Sparse linear regression
This protocol is extracted from research article:
The somatosensory cortex receives information about motor output
Sci Adv, Jul 10, 2019; DOI: 10.1126/sciadv.aaw5388

We applied a Bayesian SLiR algorithm that introduces sparse conditions for the unit/channel dimension only and not for the temporal dimension of the model. High-γ power recorded in S1 electrodes was modeled as a weighted linear combination of the neuronal activity of peripheral afferents and high-γ activity in MCx using multidimensional linear regression as followsyj,T(t)=k,lwj,k,l×xk,T(t+lδ)+bj(1)where yj,T(t) is a vector of activity of an S1 electrode j (two frequency bands of eight and six electrodes in Monkeys T and C, respectively) at time index t in a trial T, xk,T(t + lδ) is an input vector of a peripheral afferent or a cortical electrode k at time index t and time lag lδ (δ = 5 ms) in a trial T, wj,k,l is a vector of weights on a peripheral afferent or a cortical electrode k at time lag lδ, and bj is a vector of bias terms to yj,T. Because we examined how combined activities in MCx and peripheral afferents influenced activity in S1, time lag lδ (Eq. 1) was set to negative values. We used a time window of 100 ms because the prediction accuracy reached a plateau at 100 ms.

To compute the contribution of each cortical area or peripheral afferents to the reconstruction of S1 activity, we calculated each component of reconstructed activity using MCx, premotor cortices, M1, or peripheral afferent activity and their respective weight values in a decoding model that was built from combined activities in MCx and peripheral afferents. For example, the MCx component was calculated as followsy_MCxj,T(t)=k,lwj,k,l×x_MCxk,T(t+lδ)+bj(2)where y_MCxj,T(t) is a vector of the MCx component at an S1 electrode j at time index t in a trial T, x_MCxk,T(t + lδ) is an input vector of a cortical electrode k at time index t and time lag lδ in a trial T, and wj,k,l is derived from a vector of weights in Eq. 1, but with weights assigned to peripheral afferents removed.

The temporal activity of muscles was modeled as a weighted linear combination of high-γ activity in M1 or S1 using the above Eq. 1. In the analysis, yj,T(t) is a vector of EMG of a muscle j (12 and 10 muscles of Monkey T and C, respectively) at time index t in a trial T. xk,T(t + lδ) is an input vector of a channel k at time index t and time lag lδ (δ = 5 ms) in a trial T. wj,k,l is a vector of weights on a channel k at time lag lδ for a muscle j, and bj is a vector of bias terms to yj,T. As we examined how activity in M1 or S1 before movement initiation influenced the initial increase in muscle activity, time lag lδ was set to negative values. We built a model from the activity in M1 or S1 to reconstruct the subsequent muscle activity during the premovement period (−500 to 0 ms around movement onset). Then, we reconstructed EMG by applying the obtained model to the M1 or S1 activity throughout the premovement and movement periods (−500 to 2000 ms around movement onset). We used a time window of 50 ms because the prediction accuracy reached a plateau at 50 ms.

The initial peak EMG amplitude was modeled as a weighted linear combination of the high-γ activity in M1 or in S1 within an overlapping, sliding time window of 50 ms as followsyj,T=k,lwj,k,l×xk,T(t+lδ)+bj(3)where yj,T is a vector of EMG of a muscle j (12 and 10 muscles of Monkey T and C, respectively) in a trial T, xk,T(t + lδ) is an input vector of a channel k at time index t and time lag lδ in a trial T, wj,k,l is a vector of weights on a channel k at time lag lδ for a muscle j, and bj is a vector of bias terms to yj,T. As we examined how the activity in M1 or S1 influenced the initial peak amplitude of muscle activity, time lag lδ was set to negative values. We used a time window of 50 ms so that l was set to −10. To examine the point at which M1 or S1 started to encode EMG burst amplitude, we changed time index t.

Joint angles were modeled as a weighted linear combination of neuronal activities in peripheral afferents or high-γ power in M1 or S1 using multidimensional linear regression as followsyj,T(t)=k,lwj,k,l×xk,T(t+lδ)+bj(4)where yj,T(t) is a vector of kinematic variables j (joint angle) at time index t in a trial T, xk,T(t + lδ) is an input vector of unit k at time index t and time lag lδ (δ = 5 ms) in a trial T, wj,k,l is a vector of weights on a peripheral afferent or a cortical electrode k at time lag lδ, and bj is a vector of bias terms to yj,T. We considered that, in the sensory-motor closed-loop pathway, neuronal activity in M1 evokes activity in muscles, which, in turn, generate the movement of the limb. In a model of high-γ activity in M1, we set the time lag lδ (Eq. 4) to negative values. In contrast, we considered that self-generated movements evoke the neuronal activity of peripheral afferents and high-γ activity in S1; therefore, in models of peripheral afferents or high-γ activity in S1, we set the time lag lδ to positive values. By changing the length of the time window, we attained a time window (400 ms) within which the accuracy of reconstructing joint kinematics reached a plateau. We then used this time window in encoding forelimb kinematics from neural activities.

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