implanted into multiple brain areas (M1, S1, M2 and rVPL). After recovering from surgery animals continued the task while multi-neuron spikes and local field potentials (LFPs) were recorded. During the experimentation phase the manipulandum produced two different constant force fields in a block paradigm, which the rats learned to compensate for. This animal model is ideal for elucidating mathematical models that will deal with transitions between prosthetic use and non-use as well as changes in the force output needed to move different objects (such as spring, velocity or acceleration based force fields). A multiple linear regression model fit the manipulandum's position using 70 neurons and 24 LFP channels (r > .85, P <.01). We demonstrate that using a second regression model of the velocity allows us to determine the "state" of the rats neural ensemble, such as when it is about to move the manipulandum. This allows us to switch our position prediction model on or off with 100% accuracy in state transitions. Thus, our prosthetic arm will only move when the animal is truly trying to make a reaching movement.