Signatures of Covert Neuron Loss in the Local Field Potential of Motor Cortex

Abstract

Background

Covert stroke is understudied despite occurring 10 times for every symptomatic stroke and contributing to stroke's enormous global disease burden. For instance, does covert stroke replicate the neuroelectrophysiological spectrum impact of symptomatic stroke? We explored this by using our novel electrolytic lesioning platform to induce covert neuron loss.

Methods

During a multimonth arm reaching task, electrolytic lesions were delivered to the motor cortex of 2 large animals (U: $n=4$; H: $n=7$). Effects on behavioral metrics and local field potential features (bandpowers, aperiodic/periodic parameters, time‐frequency tensors) were measured using state space modeling and nonparametric permutation tests.

Results

Task success was unaffected by lesions, but shifts in aperiodic structure reduced next‐day $\gamma$ bandpower (30–100 Hz; U: $-1.38$ μV², $P<1\times {10}^{-3}$; H: $-1.66$ μV², $P=0.001$) and sensorimotor rhythms spanning 8 to 45 Hz ($\sum SMR$) were amplified (U: $8.68$ μV², $P<1\times {10}^{-3}$; H: $2.40$ μV², $P=0.004$). Additionally, state space modeling showed that perturbations to $\gamma$ and $\sum SMR$ outlasted any behavioral impact (Monkey U: Behavior = 1 d, $\gamma =$ 2 d, $\sum \mathit{\text{SMR}}$ = 2 d; Monkey H: Behavior = 0 d, $\gamma =$ 3 d, $\sum \mathit{SMR}$ = 1 d). Finally, tensor decomposition revealed interpretable, personalized perturbations to time‐frequency dynamics.

Conclusion

The neural spectrum is more sensitive to neuron loss than previously understood and could be responsive to covert stroke. This work also motivates using electrolytic lesions to bridge covert and symptomatic regimes of neuron loss, advancing our causal understanding of poststroke spectrum and behavior.

Nonstandard Abbreviations and Acronyms

CPD

canonical polyadic decomposition

LFP

local field potential

M1

primary motor cortex

MRBD

movement‐related beta decrease

PMBR

postmovement beta rebound

SMR

sensorimotor rhythm

Research Perspective.

What is New?

• Electrolytic lesions from an implanted array were used to model the functional consequences of covert stroke by inducing small amounts of neuron loss in the motor cortex of awake, behaving gyrencephalic nonhuman primates.

• Local field potential features such as $\gamma$ bandpower (30–100 Hz) and sensorimotor rhythm strength were more responsive to neuron loss than behavioral metrics, suggesting that the spectrum is more sensitive to neuron loss than behavioral assays.

What Question Should Be Addressed Next?

• How do these signatures change in response to larger lesions that also cause behavioral breakdown, and how does this inform the use of local field potential features in the clinical workup of both covert and symptomatic stroke?

Electrophysiological recordings of the peri‐infarct cortex have shown that ischemic stroke induces measurable changes in the neural spectrum, correlated with behavioral recovery and stroke severity. ¹ , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ These spectrum perturbations may provide a window into how functional networks reorganize after stroke ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ³¹ and could serve as quantitative rehabilitation targets. ³² But, accessing this scientific and translational impact requires clarity on the causal relationships between stroke, spectrum perturbations, and behavioral outcomes. For instance, if we assume that the causal structure can be represented as a graph—with the underlying stroke as the root—we cannot easily distinguish between the graphs depicted in Figure 1A. Is the spectrum perturbation caused by behavioral deficit or vice versa? Are the 2 effects generic, independent responses to stroke of a given scale? Of course, these graphs simplify a reality that is much more complex and dynamic, but the point remains: a clinically relevant theory of the poststroke neural spectrum requires mapping out this causal terrain.

Figure 1. Lesions were covert but perturbed bandpower features.

A, Causal possibilities for poststroke effects on behavior and the neural spectrum are difficult to distinguish from correlational studies reporting behavioral breakdown alongside spectrum perturbation. B, Monkeys U/H participated in a center‐out reaching task, where individual trials were kinematically represented by a reaction time (${\mathrm{T}}_{\mathrm{rxn}}$), reach speed (${\mathrm{v}}_{\text{reach}}$), and angular error (${\mathrm{\theta }}_{\mathrm{err}}$). C, An electrolytic lesioning platform ⁵³ induced covert neuron loss in the midst of longitudinal recordings (Monkey U: $\mathrm{n}=4$, Monkey H: $\mathrm{n}=7$) via the implanted microelectrode array. Lesions occurred after recording on Day 0, then neural activity and behavior were sampled $\sim$24 h later on Day 1; this was repeated multiple times. D, Kinematics were qualitatively preserved after lesions, as shown by visualizing cursor position across Day 0 (black) and Day 1 (crimson) reaches. Thin traces indicate single reaches, while thick lines indicate mean trajectory for each reaching target. Monkey U played a traditional 8‐target task and Monkey H played with 6 targets, 4 of which produced stereotyped reaches (see Detailed Methods, Figure S1A). E, F, Lesions were embedded in longitudinal recordings (E), and permutation tests of a lesion sensitivity statistic ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}$ (Detailed Methods) determined significant next‐day impacts from lesions (*P<0.05) (F). In (E), the Day 0 to Day 1 effects are marked in crimson, and the black trace is a smoothed version (Detailed Methods) of the raw gray data. Notably, task success rate (${\text{rate}}_{\mathrm{suc}}$) was unaffected (Monkey U: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=-0.01$, $P=1.000$; Monkey H: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=-0.02$, $P=0.828$), suggesting that neuron loss was covert. Other behavioral metrics were also unaffected except for ${\mathrm{T}}_{\mathrm{rxn}}$ in Monkey U (${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=2.12$, $P<1\times {10}^{-3}$). However, both monkeys experienced a significant reduction to $\mathrm{\gamma }$ power after lesions (Monkey U: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=-2.36$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=-2.47$, $P=0.001$). See all lesion sensitivity statistics in Table S2.

To resolve (and improve upon) the structures in Figure 1A, measuring spectral impact at the boundary between covert stroke (defined as ischemia occurring “without a history of acute neurological dysfunction attributable to the lesion” ³³ ) and symptomatic stroke could unify spectral shifts related to behavioral compensation ³⁴ and those that are relevant to behavioral deficit. These measurements are also motivated by the prevalence and disease burden of covert stroke, ³⁵ which occurs relative to symptomatic strokes at a rate of $\sim$10:1 ³⁶ , ³⁷ (affecting up to 30% of older people ³⁸ ) while increasing risk for dementia, ³⁹ , ⁴⁰ depression, ⁴¹ and future symptomatic strokes. ³⁹ , ⁴² , ⁴³ , ⁴⁴ Despite this, our scientific understanding of covert stroke is limited and there is “little evidence for how to investigate or manage” covert stroke in clinical contexts, as described in an official statement by the American Heart Association/American Stroke Association. ³⁵ There is thus a scientific and clinical need for basic animal models of covert stroke, the translational value of which would be maximized in the gyrencephalic primate brain due to anatomical similarities with humans in cortical organization and descending motor pathways. ⁴⁵ This need for primate stroke models ²⁰ , ⁴⁶ , ⁴⁷ , ⁴⁸ –that can connect the rodent stroke literature ²⁵ , ²⁶ , ²⁹ with human neurophysiology–has been reiterated for over 25 years by expert consortia ⁴⁵ , ⁴⁹ , ⁵⁰ , ⁵¹ and the US National Institutes of Health. ⁵² Considering the unique ethical demands of working with nonhuman primates, covert stroke is an appealing starting point.

In response to these needs, we used our novel electrolytic lesioning platform ⁵³ , ⁵⁴ to model the functional consequences of covert stroke. Although this model cannot capture all aspects of covert stroke's vascular origin and molecular/cellular pathology, it intentionally isolates covert neuron loss as the core functional consequence of covert stroke. This allowed us to measure, for the first time, the spectral impact of covert neuron loss in 2 rhesus macaques (Monkeys U and H) while recording reach‐related local field potential (LFP) data. We found that covert neuron loss, which did not affect behavioral metrics like success rate and kinematic entropy, induced spectrum perturbations that were coherent with the symptomatic stroke literature, including a prominent reduction to $\gamma$ bandpower (30–100 Hz) ⁴ , ¹⁹ , ²⁰ , ²¹ , ²² driven by shifts in the aperiodic spectrum structure, ²² , ²³ , ⁵⁵ , ⁵⁶ , ⁵⁷ alongside heterogeneous effects on movement‐related time‐frequency dynamics. ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ The lesions also increased the power of sensorimotor rhythms (SMRs) in the 8 to 45 Hz frequency range. Overall, we motivate the use of controlled neuron loss in nonhuman primates across multiple scales of injury in order to functionalize the neural spectrum as a tool for understanding and treating stroke, across covert and symptomatic regimes.

METHODS

Additional details on the following methods are available in the Supplemental Material.

Data Availability

Neural and behavioral data are available in the Brain Interfacing Laboratory data deposition in the Stanford Digital Repository (https://doi.org/10.25740/zz618yg1930). Derived data, results, visualizations, and code are available following the “archival, reproducible, and transparent science” open framework ⁵⁸ in the Stanford Digital Repository (https://doi.org/10.25740/bz926pm4806).

Animal Care

Two adult male rhesus macaques (Macaca mulatta), aged 11 (Monkey U) and 14 (Monkey H), were implanted with 96‐channel Utah arrays in the arm region of contralateral primary motor cortex (M1) (Blackrock Microsystems, Salt Lake City, UT, USA). All animal procedures were reviewed and approved by Stanford University's Institutional Animal Care and Use Committee.

Behavior

Subjects performed a center‐out reaching task for a juice reward (Figure 1B). Alongside a daily success rate (${\mathit{\text{rate}}}_{\mathit{suc}}$), reach kinematics were optically tracked and the daily medians of reaction time ($T_{\mathit{rxn}}$), reach speed ($v_{\mathit{\text{reach}}}$), and angular error (${\theta }_{\mathit{err}}$) were computed (Figure 1B). Trial inclusion criteria ensured reaches were stereotyped (Detailed Methods, Figure S1, daily rate of trial inclusion denoted ${\mathit{\text{rate}}}_{\mathit{acc}}$), and then electrophysiological data were extracted from epochs spanning 150 ms before to 350 ms after $T_{\mathit{rxn}}$. To supplement the standard behavioral features of ${\mathit{\text{rate}}}_{\mathit{suc}}$, $T_{\mathit{rxn}}$, $v_{\mathit{\text{reach}}}$, and ${\theta }_{\mathit{err}}$, a kinematic entropy measure was used where histograms of daily 2‐dimensional arm position and velocity were constructed (Figure S2A) and then entropy was computed to yield $H_p$ and $H_v$.

Electrolytic Lesions

The lesion circuit ⁵³ used pairs of adjacent electrodes as the anode/cathode to pass controlled amounts of direct current through tissue. At an amplitude of 150 to 170 μA to M1, Monkey U received 4 30‐second lesions, and Monkey H received 10 lesions mostly at a duration of 45 seconds (lesion 3 was 130 μA for 50 seconds and lesion 10 was 480 μA for 30 seconds) (Table S1). This parameter range was calibrated using histology in ex vivo ovine and porcine brains and in vivo anesthetized porcine and macaque brains ⁵³ to evoke lesion volumes on the order of $\sim$1 mm³, a fraction of $\sim$20 mm³ photothrombotic ²⁰ or $\sim$100 mm³ aspiration ⁵⁹ lesions previously reported in macaque sensorimotor cortex. Due to recording issues in lesion 1 and nonparticipation after lesion 3, only the last 7 lesions of Monkey H featured consistent daily recordings and were included for analysis. Blood testing, ear temperature, neurological/physical examinations, and extensive in‐cage monitoring were used to ensure animal well‐being after lesions; no abnormalities were documented (Table S1).

In Vivo Electrophysiology

Daily periodograms were estimated from filtered and downsampled 1 kHz LFP data between 1 and 100 Hz by taking a median across all channels and trials for a given day; canonical bandpowers were then computed ($\delta$: 1–4 Hz, $\theta$: 4–8 Hz, $\alpha$: 8–12 Hz, $\beta$: 12–30 Hz, $\gamma$: 30–100 Hz). A time‐frequency tensor was formed using squared wavelet coefficients (complex Morlet ⁶⁰ , ⁶¹ ; center frequency: 1 Hz; bandwidth: 2 Hz ⁶² ) from 8 to 100 Hz in increments of 1 Hz and in 10 ms temporal increments from −320 to 120 ms relative to $T_{\mathit{rxn}}$.

For daily periodogram data, spectral parametrization ⁵⁵ hyperparameters were selected (Figure S3B), yielding an aperiodic exponent ($a{p}_{\mathit{exp}}$) and offset ($a{p}_{\mathit{off}}$), alongside the locations, heights, and widths of oscillatory peaks (Figure 2A). Two recurring SMRs in the $\alpha /\beta$ range were identified where possible ($\mathit{SM}{R}_{\downarrow }$, $\mathit{SM}{R}_{\uparrow }$) alongside their powers ($\mathit{SM}{R}_{\downarrow }^P$, $\mathit{SM}{R}_{\uparrow }^P$), frequencies ($\mathit{SM}{R}_{\downarrow }^f$, $\mathit{SM}{R}_{\uparrow }^f$), and widths ($\mathit{SM}{R}_{\downarrow }^W$, $\mathit{SM}{R}_{\uparrow }^W$). An aggregate SMR power was estimated each day from 8 to 45 Hz, denoted $\sum \mathit{SMR}$.

Figure 2. Bandpower effects were driven by perturbed aperiodic and periodic parameters.

A, Using spectral parametrization, ⁵⁵ daily periodograms (black) were represented as aperiodic (gray) and periodic (blue shows aperiodic + periodic) components. Shown are representative fits to Monkey U's spectrum on December 1, 2020 (${\mathrm{ap}}_{\mathrm{off}}=2.33\log$μV², ${\mathrm{ap}}_{\exp }=1.73$, peaks at $16.6/34.1/51.3$ Hz) and Monkey H's spectrum on February 16, 2020 (${\mathrm{ap}}_{\mathrm{off}}=2.02\log$μV², ${\mathrm{ap}}_{\exp }=1.62$, peaks at $21.3$/$35.3$/$52.7$/$66.9$ Hz). B–E, Longitudinal recordings of aperiodic features ($\mathrm{a}{\mathrm{p}}_{\exp }$, $\mathrm{a}{\mathrm{p}}_{\mathrm{off}}$) and the aggregate SMR power between 8 and 45 Hz ($\sum \mathrm{SMR}$) (B) are shown alongside lesion sensitivity estimates ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}$(C) (*$P<0.05$). Aperiodic shifts drove reductions to postlesion $\mathrm{\gamma }$ power (Figure 1E and 1F) as shown across individual lesions (D). In both monkeys, $\sum \mathrm{SMR}$ increased after lesions (Monkey U: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=2.35$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=1.26$, $P=0.004$) (C) as shown by visualizing the periodic component across individual lesions (E); the gray region indicates the frequency range used to aggregate SMR power into $\sum \mathrm{SMR}$. Note that the power of SMRs was generally stronger in Monkey U (see A as well as bottom of B); this $\sum \mathrm{SMR}$ amplification likely drove increased postlesion $\mathrm{\beta }$ power in Monkey U (Figure S1B and S1C), whereas Monkey H's $\mathrm{\beta }$ power decrease was likely driven by aperiodic shifts. All lesion sensitivity statistics are shown in Table S2. SMR indicates sensorimotor rhythm.

Statistical Analysis

To identify next‐day lesion effects, $z$‐scored first differences of aforementioned features between the prelesion recording session (Day 0 in Figure 1C) to another session $\approx$24 hours later (Day 1 in Figure 1C) were averaged, yielding the standardized statistic ${⟨\Delta ⟩}_L$. Next, a linear Gaussian state space model was used as an alternate model of lesion impact that also measured its temporal extent. ⁶³ Given a $z$‐scored time series sampled at times $t$ ($y_t$), we modeled this as having 3 components: a component arising from a linear dynamical system ($x_t$), a component that was driven by inputs ($u_t$), and a noise component. The lesions were modeled as the input $u_t$, capable of influencing the time series for 5 days after a lesion occurred. To do so, $u_t$ was a 5‐vector where the $i$th index was $1$ when it was $i$ days after a lesion and $0$ otherwise (Figure 3A). The strength of this influence was captured by the standardized lesion input coefficients $d_1,d_2,\dots ,d_5$. Three such models were fit to $z$‐scored Behavior, Periodogram, and Tensor data sets; for each feature, the marginal log‐likelihood (${\mathit{SSM}}_{\mathit{LL}}$) and lesion input coefficients ($d_1,d_2,\dots ,d_5$) were analyzed for significance.

Figure 3. Spectrum perturbations outlasted behavioral effects.

A, A LG‐SSM was used as an alternative framework to quantify the impact of lesions; this approach also quantified a temporal extent of lesion impact. Specifically, the model represented lesions as 5‐d external inputs (${\mathrm{u}}_{\mathrm{t}}$) on observed features (${\mathrm{y}}_{\mathrm{t}}$) that could not be accounted for by the linear dynamics of a low‐dimensional state (${\mathrm{x}}_{\mathrm{t}}$) (see Detailed Methods). Lesion inputs were a vector of 5 values, where the value at index $\mathrm{i}$ was 1 if it was $\mathrm{i}$ d after a lesion, and 0 otherwise; this is shown by the crimson and black dots. By fitting this model to collections of $\mathrm{z}$‐scored time series, this allowed estimation of lesion impact across the 5‐d, post‐lesion period. For each feature, this was measured by ${\mathrm{d}}_1,{\mathrm{d}}_2,\dots ,{\mathrm{d}}_5$ (not shown), the standardized input strength of lesions on each postlesion d. Note that this graphical model captures only a small segment of the longitudinal time series that contained multiple lesions. B, C, On the Behavior (B) and Periodogram (C) data sets, permutation tests determined the significance of ${\mathrm{SSM}}_{\mathrm{LL}}$(top) and ${\mathrm{d}}_{\mathrm{i}}$ (bottom) (*$P<0.05$). Gray shading indicates 95% intervals for ${\mathrm{SSM}}_{\mathrm{LL}}$ fitting curves (top) or input estimates (bottom) across 1000 permuted null models. Lesion inputs increased ${\mathrm{SSM}}_{\mathrm{LL}}$ for the Behavior data set in Monkey U (B, top) and the Periodogram data set (C, top) in both monkeys. This approach confirmed the only detectable behavioral effect of lesions, a 1‐d increase to ${\mathrm{T}}_{\mathrm{rxn}}$ in Monkey U (B, bottom). It also confirmed the reduction to $\mathrm{\gamma }$ power and increase to $\sum \mathrm{SMR}$ (C, bottom). These spectral effects outlasted any behavioral impact (Monkey U: Behavior = 1 d, $\mathrm{\gamma }$2 d, $\sum \mathrm{SMR}$ = 2 d; Monkey H: Behavior = 0 d, $\mathrm{\gamma }$ = 3 d, $\sum \mathrm{SMR}$ = 1 d), suggesting that the spectrum is more sensitive than behavioral metrics to neuron loss. As visible on the bottom of (B) and (C), effect sizes were on the order of a SD. For full LG‐SSM statistics, see Tables S7 through S10; additional visualizations are in Figure S7. LG‐SSM indicates linear Gaussian state space model; and SMR, sensorimotor rhythm.

Significance of ${⟨\Delta ⟩}_L$/${\mathit{SSM}}_{\mathit{LL}}$/$d_i$ statistics was determined using nonparametric within‐subject permutation tests, ⁶⁴ , ⁶⁵ using the null hypothesis that observed data would be equally likely if lesion days had been randomly reassigned. This approach means that monkeys acted as their own statistical control, where lesion impact was measured against empirical fluctuations in recorded longitudinal data. This permitted adherence to the systems neuroscience ethical standard of 2 monkeys. The false discovery rate was used to control the family‐wise error rate at $0.05$ for each group of tests. ⁶⁶ Beyond considering statistical significance, the ${⟨\Delta ⟩}_L$/$d_i$ statistics report a standardized impact of lesions on the relevant feature, providing an effect size interpretable in feature SDs. These statistics are also disclosed in natural units (eg, μV²) in the relevant Supplemental Tables—Supplemental Material. See the Detailed Methods for additional statistical descriptions, including approaches for behavioral correlation, spatial correlation, and recurrent lesion effects.

Tensor Decomposition

In addition, the temporal dynamics of average wavelet coefficients in 8 Hz bands around median $\mathit{SM}{R}_{\uparrow }^f$ were analyzed (Monkey U: 29–37 Hz; Monkey H: 31–39 Hz), and a premovement baseline (${\beta }_{\mathit{ref}}$) was computed alongside a normalized movement‐related beta decrease ($\mathit{\text{MRBD}}$) and postmovement beta rebound ($\mathit{\text{PMBR}}$). Next, the nonnegative canonical polyadic decomposition (CPD) reduced the time‐frequency tensor to a sum of rank‐one component tensors. ⁶⁷ , ⁶⁸ , ⁶⁹ , ⁷⁰ A rank $R$ CPD provided $R$ factors across days (${\tau }_r^d$), frequency (${\tau }_r^f$), and time (${\tau }_r^t$) which approximated the original tensor (Figure 4A). Ranks of $R=4$/$R=3$ were selected for Monkeys U/H (Detailed Methods).

Figure 4. Signatures of lesions in time‐frequency dynamics were personalized.

A, Squared wavelet coefficients yielded a time‐frequency tensor across days. An $\mathrm{R}$‐rank approximation was found using the CPD, identifying constituent factors across days (${\mathrm{\tau }}_{\mathrm{r}}^{\mathrm{d}}$), frequency (${\mathrm{\tau }}_{\mathrm{r}}^{\mathrm{f}}$) and time (${\mathrm{\tau }}_{\mathrm{r}}^{\mathrm{t}}$). B, Based on high reconstruction score, increasing cross‐validation score, and high model similarity across initializations, $\mathrm{R}=4$ and $\mathrm{R}=3$ were chosen for Monkeys U and H. Lines are the mean with shaded 95% percentile intervals. Reconstructions scores were computed across 1000 initializations for each rank, and 50 cross‐validation scores were computed from 25 instances of 2‐fold cross‐validation. Similarity scores captured the 999 similarities (Detailed Methods) with the highest‐scoring initialization; “+” markers isolate the mean similarity of the 99 next‐best models. Note that this metric drops off meaningfully after the selected ranks in each monkey. C, D, Both ${\mathrm{\tau }}_1$ and ${\mathrm{\tau }}_2$ had broad, unimodal temporal weights alongside broad frequency weights, although ${\mathrm{\tau }}_1$ had increased relative weight on $\mathrm{\gamma }$ frequencies (D). In both monkeys, ${\mathrm{\tau }}_1^{\mathrm{d}}$ was reduced by lesions (Monkey U: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}-2.71=$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=-1.47$, $P<1\times {10}^{-3}$), echoing the impact on $\mathrm{\gamma }$ bandpower previously observed, while ${\mathrm{\tau }}_2^{\mathrm{d}}$ was preserved in Monkey H (${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=-0.15$, $P=0.668$) and increased in Monkey U (${⟨\mathrm{\Delta }⟩}_{\mathrm{L}}=2.62$, $P<1\times {10}^{-3}$) (C) (*$P<0.05$). Meanwhile, ${\mathrm{\tau }}_3$ had bimodal frequency and temporal weights, reflecting movement‐related $\mathrm{\beta }$ modulations, whereas ${\mathrm{\tau }}_4$ was unique to Monkey U and captured premovement $\mathrm{\alpha }$ and $\mathrm{\beta }$ power. Effects on these factors revealed a divergent lesion impact on SMR dynamics, mirroring the analysis of ${\mathrm{\beta }}_{\mathrm{ref}}$/movement‐related beta decrease/postmovement beta rebound in Figure S8. E, The lesion sensitivity of individual wavelet coefficients, shown here, was demixed by the CPD (mask indicates significance at $P<0.05$). F, State space modeling affirmed that lesion inputs improved ${\mathrm{SSM}}_{\mathrm{LL}}$ of the ${\mathrm{\tau }}_{\mathrm{r}}^{\mathrm{d}}$ (Table S7) and revealed a 2 d reduction to ${\mathrm{\tau }}_1^{\mathrm{d}}$ in Monkey U and a 1 d reduction in Monkey H (*$P<0.05$) (Table S10). CPD indicates canonical polyadic decomposition; and SSM, sensorimotor rhythm.

RESULTS

Covert Lesions Perturbed Bandpower Features

Monkeys U and H performed a center‐out reaching task almost every day for months (Monkey U: 102/103 days; Monkey H: 70/76 days) during simultaneous LFP recordings from M1 (Figure 1B, left). Monkey U played a standard radial reaching task to 8 targets, and Monkey H had the bottom and bottom left targets removed due to a visual deficit; in addition, reaches to the top and top right were poorly stereotyped and were discarded, leaving four reach conditions (Figure S1A, Detailed Methods). Up to 750 successful reaches were included in the data set on each recording day yielding a total of 74 054 trials for Monkey U and 36 827 trials for Monkey H. In this period, electrolytic lesions were performed in M1 via the implanted array (Monkey U: 4 lesions, Monkey H: 7 lesions) ⁵³ (Figure 1C). Lesion parameters were selected to be covert, inducing neuron loss while preserving the ability of the animal to complete the arm‐reaching task. By “covert,” we mean that the animal's success rate (${\mathit{\text{rate}}}_{\mathit{suc}}$) was not affected by neuron loss, in accordance with animal stroke models analyzing success rates in pellet reaching tasks. ²³ , ⁵⁶ , ⁷¹ , ⁷² , ⁷³ , ⁷⁴ , ⁷⁵

Near‐identical reach kinematics were observed for trials before and after lesions (0–1 days to lesion in Figure 1C; kinematics shown in Figure 1D), suggesting a covert effect. To make this concrete, we leveraged the fact that lesion‐induced fluctuations were sparsely embedded within longitudinal time series of neural recordings and behavior (crimson markings in Figure 1E). Thus, lesion perturbations for a given feature were compared with the empirical distribution of day‐to‐day fluctuations by permutation tests of the statistic ${⟨\Delta ⟩}_L$ (mean, $z$‐scored, lesion‐induced fluctuation). Applied to ${\mathit{\text{rate}}}_{\mathit{suc}}$, no lesion impact was detected (Monkey U: ${⟨\Delta ⟩}_L=-0.01$, $P=1.000$; Monkey H: ${⟨\Delta ⟩}_L=-0.02$, $P=0.828$; top of Figure 1F); in fact, ${\mathit{\text{rate}}}_{\mathit{suc}}$ was >99.5% on all postlesion days in each animal (top of Figure 1E). When considering other behavioral metrics, no impact was detected except for an increase to $T_{\mathit{rxn}}$ for Monkey U (${⟨\Delta ⟩}_L=2.12$, $P<1\times {10}^{-3}$) (Figure 1E and 1F), amounting to a mean slowing of $\sim$17 ms. The rate at which trials were included for analysis based on passing behavioral filters (${\mathit{\text{rate}}}_{\mathit{acc}}$) was also unaffected (Figure S1B and S1C, complete ${⟨\Delta ⟩}_L$ statistics in original and $z$‐scored units are in Table S2).

To further validate the covert impact of the lesions, the behavioral metrics analyzed were paired with the entropy of daily position/velocity kinematic distributions (Figure S2A). Reduction in movement entropy has a history of use in sports science as a summary statistic for tracking increased motor efficiency and skill throughout learning. ⁷⁶ , ⁷⁷ Increased entropy of gait patterns has also been measured after acute peripheral ischemia–reperfusion. ⁷⁸ Thus, this measure offered a sensitive, data‐driven supplement to our behavioral characterization. Position and velocity entropy ($H_p$ and $H_v$) were computed each day (Figure S2B), and lesion impact was not observed for either $H_p$ (Monkey U: ${⟨\Delta ⟩}_L=0.03$, $P=1.000$; Monkey H: ${⟨\Delta ⟩}_L=0.64$, $P=0.124$) or $H_v$ (Monkey U: ${⟨\Delta ⟩}_L=-0.26$, $P=0.742$; Monkey H: ${⟨\Delta ⟩}_L=0.15$, $p=0.817$) (Figure S2C, Table S2). In summary, across consideration of reaching ability (${\mathit{\text{rate}}}_{\mathit{suc}}$), standard metrics ($T_{\mathit{rxn}}$, $v_{\mathit{\text{reach}}}$, ${\theta }_{\mathit{err}}$), and entropy ($H_p$, $H_v$), the lesions had no impact besides an increase to Monkey U's $T_{\mathit{rxn}}$, in alignment with our definition of “covert.”

Contrasting the sparse behavioral impact, a robust $\gamma$ power decrease on the order of 2 SDs was observed in both monkeys (Monkey U: ${⟨\Delta ⟩}_L=-2.36$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\Delta ⟩}_L=-2.47$, $P=0.001$; bottom row of Figure 1E and 1F). Lesion impacts were also observed in other bands, such as an increase in $\alpha$ and $\beta$ activity in Monkey U alongside a reduction in $\delta$, $\theta$, $\alpha$, and $\beta$ power in Monkey H (Figure S1B and S1C, Table S2). Interestingly, this pronounced loss of high‐frequency power ⁴ , ¹⁹ , ²⁰ , ²¹ , ²² (or a relative increase in low‐frequency power ² , ³ , ⁵ , ⁷ , ⁸ , ⁷⁹ , ⁸⁰ , ⁸¹ , ⁸² ) has been previously observed in symptomatic stroke. However, interpreting bandpower shifts is tenuous without differentiating between the periodic oscillations existing atop the aperiodic, power‐law structure of the spectrum. ⁵⁵ , ⁸³ The $\gamma$ reduction observed here may be compatible with a shift in the aperiodic power law, ²² , ²³ , ⁵⁶ , ⁵⁷ whereas the heterogeneity in the $\alpha$ and $\beta$ bands may relate to shifts in SMRs known to occupy those frequency ranges. ⁸⁴ , ⁸⁵ , ⁸⁶ , ⁸⁷ As such, spectral parametrization was then applied. ⁵⁵

Bandpower Effects Were Driven by Perturbed Aperiodic/Periodic Parameters

After model selection (Figure S3B, Detailed Methods) and peak identification (Figure S3A), daily spectra were represented by their aperiodic parameters ($a{p}_{\mathit{exp}}$, $a{p}_{\mathit{off}}$) as well as the properties of oscillatory peaks; total periodic SMR power from 8 to 45 Hz was aggregated into the daily summary statistic $\sum \mathit{SMR}$. The parameters of 2 individual SMRs ($\mathit{SM}{R}_{\downarrow }$, $\mathit{SM}{R}_{\uparrow }$)—including power ($\mathit{SM}{R}_{\downarrow }^P$, $\mathit{SM}{R}_{\uparrow }^P$), frequency ($\mathit{SM}{R}_{\downarrow }^f$, $\mathit{SM}{R}_{\uparrow }^f$), and width ($\mathit{SM}{R}_{\downarrow }^W$, $\mathit{SM}{R}_{\uparrow }^W$)—were also analyzed (see Figure S3C and S3D). The model consistently had high goodness‐of‐fit (median $R^2$ across days [interquartile range]; Monkey U: 0.9947 [0.9941–0.9952]; Monkey H: 0.9977 [0.9960–0.9987]), which was not affected by the lesions (Figure S3C and S3D). Monkey U showed a significant increase in $a{p}_{\mathit{exp}}$ (${⟨\Delta ⟩}_L=1.61$, $P=0.003$) whereas $a{p}_{\mathit{off}}$ was unaffected (Figure 2B and 2C). This perturbed aperiodic structure (Figure 2D, top) in a way compatible with $\gamma$ power loss, as observed previously. ²² , ²³ , ⁵⁶ , ⁵⁷ In Monkey H, there was a marginally insignificant effect on $a{p}_{\mathit{off}}$(${⟨\Delta ⟩}_L=-0.81$, $P=0.079$) (Figure 2B and 2C); resultant aperiodic shifts also visibly reduced $\gamma$ power (Figure 2D, bottom). The close relationship between aperiodic activity and $\gamma$ power is further supported by the fact that aperiodic $\gamma$ power explained a large proportion of $\gamma$ power variance ($R^2$; Monkey U: 0.84; Monkey H: 0.71) and periodic $\gamma$ power did not ($R^2$; Monkey U: 0.02; Monkey H: 0.03).

Meanwhile, lesions increased $\sum \mathit{SMR}$ in both monkeys (Monkey U: ${⟨\Delta ⟩}_L=2.35$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\Delta ⟩}_L=1.26$, $P=0.004$). Interestingly, this effect size was larger in Monkey U compared with Monkey H ($\approx$2 versus $\approx$1 SD). Monkey U also had stronger periodic power content (median $\sum \mathit{SMR}$ [interquartile range]; Monkey U: 40.36 [38.02–43.12] μV²; Monkey H: 23.68 [22.20–25.56] μV²) as visible in Figure 2A and 2B. Accordingly, periodic $\beta$ power explained more $\beta$ variance in Monkey U than Monkey H ($R^2$; Monkey U: 0.63; Monkey H: 0.12); this reversed when considering $\mathit{log}$ aperiodic $\beta$ content ($R^2$; Monkey U: 0.02; Monkey H: 0.66). This difference may also be supported by Monkey H having a flatter neural spectrum (median $a{p}_{\mathit{exp}}$ [interquartile range]; Monkey U: 1.75 [1.74–1.78]; Monkey H: 1.64 [1.59, 1.74]). Note that when analyzing individual SMRs, this increase in power was also detected ($\mathit{SM}{R}_{\downarrow }^P$ and $\mathit{SM}{R}_{\uparrow }^P$); in addition, peak frequencies ($\mathit{SM}{R}_{\downarrow }^f$ and $\mathit{SM}{R}_{\uparrow }^f$) were reduced in Monkey U whereas effects on peak widths ($\mathit{SM}{R}_{\downarrow }^W$ and $\mathit{SM}{R}_{\uparrow }^W$) were mixed (Figure S3C and S3D, Table S2).

Taken together, spectral parametrization resolved the observed bandpower shifts into 2 underlying phenomena: aperiodic shifts ²² , ²³ , ⁵⁶ , ⁵⁷ and potentiation of $\sum \mathit{SMR}$. These results also show that agreement at the level of bandpower may only exist insofar as a band has a similar aperiodic‐periodic constitution across subjects. Here, aperiodic activity originated $\gamma$ power in both monkeys, hence the consistent decrease. However, periodic/aperiodic activity were the main drivers of $\beta$ power in Monkeys U/H respectively, hence the opposing lesion effects. This underlines how critical it is to frame bandpower‐centric analyses with spectral parameters. Finally, these effects can also comment on the increase in $T_{\mathit{rxn}}$ exclusively observed in Monkey U. Across both monkeys, a moderate correlation existed between $T_{\mathit{rxn}}$ and both $\alpha$ power (Monkey U: $\rho =0.41$, $P<1\times {10}^{-3}$, $N=100$; Monkey H: $\rho =0.37$, $P=0.035$, $N=65$) and $\beta$ power (Monkey U: $\rho =0.39$, $P<1\times {10}^{-3}$, $N=100$; Monkey H: $\rho =0.33$, $P=0.051$, $N=65$), replicating past work ⁸⁸ , ⁸⁹ , ⁹⁰ on a longitudinal scale (all statistics in Tables S3 and S4). As such, it is reasonable that in Monkey U, where SMRs were amplified to the degree of increasing these bandpowers, $T_{\mathit{rxn}}$ also increased; in Monkey H, where SMRs were not constitutive of these bandpowers and were not amplified as strongly, no such increase was observed.

Spectrum Perturbations Were Movement‐Specific, Spatially Diffuse, and Temporally Unordered

All analyzed data so far have been locked to the initiation of arm reaches (ie, $T_{\mathit{rxn}}$), and it remains unclear whether these perturbations are movement‐specific or reflect a global shift in motor cortex function. Our experimental flow did not include a prescribed rest period, but we recomputed spectral features using a window of time immediately before the reach stimulus where the animal was returning their cursor to the center of the screen and awaiting the next trial. Although this is not an interpretable rest period, it presents the motor cortex in a different operational mode (performing a predictable movement and holding still at the center). Single‐trial arm speeds are shown for both the pretrial and movement periods in Figure S4A. Neither the $\gamma$ (Monkey U: ${⟨\Delta ⟩}_L=0.72$, $P=0.140$; Monkey H: ${⟨\Delta ⟩}_L=-2.42$, $P<1\times {10}^{-3}$) nor $\sum \mathit{SMR}$ (Monkey U: ${⟨\Delta ⟩}_L=1.83$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\Delta ⟩}_L=0.69$, $P=0.060$) perturbation was replicated in both animals using the pretrial period (Figure S4B, see full statistics in Table S5). Specifically, the strength of the $\sum \mathit{SMR}$ increase was attenuated in each animal (Figure S4C) and became insignificant in Monkey H (pretrial versus move; Monkey U: ${⟨\Delta ⟩}_L=1.83$ versus ${⟨\Delta ⟩}_L=2.35$; Monkey H: ${⟨\Delta ⟩}_L=0.69$ versus ${⟨\Delta ⟩}_L=1.26$). Meanwhile, although Monkey H showed consistent effects on aperiodic parameters and $\gamma$ power, Monkey U was less consistent (Figure S4C). These results indicate that movement may be relevant for demonstrating the spectral effects of covert neuron loss.

Next, we considered whether spectral effects were spatially organized based on proximity to the 2 electrodes (anode/cathode) for each lesion. Thus far, channels and trials have been aggregated in order to denoise periodogram estimates (Figure S5A); instead, we computed spectral features (eg, $\gamma$ and $\sum \mathit{SMR}$) for each channel by only aggregating across included trials (Figure S5B). By visualizing the $z$‐scored first difference induced by each lesion (denoted $\Delta$) on $\gamma$, the $\gamma$ reduction was diffused across the entire array and was not condensed to the region surrounding the lesion electrodes (Figure S5C). Similarly, $\sum \mathit{SMR}$ increased after most lesions in a way that was not spatially focalized (Figure S5D). This was made concrete by computing Spearman correlation between $\Delta$ for each channel/lesion with its Manhattan distance to the nearest lesion electrode, where electrodes were spaced with a pitch of 400 μm (Figure S6A). There was no spatial correlation for $\gamma$ (Monkey U: $\rho =0.00$, $P=0.997$, $N=384$; Monkey H: $\rho =-0.04$, $P=0.471$, $N=672$) and only a weak spatial correlation for $\sum \mathit{SMR}$ in Monkey H (Monkey U: $\rho =0.00$, $P=0.966$, $N=384$; Monkey H: $\rho =0.14$, $P=0.002$, $N=672$). Additional spatial correlation statistics for other spectral features are reported in Table S6.

Finally, a unique aspect of our approach is that lesions were repeated within a single animal (Monkey U: $n=4$; Monkey H: $n=7$). This invites the possibility that, via mechanisms such as glial remodeling or neural/behavioral compensation, lesion impact could be temporally ordered (ie, increasing or decreasing with additional lesions). To test this, we considered lesions as repeated measures of the magnitude of $z$‐scored first differences ($\left|\Delta \right|$) for behavioral and spectral features. This totaled 22 features across 4 lesions in Monkey U and 19 features across 7 lesions in Monkey H (Detailed Methods). A Friedman test identified a small, marginally insignificant difference in $\left|\Delta \right|$ across lesions for Monkey U (${\chi }^2\left(3\right)=6.90$, $W=0.10$, $P=0.075$) but not for Monkey H (${\chi }^2\left(6\right)=9.98$, $W=0.09$, $P=0.126$). Corrected, pairwise Wilcoxon signed‐rank tests (2 tailed) found that effects weakly decreased from lesion 1 to both of lesions 2/3 in Monkey U (1 versus 2: $T=45$, 68.2% decreased, $p=0.075$; 1 versus 3: $T=43$, 63.6% decreased, $P=0.075$; Figure S6B). This suggested the possibility of a decreasing trend in effects with repeated lesions, however Page's trend test for this directional hypothesis failed to reject the null hypothesis in both animals (Monkey U: $L=555.0$, $P=0.741$; Monkey H: $L=2145.0$, $P=0.742$). Similarly, by computing Spearman correlation between $\left|\Delta \right|$ and the temporal position of the corresponding lesion (ie, $1,2,\dots$), there was not a significant correlation (Monkey U: $\rho =-0.03$, $P=0.810$, $N=88$; Monkey H: $\rho =0.07$, $P=0.437$, $N=133$). This suggests that although repeated lesions may have been heterogeneous, there was no temporal ordering of effect sizes.

Spectrum Perturbations Outlasted Behavioral Effects in a State Space Model

So far, lesion impact has been assessed by permutation tests on a univariate lesion sensitivity statistic ${⟨\Delta ⟩}_L$. But this approach does not estimate the duration of lesion impact, only the presence of a next‐day effect. To strengthen these results, we set up a linear Gaussian state space model ⁶³ , ⁹¹ (Figure 3A). This decomposed observed time series ($y$ in Figure 3A) into a component arising from a linear dynamical system (ie, from $x$), a component driven by inputs (ie, from $u$), and noise. By treating the lesions as inputs, this model discerned the duration of time for which lesions had a significant input on the time‐series that could not be explained by underlying temporal dynamics. This confirmed and further differentiated the sensitivity of spectral and behavioral features to neuron loss.

We first fit the model to Behavior ($T_{\mathit{rxn}}$, $v_{\mathit{\text{reach}}}$, ${\theta }_{\mathit{err}}$) and Periodogram ($a{p}_{\mathit{exp}}$, $a{p}_{\mathit{off}}$, $\sum \mathit{SMR}$, $\delta$, $\theta$, $\alpha$, $\beta$, $\gamma$) data sets (example reconstructions are shown in Figure S7A). Permutation of lesion days tested the significance of the 5‐day lesion input for each feature ($d_1,d_2,\dots ,d_5$) and determined whether structured lesion inputs improved marginal log likelihood (${\mathit{SSM}}_{\mathit{LL}}$). As expected, lesion inputs significantly improved ${\mathit{SSM}}_{\mathit{LL}}$ for all data sets except for Behavior in Monkey H (top of Figure 3B and 3C, see likelihoods and $P$ values in Table S7). Accordingly, the only significant behavioral input was a 1 d increase to $T_{\mathit{rxn}}$ in Monkey U ($d_1=1.92$, $P=0.030$) (bottom of Figure 3B). Meanwhile, the model estimated a multiday reduction to $\gamma$ power (duration; Monkey U: 2 d; Monkey H: 3 d), with effects on the order of a SD for 3 days (Monkey U: $d_1=-1.89$, $P=0.020$, $d_2=-1.25$, $P=0.040$, $d_3=-1.17$, $P=0.053$; Monkey H: $d_1=-1.28$, $P=0.008$, $d_2=-1.23$, $P=0.008$, $d_3=-0.85$, $P=0.020$) (bottom right of Figure 3C). There was also an increase to $\sum \mathit{SMR}$ (Monkey U: 2 d; Monkey H: 1 d) with effects of a similar magnitude (Monkey U: $d_1=1.20$, $P=0.020$, $d_2=1.28$, $P=0.020$; Monkey: $d_1=0.95$, $P=0.011$) (see all parameters in Tables S8 and S9). Additional behavioral and spectral features can be seen in Figure S7B and S7C. Overall, spectral effects outlasted behavioral effects for each monkey (ie, elevated $T_{\mathit{rxn}}$ for 1 d in Monkey U), suggesting a stronger influence of neuron loss on the spectrum, relative to behavior, in this covert context.

Time‐Frequency Signatures of Lesions Were Personalized

The analysis so far has used static descriptions of spectral activity during arm reaching, but it is known that $\alpha$ and $\beta$ activity is modulated while preparing, ⁹² , ⁹³ , ⁹⁴ initiating, ⁸⁴ , ⁹⁵ , ⁹⁶ and carrying out ⁹⁷ , ⁹⁸ motor commands, and that these time‐frequency dynamics are perturbed in symptomatic stroke. ¹ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ As such, a nonnegative time‐frequency tensor was formed with squared wavelet coefficients across days (Figure 4A, left; see Detailed Methods). This is a high‐dimensional, multiway data structure; to generate a parsimonious representation that is useful scientifically, one can use domain knowledge to extract classical features (eg, bandpower) or use a data‐driven parametrization (eg, spectral parametrization). Here, classical features measure the movement‐related dynamics of $\beta$ activity which is known to desynchronize at movement onset ($\mathit{\text{MRBD}}$) and resynchronize at movement cessation ($\mathit{\text{PMBR}}$). ⁸⁶ , ⁸⁷ These variables ($\mathit{\text{MRBD}}$, $\mathit{\text{PMBR}}$) were computed by normalizing wavelet power around median $\mathit{SM}{R}_{\uparrow }^f$ in each animal (visualized as ${\beta }_{\mathit{tf}}$ in Figure S8A) relative to a baseline (${\beta }_{\mathit{ref}}$) (Figure S8B). The diverging impact on $\beta$ bandpower observed previously also appeared in ${\beta }_{\mathit{ref}}$ (Monkey U: ${⟨\Delta ⟩}_L=1.18$, $P=0.015$; Monkey H: ${⟨\Delta ⟩}_L=-2.11$, $P<1\times {10}^{-3}$). This effectively increased the dynamic range for $\mathit{\text{MRBD}}$/$\mathit{\text{PMBR}}$ activity in Monkey U while shrinking this range in Monkey H; accordingly, $\mathit{\text{MRBD}}$ was augmented (ie, larger decrease) in Monkey U (${⟨\Delta ⟩}_L=-1.31$, $P=0.005$) but attenuated (ie, smaller decrease) in Monkey H (${⟨\Delta ⟩}_L=0.958$, $P=0.019$) (Figure S8C, Table S2). Meanwhile, $\mathit{\text{PMBR}}$ decreased in Monkey U (${⟨\Delta ⟩}_L=-1.46$, $P=0.005$) but was unaffected in Monkey H (${⟨\Delta ⟩}_L=0.641$, $P=0.086$). This agrees with literature showing heterogeneous measurements of $\mathit{\text{MRBD}}$/$\mathit{\text{PMBR}}$ changes in cohorts with stroke. ¹³ , ¹⁵ , ¹⁶

However, these perturbations may be driven by lesion impacts that are temporally dynamic/static or focused on a wide/narrow range of frequencies. To make this distinction, dimensionality reduction techniques can reduce high‐dimensional data into constitutive factors. ⁹⁹ For our longitudinal time‐frequency tensor, the nonnegative CPD ⁶⁷ , ⁶⁸ , ⁶⁹ was used to approximate the tensor as a sum of $R$ rank 1 component tensors (Figure 4A). The CPD has been used in both electroencephalography studies ⁶² , ¹⁰⁰ , ¹⁰¹ and invasive population recordings. ¹⁰² , ¹⁰³ Simulation work has also shown it to be a suitable model for LFP recordings, ¹⁰⁴ but use has been limited, especially for longitudinal data sets. ¹⁰⁵ , ¹⁰⁶ Importantly, the CPD has strong uniqueness properties, contrasting approaches like principal component analysis which impose constraints on uncovered factors such as orthogonality. ¹⁰² , ¹⁰⁷ If this unique solution can be discovered, then the decomposition factors can be directly interpreted.

Model selection metrics, such as high model similarity across initializations (Detailed Methods, Figure 4B, Figure S9A) suggested ranks of $R=4$ for Monkey U and $R=3$ for Monkey H. The estimated time‐frequency factors (${\tau }_r^f$ and ${\tau }_r^t$) are shown in Figure 4D alongside the lesion sensitivity of date factors ${\tau }_r^d$ (Figure 4C, see ${\tau }_r^d$ trends in Figure S9A). In both monkeys, ${\tau }_1^f$ and ${\tau }_2^f$ had broad frequency content with ${\tau }_1^f$ showing stronger relative frequency weight on the $\gamma$ range. Both temporal factors (${\tau }_1^t$ and ${\tau }_2^t$) had broad, unimodal weights. In addition, ${\tau }_1^d$ was reduced by lesions (Monkey U: ${⟨\Delta ⟩}_L=-2.71$, $P<1\times {10}^{-3}$; Monkey H: ${⟨\Delta ⟩}_L=-1.47$, $P<1\times {10}^{-3}$) whereas ${\tau }_2^d$ was preserved in Monkey H (${⟨\Delta ⟩}_L=-0.15$, $P=0.668$) and increased in Monkey U (${⟨\Delta ⟩}_L=2.62$, $P<1\times {10}^{-3}$) (Figure 4C). These factors recapitulated results from the static spectrum analysis, where ${\tau }_1$ captured a broad power reduction (especially in $\gamma$ frequencies), and ${\tau }_2$ reflected the relative preservation of activity in $\alpha$ and $\beta$ bands from increased $\sum \mathit{SMR}$. ${\tau }_2^d$ also had a moderate correlation with $T_{\mathit{rxn}}$ (Monkey U: $\rho =0.42$, $P<1\times {10}^{-3}$, $N=100$; Monkey H: $\rho =0.37$, $P=0.008$, $N=65$) (Tables S3 and S4) just like $\alpha$/$\beta$ power. Meanwhile, ${\tau }_3$ captured movement‐related modulations of SMRs featuring a bimodal ${\tau }_3^f$ alongside a bimodal ${\tau }_3^t$ with a similar temporal trajectory as empirically computed for ${\beta }_{\mathit{tf}}$ in Figure S8A. These movement‐related dynamics were thus demixed from the more static factors (${\tau }_1$ and ${\tau }_2$) (Figure 4D). In Monkey U, this factor was also paired with ${\tau }_4$ which had a sharp temporal activation before movement onset and concentrated frequency content in the $\alpha$ and $\beta$ range. These factors reiterated the personalized signature of lesions in ${\beta }_{\mathit{tf}}$ activity. For Monkey U, ${\tau }_4^d$ was elevated (${⟨\Delta ⟩}_L=2.01$, $p<1\times {10}^{-3}$) and ${\tau }_3^d$ was preserved (${⟨\Delta ⟩}_L=0.29$, $P=0.522$), compatible with elevated ${\beta }_{\mathit{ref}}$ increasing the $\mathit{\text{MRBD}}$ dynamic range. In Monkey H, ${\tau }_3^d$ was reduced (${⟨\Delta ⟩}_L=-1.49$, $P<1\times {10}^{-3}$), compatible with a generic shrinking of $\mathit{\text{MRBD}}$ dynamic range (Figure 4D). Finally, a linear Gaussian state space model model was also fit to the ${\tau }_r^d$; structured lesion inputs improved the model (left of Figure 4F, Table S7) and featured a 2 d post‐lesion reduction to ${\tau }_1^d$ in Monkey U alongside a 1 d reduction in Monkey H (right of Figure 4F) while confirming the lesion impact on other factors (full statistics in Table S10). Overall, tensor decomposition demixed the lesion effects on individual wavelet coefficients (Figure 4E), unifying static spectrum impact with the personalized effect on $\mathit{\text{MRBD}}$/$\mathit{\text{PMBR}}$ metrics.

DISCUSSION

This study measured the previously unexplored effects of covert neuron loss in LFP data as a foundation for clarifying the causal relationships between functional motor impairment and spectrum shifts after stroke. Covert neuron loss—which preserved success rates and minimally impacted reaching behavior—was repeated within 2 nonhuman primates. Certain spectral signatures of symptomatic stroke were recapitulated, while still more effects were suggested, despite the preservation of behavioral ability. For instance, just as in symptomatic stroke, a pronounced reduction in $\gamma$ power was observed alongside other bandpower perturbations. ⁴ , ¹⁹ , ²⁰ , ²¹ , ²² In alignment with modern analyses of the poststroke spectrum, ²² , ²³ , ⁵⁶ , ⁵⁷ this effect was driven by aperiodic shifts. ⁵⁵ Spectral parametrization also revealed that the power of $\alpha$/$\beta$ SMRs ($\sum \mathit{SMR}$) increased after lesions. Additional analyses determined that these spectral perturbations were accentuated during movement‐related epochs, spatially diffused across the channels of the Utah array, and did not show an ordering of effect size with repeated lesions.

These findings contrast a recent study that observed a reduced low $\gamma$ rhythm at 7 days post ischemia in mice, ²² although a direct comparison is challenging as recordings were made under general anesthesia. A similar study analyzed the postinjury movement‐related spectrum, ²³ but found that peak power in the 15 to 16 Hz range was unperturbed. This discrepancy may be driven by imperfect identifiability of spectral parametrization, ¹⁰⁸ differences in rodent and primate neurophysiology, or may reflect a difference in covert and symptomatic spectral responses that could have functional significance.

This latter lens is what relates these results to clinical interest in covert stroke ³⁵ , ³⁸ as well as to theoretical work modeling the recovery boundary, a threshold of neuron loss beyond which a cortical network cannot rapidly compensate and maintain its function. ³⁴ In past stroke research, measurements have been made almost exclusively beyond this boundary, where spectrum shifts coincide with behavioral breakdown. This has produced correlations between features such as the $a{p}_{\mathit{exp}}$ ²³ , ⁵⁶ , ⁵⁷ and the $\delta$‐$\alpha$ ratio ⁵ , ⁷ with behavioral recovery. Here, we show that the spectrum is perhaps more sensitive to neuron loss than previously understood, and that spectrum perturbations can be induced by covert injury independent of substantial behavioral deficit. In fact, the only behavioral consequence of the lesions was a 1‐day increase to $T_{\mathit{rxn}}$ in Monkey U ranging from $\sim$14 to 17 ms across lesion sensitivity and state space modeling statistics (see Tables S2 and S8). This coheres with previous reports that covert neurological symptoms can act as indicators for covert stroke, ¹⁰⁹ although these measurements show that spectral features, which had pronounced, multiday signatures of covert neuron loss, may be more effective. This work thus adds more causal context to previously observed correlations, ³ , ²³ and although these results are exploratory and do not definitively defend a causal structure, they motivate further work leveraging controlled neuron loss across various scales. As a reference, reaching deficits have been recorded across a 5‐week timescale after complete aspiration of the arm motor cortex, ¹¹⁰ suggesting some intermediate injury severity ³⁴ at which acute, next‐day symptoms should emerge. Pursuing larger lesions with increased current or duration is an important next step in order to induce more substantial behavioral breakdown, which might be articulated by the disappearance, emergence, or intensification of certain LFP signatures. For instance, recent work has proposed that restoring disrupted movement‐related $\delta$ oscillations after stroke may be a useful therapeutic target, ¹⁷ , ¹⁸ , ¹¹¹ although such a disruption was not identified in this data set. In addition, the observed increase of $\sum \mathit{SMR}$ may signify covert compensation and become undetectable at the clinical boundary, as suggested by recent work. ²³

One possible interpretation for aspects of the lesion response is an increase in local cortical inhibition, shifting excitation‐inhibition (E:I) balance. Slowing and magnification of $\beta$ rhythms have been measured upon treatment with diazepam, a GABA‐ergic agonist that increases the amplitude of inhibitory postsynaptic potentials. ¹¹² , ¹¹³ , ¹¹⁴ Moreover, $a{p}_{\mathit{exp}}$ has been shown to steepen with increased inhibitory conductance in simulation, increased excitation‐inhibition synaptic density balance, and upon delivery of anesthesia in monkeys. ¹¹⁵ All of these inhibitory signatures were represented in Monkey U's response, while elements were also present (such as SMR magnification) in Monkey H. Importantly, this interpretation bridges the current study with observations of increased local inhibition after stroke, ²² , ¹¹⁶ , ¹¹⁷ , ¹¹⁸ , ¹¹⁹ , ¹²⁰ although most prior work has emphasized how elevated tonic inhibition—related to extrasynaptic GABA receptors and the concentration of ambient extracellular GABA—impedes behavioral recovery, ²² , ¹¹⁶ , ¹¹⁷ , ¹¹⁸ , ¹¹⁹ whereas the aforementioned LFP features are more closely tied to synaptic, phasic inhibition. ¹²⁰ , ¹²¹ This suggests that mechanisms such as insertion of synaptic GABA receptors may be activated following covert neuron loss to mitigate excitotoxic neuron loss, ¹²⁰ , ¹²² but this cannot be confirmed without additional data. ¹¹⁶ , ¹²⁰ , ¹²³ The observed responses may also reflect local neuroinflammation as there is emerging evidence that both microglia ¹²⁴ and astrocyte ¹²⁵ recruitment can alter neural network oscillations. Untangling the interplay between phasic and tonic inhibition, as well as neuroinflammation, in postinjury cortical networks may be crucial for advancing stroke treatments.

Complementing the analysis of static, perimovement spectra, the exploration of movement‐related time‐frequency dynamics revealed diverging effects on baseline, premovement $\beta$ activity (${\beta }_{\mathit{ref}}$) in the 2 animals, leading to increased dynamic range and exaggerated $\mathit{\text{MRBD}}$ in Monkey U and the opposite effect in Monkey H. This was paired with a novel application of the CPD—an interpretable tensor decomposition—which recapitulated aspects of the static spectral signatures described previously while affirming this divergent effect on movement‐related $\beta$ dynamics. Interestingly, this heterogeneity is also consistent with the sparse literature examining movement‐related $\beta$ modulations after stroke. For example, a recent study showed that patients starting with strong $\alpha$ desynchronization further increased this desynchronization during rehabilitation (like Monkey U), and weak desynchronization was further decreased (as in Monkey H). ¹⁶ Other studies have failed to identify a cohort‐level effect on $\mathit{\text{MRBD}}$ ¹⁵ or have reported an overall reduction. ¹³ These results signify that part of the response to neuron loss may be personalized, where consequences are dictated by bio‐behavioral statistics. For instance, Monkey H was 14 and near end of life whereas Monkey U was 11 and in good health at the time of recording. Age ¹²⁶ , ¹²⁷ and general health ¹²⁶ , ¹²⁸ have been associated with worsened functional and biological consequences of ischemia (although other measurements challenge these correlations ¹²⁹ ); moreover, age is known to erode endogenous inhibitory tone ¹³⁰ while shifting the neural spectrum's aperiodic‐periodic constitution by flattening $a{p}_{\mathit{exp}}$ and reducing $\sum \mathit{SMR},$ ⁵⁵ , ¹³¹ as can be seen when comparing Monkeys U/H in Figure 2A and 2B. Additional data will be critical for dissecting the relationships between age/health, spectral statistics, and the neural‐behavioral response to neuron loss.

Two methodological considerations were important to this work. First, spectral parametrization, ⁵⁵ state space modeling, ⁹¹ and tensor decomposition ⁶⁹ all added interpretive depth to the measured impact of neuron loss, complementing the information extracted from classical LFP features. Spectral parametrization improved interpretability of estimated bandpower effects by decoupling an enhancement in periodic rhythms from a shift in aperiodic structure. State space modeling leveraged the time‐series structure of the data to estimate the duration of lesion inputs and to ensure that these effects did not arise from underlying temporal dynamics. Meanwhile, tensor decomposition is an emerging framework for visualizing and analyzing neuroscience tensors, ¹⁰² , ¹⁰³ , ¹⁰⁴ and was used to find interpretable time‐frequency dynamics affected by lesions. Although spectral parametrization approaches are becoming clinically relevant, ⁵⁷ the state space modeling and tensor decomposition approaches were tailored to our data set in order to answer specific scientific questions. We advocate for their use in data sets with similar properties (longitudinal designs with known intervention points), but it is unlikely that these techniques can be immediately implemented in the clinic.

A second methodological consideration was the electrolytic lesion platform. ⁵³ The platform permits precise, mm‐level control of lesion extent by tuning electrical current and duration; this facilitated calibration to an approximate lesion volume of $\sim$1 mm^{3. 53} Moreover, this lesioning platform is neuroelectrophysiology compatible; it induced neuron loss from an already implanted array, permitting immediate pre‐/postlesion recordings during behavior. Such recordings are more difficult in contemporary approaches to neuronal termination such as endovascular occlusion ¹³² or photothrombosis, ¹³³ both of which require a surgery that can disrupt an already implanted neuroelectrophysiology device. In a similar vein, this platform permits repeated lesions (that do not cause array degradation ⁵⁴ ) without additional surgeries. Collectively, these features permitted recording of longitudinal, baseline‐referenced responses to covert neuron loss. In addition, the platform enabled a within‐subject experimental design using permutation testing, factoring out interindividual heterogeneity and enabling sensitive detection of neuron loss impact.

A first limitation is that, although interanimal variability in age or health will become a strength of our paradigm with more subjects, the study's broader conclusions are limited without going beyond the 2‐monkey convention of primate systems neuroscience. However, we used strict behavioral filtering (Detailed Methods) to include well‐stereotyped behavioral conditions in each animal (eg, unaffected by Monkey H's visual deficit). Moreover, our statistical approach used each monkey as their own empirical control, ensuring that lesion impacts reflected genuine departures from expected day‐to‐day, animal‐specific spectral/behavioral fluctuations. A second limitation is that 2‐dimensional end point position in a simple reaching behavior may not be adequate to reveal subtle lesion effects. Although this behavior is standard in motor systems neuroscience, and was analyzed from multiple analytic perspectives, coupling this lesion model with higher‐dimensional reach/grasp representations ¹³⁴ or ethological models ¹³⁵ of naturalistic behavior ¹³⁶ , ¹³⁷ , ¹³⁸ may unify brain‐behavior responses to neuron loss. A third limitation is that although these results point to the scientific potential of the lesions for studying covert and symptomatic stroke, the analogy to ischemic injury is incomplete. For one, $\sim$90% of covert strokes are subcortical. ³⁵ However, the lesion platform is compatible with linear microelectrode arrays as shown in our previous work. ⁵³ These arrays permit subcortical lesions, contrasting the capacity of optical approaches like photothrombosis or the consequences of distal middle cerebral artery occlusion. Subcortical lesions are an attractive direction for future work, especially due to our expanding perspective on the role subcortical circuits play in expressing innate and learned motor skills, including the arm reaches studied in our paradigm. ¹³⁹ Second, epidemiological studies of covert stroke have found that advanced age ³⁸ and hypertension ³⁵ , ³⁷ , ³⁸ , ⁴¹ , ¹⁴⁰ are the largest risk factors, whereas the monkeys lesioned here were middle aged (11–14 years) without known cardiovascular dysfunction. This mismatch encourages the replication of our results in older, hypertensive ¹⁴¹ macaques. Third, electrolytic lesions are not vascular injuries, despite inducing a similar consequence (neuron loss). Our model does not capture the vascular origin and molecular/cellular pathology of covert stroke. However, the motivating principle of our model views neuron loss as the core functional consequence of stroke, wherein functional recovery takes place alongside reorganization ²⁶ , ²⁷ , ²⁸ , ³¹ , ¹⁴² or potentiation ²⁹ of the remaining neuronal population. Our model allows us to track changes in the LFP in relation to neuron loss, a relation that we believe should exist regardless of pathophysiological mechanism. This is supported by recent work showing that ministrokes of cerebral cortex decoupled cerebral blood flow and LFP, and found that the LFP more robustly indicated the functional consequences of neuron loss beyond the subacute phase. ¹⁴³ As such, the LFP describes functional outcomes more than acute vascular dysfunction. Our results, and their integration with the spectral impact of symptomatic stroke, further support this. Overall, the decoupling of neuron loss from vascular pathology is an intentional aspect of this model, which complements other animal models of stroke that use a vascular mechanism. ¹⁴³ , ¹⁴⁴ , ¹⁴⁵ A future opportunity for animal model revision is the unification of the vascular‐origin infarcts with chronic longitudinal neuroelectrophysiology.

A final limitation is that, although this work focused on LFP, it is at the resolution of neuronal population spiking activity where computations related to motor planning and execution appear to occur. ¹⁴⁶ Already, population statistics are shedding light on poststroke reorganization ¹¹¹ , ¹⁴⁷ ; fortunately, these data are also recorded from the implanted array, and it will be imperative to explore spiking‐level lesion signatures in future work.

CONCLUSIONS

This study presents a novel animal model for covert stroke, inducing covert neuron loss via electrolytic lesions from an implanted microelectrode array in the motor cortex. We conclude that the motor cortical LFP is sensitive to covert degrees of neuron loss and may be a useful signal in both scientific and clinical capacities for modeling stroke recovery.

APPENDIX

The members of the Brain Interfacing Laboratory additionally include Michelle S Wechsler, Mackenzie Risch, Alexandra Paraskevopoulou, Alissa S Ling, Elizabeth J Jun, Michael P Silvernagel, Lisa Yamada, Yuxin Wu, Alice Tor, Muhammad U Abdulla, and Sydney Hunt.

Sources of Funding

Kenji Marshall was supported by a Fulbright Canada Student Award. Stephen E. Clarke was supported by a Stanford School of Medicine's Dean's Posdoctoral Fellowship. This work was supported by a Stanford Human‐Centered AI Seed Research Grant to Stephen E. Clarke and Paul Nuyujukian. This work was additionally supported by the following to Paul Nuyujukian: the National Institutes of Health (R01NS123517, R01NS130789, U19NS118284) and the Stanford Wu Tsai Neurosciences Institute.

Disclosures

The authors have nothing to disclose.

Supporting information

Detailed Methods

Tables S1–S10

Figures S1–S9

References 148–167

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