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Stimulus-Evoked Network Dynamics in Human Cortical Organoids: From a Graph-Computational Framework to Repeated-Stimulation Depression
Esmaeil S. Nadimi, Vinay C. Gogineni, Jan-Matthias Braun, Martin Røssel Larsen, Victoria Blanes-Vidal, Helle Bogetofte Barnkob
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Summary
This study investigates stimulus-evoked network dynamics in human cortical organoids using a graph-computational framework and high-density microelectrode arrays (HD-MEA). The research challenges the assumption of structured information propagation, finding instead that evoked responses are near-synchronous network bursts with no measurable outward propagation. A key finding is that repeated daily stimulation leads to a progressive depression and spatial contraction of the evoked response, distinct from developmental maturation, as demonstrated by a stimulation-naive control group.
Entities (10)
Relation Signals (6)
Human Cortical Organoids → exhibits → Near-synchronous Network Burst
confidence 95% · the evoked response proved to be a fast, near-synchronous network burst with no measurable outward propagation
Repeated Stimulation → causes → Repeated-Stimulation Depression
confidence 94% · repeated daily stimulation progressively depressed and spatially contracted the evoked response
Organoid 612 → servesas → Stimulation-Naive Control
confidence 92% · We break that confound with a developmentally-matched, stimulation-naive control... Organoid 612... stimulated only at day 7
Graph-Computational Framework → usedtoquantify → Stimulus-Evoked Propagation
confidence 90% · We developed a graph-computational framework to quantify stimulus-evoked propagation
HD-MEA → usedfor → Longitudinal Recordings
confidence 88% · We carried this program out in full on longitudinal HD-MEA recordings from three organoids
Effective Integration Depth (Deff) → boundedby → Maximal Propagation Distance (dmax)
confidence 85% · biological message-passing principle bounding integration depth by observable propagation depth (Deff >= dmax)
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Abstract
Abstract:Human cortical organoids provide an experimentally accessible model of early neural circuit formation, yet whether their activity reflects structured information processing rather than spontaneous synchronization is unclear. We developed a graph-computational framework to quantify stimulus-evoked propagation. This includes stimulus-conditioned functional graphs, a graph-constrained dynamical (graph-neural-network) model used as a system-identification tool, a biological message-passing principle bounding integration depth by observable propagation depth, and a suite of graph-level metrics. We carried this program out in full on longitudinal HD-MEA recordings from three organoids. Once the true acquisition sampling rate and stimulus timing were recovered, the evoked response proved to be a fast, near-synchronous network burst with no measurable outward propagation (peak-latency vs. distance slope = 0). The propagation/integration-depth metrics (Deff ,reachability index, dmax) therefore do not apply, and per-day connectivity graphs were not reliably estimable at the available trial count, a negative result with methodological consequences for applying such metrics to organoid data. Reframing around synchrony, response-population size and shared variability revealed a control-validated phenomenon, i.e., repeated daily stimulation progressively depressed and spatially contracted the evoked response. That repeated stimulation reshapes organoid networks is established, but longitudinal designs in which every preparation is stimulated cannot separate this from developmental maturation. We break that confound with a developmentally-matched, stimulation-naive control, where at day 7, an organoid receiving its first-ever stimulation engaged 93% of the array, whereas organoids with five prior sessions engaged 10%.
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- Source: https://arxiv.org/abs/2607.28068v1
- Canonical: https://arxiv.org/abs/2607.28068v1
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Stimulus-Evoked Network Dynamics in Human Cortical Organoids: From a Graph-Computational Framework to Repeated-Stimulation Depression Esmaeil S. Nadimi [Applied AI and Data Science Unit, Maersk Mc-Kinney Moller Institute, Faculty of Engineering, University of Southern Denmark] Vinay C. Gogineni [Applied AI and Data Science Unit, Maersk Mc-Kinney Moller Institute, Faculty of Engineering, University of Southern Denmark] Jan-Matthias Braun [Applied AI and Data Science Unit, Maersk Mc-Kinney Moller Institute, Faculty of Engineering, University of Southern Denmark] Martin Røssel Larsen [Biomedical Mass Spectrometry and System Biology Unit, Department of Biochemistry and Molecular Biology, Faculty of Science, University of Southern Denmark] Victoria Blanes-Vidal [Applied AI and Data Science Unit, Maersk Mc-Kinney Moller Institute, Faculty of Engineering, University of Southern Denmark] Helle Bogetofte Barnkob [Biomedical Mass Spectrometry and System Biology Unit, Department of Biochemistry and Molecular Biology, Faculty of Science, University of Southern Denmark] Abstract Human cortical organoids provide an experimentally accessible model of early neural circuit formation, yet whether their activity reflects structured information processing rather than spontaneous synchronization is unclear. We developed a graph-computational framework to quantify stimulus-evoked propagation. This includes stimulus-conditioned functional graphs, a graph-constrained dynamical (graph-neural-network) model used as a system-identification tool, a biological message-passing principle bounding integration depth by observable propagation depth (Deff≥dmaxD_eff≥ d_ ), and a suite of graph-level metrics. We carried this program out in full on longitudinal HD-MEA recordings from three organoids. Once the true acquisition sampling rate and stimulus timing were recovered, the evoked response proved to be a fast, near-synchronous network burst with no measurable outward propagation (peak-latency vs. distance slope ≈0≈ 0). The propagation/integration-depth metrics (DeffD_eff, reachability index, dmaxd_ ) therefore do not apply, and per-day connectivity graphs were not reliably estimable at the available trial count, a negative result with methodological consequences for applying such metrics to organoid data. Reframing around synchrony, response-population size and shared variability revealed a control-validated phenomenon, i.e., repeated daily stimulation progressively depressed and spatially contracted the evoked response. That repeated stimulation reshapes organoid networks is established, but longitudinal designs in which every preparation is stimulated cannot separate this from developmental maturation. We break that confound with a developmentally-matched, stimulation-naïve control, where at day 7, an organoid receiving its first-ever stimulation engaged ∼93% 93\% of the array, whereas organoids with five prior sessions engaged ∼10% 10\%. We further dissociate a preserved first-trial response capacity from a degrading within-session endurance, and identify independent within-session desynchronization. 1 Introduction 1.1 Biological neural networks as perturbation-accessible computational systems The human cerebral cortex performs adaptive computation through distributed, recurrent neural circuits operating under strict energetic and developmental constraints. Biological neural networks self-organize through development, integrate information via local synaptic interactions, and adapt through activity-dependent plasticity [20]. Human cortical organoids provide an experimentally accessible model of developing neural tissue that recapitulates key features of early corticogenesis, including excitatory–inhibitory diversity, radial organization, and spontaneous network activity [10, 21]. Whether organoids exhibit structured distributed computation beyond spontaneous synchrony remains unclear [22, 23, 11, 24, 12, 25]. High-density microelectrode arrays (HD-MEAs) enable simultaneous focal stimulation and large-scale recording, providing a perturbation-based window onto how activity spreads through recurrent circuitry following localized input. 1.2 A graph-computational framework for evoked propagation We represent the recorded network as a graph G=(V,E,)G=(V,E, A), where nodes V are recorded units (electrode-level multi-unit channels), edges E are effective interactions, and A is the weighted adjacency matrix [1]. Under stimulation, activity propagates along edges through successive local integrations, so stimulus-evoked dynamics can be read as graph-constrained signal transmission [1]. Graph topology then constrains computation along principled axes, such as integration depth, reachability/controllability, encoding diversity, dynamical dimensionality, and plasticity-induced reconfiguration [4]. We formalize each of these in Section 2.5. 1.2.1 Biological message-passing theorem Inspired by Shannon’s channel capacity, defined by the maximum rate of reliable transmission over a channel and obtained by maximizing the mutual information I(⋅;⋅)I(·;·) between input and output [2], we propose: Theorem 1 (Biological message passing). The effective integration depth required to predict stimulus-evoked responses in a biological neural network is bounded below by the minimum number of graph hops separating the stimulation site from the furthest reliably activated node. Formally, if stimulus information S is preserved at node v, i.e. the channel capacity satisfies I(S;Xv)=maxp(s)[H(Xv)−H(Xv∣S)]> 0,I(S;X_v)\;=\; _p(s)\; [\,H(X_v)-H(X_v S)\, ]\;>\;0, (1) and v lies k=distG(vs,v)k=dist_G(v_s,v) hops from the stimulation node vsv_s, then the network supports at least k-hop information propagation, and consequently Deff≥dmax=maxv∈VactivedistG(vs,v),D_eff\;≥\;d_ \;=\; _v∈ V_activedist_G(v_s,v), (2) where DeffD_eff is the minimal message-passing depth reproducing the evoked dynamics (Section 2.4) and VactiveV_active represents the set of reliably activated nodes. Equation (2) is the testable core of the framework, as it predicts that the model depth needed to reproduce responses grows with the spatial reach of evoked activity. Section 3.1 reports the direct empirical test of its premise. 1.3 Longitudinal stimulation and the direction of plasticity A complementary aim of this study was longitudinal, i.e., repeated daily stimulation could potentiate the evoked response, depress it (habituation / synaptic depression), or track developmental maturation [19, 27, 20]. Distinguishing these requires both a longitudinal design and a control that separates stimulation history from age. We therefore stimulated two organoids on days 1,2,3,4,71,2,3,4,7 and included a third recorded spontaneously at day 1 and stimulated for the first time only at day 7, resulting in a single-stimulation, developmentally-matched control. This allowed us to study synchronous-burst regime (participation-ratio dimensionality; the spirit of the reconfiguration index) and augment them with measures appropriate to the observed response, i.e., magnitude, synchrony, responsive-population size and spatial extent, and population coherence (Section 2.6). 2 Methods 2.1 Preparations, stimulation protocol, and recordings Evoked activity was recorded from three cortical organoids (HD-MEA identifiers 552,613,612552,613,612) on a 3Brain HD-MEA with 40964096 electrodes in a 64×6464× 64 grid [5, 6, 28]; electrode identity follows id=64r+cid=64\,r+c for row r and column c (zero-indexed). Stimulation was delivered through the array as a vertical line of electrodes (one column over a contiguous row range). Each session comprised Nstim=10N_stim=10 biphasic stimuli (nominal 100μ100~ , 400μ400~ /phase) at a fixed inter-stimulus interval Δ=30 =30 s. Stimulator and recording shared the same hardware clock. Table 1: Stimulation geometry per organoid. Organoid Stim column Stim rows # electrodes Electrode IDs 552 29 10–38 29 669–2461 613 13 17–42 26 1101–2701 612 13 17–42 26 1101–2701 Longitudinal design. Organoids 552552 and 613613 were stimulated on days 1,2,3,4,71,2,3,4,7 (repeated). Organoid 612612 was recorded spontaneously at day 1 and stimulated only at day 7 (single-stimulation control), sharing geometry with 613613. 2.2 Sampling-rate correction and data-driven stimulus-time recovery Recordings were stored in BrainWave 6 .bxr format. The true acquisition rate fs=19,753.775f_s=19,753.775 Hz was read per file from the metadata field TimeConverter.FrameRate; an incorrect default rate rescales spike times by a factor fs/fsdefaultf_s/f_s^default and progressively misaligns them from stimulus onsets (by up to tens of seconds over a six-minute recording). Recordings were ∼360 360 s; two day-4 recordings ended earlier (300300–306306 s). The files contained no explicit stimulus markers, and the nominal stimulation start varied between sessions. We therefore recovered stimulus onsets from the data. Let ρ(τ)ρ(τ) be the population firing-rate trace (bin width 5050 ms). Candidate bursts are the supra-threshold events of ρ, with a robust threshold θ=median(ρ)+ 5⋅1.4826⋅MAD(ρ).θ\;=\;median(ρ)\;+\;5· 1.4826·MAD(ρ). (3) where MAD stands for Median Absolute Deviation. Given the known protocol (ten events spaced Δ ), we fit a periodic grid t0+(j−1)Δj=110\t_0+(j-1) \_j=1^10 by selecting the start t0t_0 that maximizes the total matched strength (peak rate) over grid positions, assigning to each position the strongest candidate within a tolerance window and rejecting weaker spontaneous bursts and edge artifacts: t0⋆=argmaxt0∑j=110maxb:|τb−(t0+(j−1)Δ)|≤δρ(τb),δ=0.25Δ.t_0 \;=\; _t_0\; _j=1^10\; _\,b\,:\,| _b-(t_0+(j-1) )|≤δ\;ρ( _b), δ=0.25\, . (4) Each evoked onset tjt_j is the local rise of its matched burst (walk-back from the rate peak to the threshold crossing). This procedure was validated against trial-by-trial inspection. 2.3 Stimulus-conditioned functional graph construction For each session we constructed a directed functional dynamic graph as a sequence of snapshots Gt=(Vt,Et,t,t),G_t=(V_t,E_t, X_t, A_t), (5) with node-feature matrices t∈ℝN×F X_t ^N× F (binned spike counts, F=1F=1 in the primary analysis; bin width 1010 ms) and adjacency t∈ℝN×N A_t ^N× N. An edge j→ij→ i was included when activity at j reliably preceded activation at i within the post-stimulus window, exceeding a permutation threshold (p<0.05p<0.05, False-Discovery-Rate (FDR)-corrected), with weight proportional to the normalized evoked cross-correlation [16, 21]: Aij∝maxΔt>0(xj⋆xi)(Δt)(xj⋆xj)(0)(xi⋆xi)(0),A_ij\; \; _ t>0\; (x_j x_i )( t) (x_j x_j)(0)\,(x_i x_i)(0), (6) where ⋆ denotes cross-correlation over the evoked window and Δt>0 t>0 enforces j-before-i precedence. The adjacency was symmetrically normalized for message passing [3], ^=−1/2(+)−1/2,Dii=∑j(+)ij. A\;=\; D^-1/2\,( A+ I)\, D^-1/2, D_i= _j( A+ I)_ij. (7) External stimulation is encoded as t∈ℝN S_t ^N with St,i≠0S_t,i≠ 0 only for stimulation electrodes at stimulation bins. These graphs were constructed for every organoid and day; where their cross-day analysis is reported in Section 3.6. 2.4 Graph-constrained dynamical (GNN) model and effective depth Stimulus-evoked dynamics were modeled as a discrete-time graph-structured system [4], t+1=Fθ(t,t;^)=σ(^tneigh+tstim), X_t+1\;=\;F_θ( X_t, S_t; A)\;=\;σ\! ( A\, X_t\, W_neigh\;+\; S_t\, W_stim ), (8) with learnable neigh∈ℝF×F W_neigh ^F× F, stim∈ℝ1×F W_stim ^1× F, and σ=ReLUσ=ReLU (Xavier initialization; Adam, learning rate 1.0e−31.0e-3, weight decay 1.0e−41.0e-4, with cosine-annealing schedule). For a model with k stacked aggregation steps per time step, Fθ(k)F_θ^(k) applies k successive neighborhood aggregations, and the trajectory error over T post-stimulus bins is ℒk=1T∑t=1T‖tpred−tobs‖22.L_k\;=\; 1T _t=1^T X_t^pred- X_t^obs _2^2. (9) The effective message-passing depth is Deff=argminkℒk,D_eff\;=\; _k\;L_k, (10) cross-validated across trials and stimulation sites. Data were split 70/15/15%70/15/15\% (train/validation/test); empirical, degree-preserving randomized, fully-connected, and non-graph recurrent baselines were compared by paired permutation tests. 2.5 Graph-computational metric suite (as evaluated) We define the full metric suite, while Section 3.8 presents the empirical status of each metric, given the findings. Effective integration capacity (EIC). EIC=Deff.EIC\;=\;D_eff. (11) EIC=1EIC=1 indicates localized activation proximal to the stimulation site; while EIC>1EIC>1 indicates multi-hop recruitment. Reachability index (RI). With R(vs)=v∈V:distG(vs,v)<∞R(v_s)=\v∈ V:dist_G(v_s,v)<∞\, RI=|R(vs)|N∈[0,1],RI\;=\; |R(v_s)|N\;∈\;[0,1], (12) the fraction of nodes reachable from the stimulation site. Maximal propagation distance and BMP test. dmax=maxv∈VactivedistG(vs,v),test: Deff≥dmax(Eq. (2)).d_ = _v∈ V_activedist_G(v_s,v), : D_eff≥ d_ \;\;(Eq.~ eq:bmp). (13) Stimulus separability index (SSI). For stimulus s with population response vectors s,k∈ℝN x_s,k ^N over trials k, mean ¯s x_s, d(s1,s2)=‖¯s1−¯s2‖2,σs2=1Ks∑k=1Ks‖s,k−¯s‖22,SSI=[d(s1,s2)][σs].d(s_1,s_2)= x_s_1- x_s_2 _2, _s^2= 1K_s _k=1^K_s x_s,k- x_s _2^2, = E[\,d(s_1,s_2)\,]E[\, _s\,]. (14) Dynamical dimensionality (participation ratio, PR). With response covariance =1T∑t(t−¯)(t−¯)⊤,PR=(∑iλi)2∑iλi2, C= 1T _t( X_t- X)( X_t- X) , = ( _i _i )^2 _i _i^2, (15) where λi\ _i\ are the eigenvalues of C. PR→1PR→ 1 for a single global mode (synchronized bursting), while larger PR indicates variance spread across independent modes [7, 8]. Computational reconfiguration index (CRI). For epochs e1,e2e_1,e_2 with adjacency e A_e, integration Deff(e)D_eff^(e), and dimensionality PR(e)PR^(e), Δ=‖e2−e1‖F,CRI=αΔ+β|Deff(e2)−Deff(e1)|+γ|PR(e2)−PR(e1)|, A= A_e_2- A_e_1 _F, =α\, A+β\, |D_eff^(e_2)-D_eff^(e_1) |+γ\, |PR^(e_2)-PR^(e_1) |, (16) with nonnegative weights α,β,γα,β,γ. 2.6 Reframed evoked-response read-outs Let the response window be Wr=[0,200]W_r=[0,200] ms and baseline Wb=[−250,−50]W_b=[-250,-50] ms (equal widths, |Wr|=|Wb||W_r|=|W_b|). For trial k and electrode i, let RikR_ik and BikB_ik be the evoked and baseline spike counts. We define three independent per-trial read-outs [9]. Magnitude. Mk=∑i=1NRik−|Wr||Wb|∑i=1NBik.M_k\;=\; _i=1^NR_ik\;-\; |W_r||W_b| _i=1^NB_ik. (17) Synchrony. Let τm\ _m\ be the evoked spike times (relative to onset) in WrW_r on trial k. With temporal dispersion ςk=SD(τm) _k=SD(\ _m\), k=1ςk,S_k\;=\; 1 _k, (18) defined only when the window contains at least 5050 spikes (else undefined). In this context, smaller dispersion meant higher synchrony. Dimensionality (per-trial participation ratio). With response vector k=(R1k,…,RNk) r_k=(R_1k,…,R_Nk), k=(∑iRik)2∑iRik2,D_k\;=\; ( _iR_ik )^2 _iR_ik^2, (19) the effective number of contributing electrodes (a per-trial PR, Eq. (15)). Responsive electrodes (adaptive). Electrode i is responsive on a given day if its evoked count reliably exceeds baseline across K trials. With dik=Rik−Bikd_ik=R_ik-B_ik, mean d¯i d_i, SD sis_i, the one-sided paired statistic is ti=d¯isi/K,pi=1−K−1(ti),t_i\;=\; d_is_i/ K, p_i=1-T_K-1(t_i), (20) with K−1T_K-1 the Student-t CDF; i is responsive if the Benjamini–Hochberg FDR-adjusted pi<qp_i<q (q=0.05q=0.05) and d¯i>0 d_i>0 [17]. The responsive set is respV_resp, of size nresp=|resp|n_resp=|V_resp|. Within-session trend. For a per-trial read-out yky_k (k=1,…,Kk=1,…,K) the within-session trend is the Theil–Sen slope [18] β^=mediank<lyl−ykl−k, β=median_k<l y_l-y_k\,l-k\,, (21) with significance from Spearman’s rank correlation between yky_k and k (validly detected trials only). Negative β β for magnitude MkM_k or synchrony kS_k indicates within-session depression / desynchronization. Detrending and population coherence (PC1). To remove the shared within-session trend before assessing co-variation, each electrode’s response series is linearly detrended, i.e., with design =(1,2,…,K)⊤ u=(1,2,…,K) centered as ~=−u¯ u= u- u, the residual for electrode i is R~ik=Rik−(R¯i+s^iu~k),s^i=∑ku~k(Rik−R¯i)∑ku~k2. R_ik\;=\;R_ik- ( R_i+ s_i\, u_k ), s_i= _k u_k\,(R_ik- R_i) _k u_k^2. (22) Population coherence is the fraction of variance on the first principal component of the detrended responsive-population matrix ~∈ℝK×nresp R ^K× n_resp: PC1=λ1∑mλm,λm=eigm(1nresp~~⊤).PC1\;=\; _1 _m _m, _m=eig_m\! ( 1n_resp\, R\, R ). (23) Computing PC1 on detrended data ensures it reflects genuine shared trial-to-trial variability rather than the shared depression trend. PC1 is a stable, low-trial-count substitute for an edge-level connectivity graph. Spatial extent. For responsive positions presented by rows and columns (ri,ci)i∈resp\(r_i,c_i)\_i _resp, the spatial spread is Σ=Var(ri)+Var(ci). \;=\; \,Var(r_i)+Var(c_i)\,. (24) 2.7 Statistical and interpretive notes In this study, we deployed two repeatedly-stimulated organoids and one single-stimulation control. Findings are reported as reproducible, control-supported observations rather than population-level statistics. Across-day comparisons report both the first-trial (“fresh”) response and the session mean. Per-day pairwise connectivity (edge) graphs were constructed and evaluated, but are not a primary result because at K=10K=10 trials the pairwise correlation estimates are not reliably thresholdable (Section 3.6). Supplementary preprocessing included band-pass 300300–60006000 Hz; stimulus-artifact blanking; threshold detection at −5×-5× baseline noise SD and optional spike sorting with curation. 3 Results 3.1 The evoked response is a near-synchronous network burst, not a propagating wave Each stimulus reliably evoked a large population burst. Across all sessions, the ten stimuli produced ten regularly-spaced bursts (inter-burst interval 30.130.1 s, SD ≈0≈ 0 s), confirming reliable locking once timing was recovered (Eq. (4)). At millisecond resolution the burst peaked within tens of milliseconds of onset. Direct test of Theorem 1 indicated that grouping responses by distance from the stimulation line, the peak-latency vs. distance slope was ≈0≈ 0 ms per electrode-column, meaning that the distal and proximal electrodes responded essentially simultaneously. The evoked response was a near-synchronous, network-wide burst, not an outward-propagating wave. Hence dmaxd_ (Eq. (13)) did not index a real spreading process, and EICEIC (Eq. (11)), RIRI (Eq. (12)), and the Deff≥dmaxD_eff≥ d_ test were not applicable to these recordings. This is consistent with the dense recurrent connectivity expected in three-dimensional cultures, which promotes rapid global synchronization. We proceed with the reframed read-outs (Section 2.6). 3.2 Repeated stimulation depresses the evoked response across days Across days, the overall evoked response of the repeatedly-stimulated organoids declined markedly by day 7 (session-level response-to-baseline ratio): Table 2: Session-level evoked response strength (response/baseline ratio). Organoid D1 D2 D3 D4 D7 552 (repeated) 1123 1411 1802 1450 206 613 (repeated) 487 897 230 1128 268 612 (single-stim control) — — — — 1914 The single-stimulation control isolates stimulation history from age. At day 7 the repeatedly-stimulated organoids were strongly depressed (ratios 206206, 268268), whereas control 612612, the same age but stimulation-naïve until day 7 produced the strongest response in the dataset (19141914), ∼7 7–9×9× larger. Because 612612 was developmentally matched, the day-7 depression in 552552 and 613613 is driven by repeated-stimulation history rather than maturation. It is worth mentioning that Organoid 613613 was non-monotonic across days (low D3, high D4), unlike the cleaner rise-then-fall of 552552. The depressed D7 endpoint is consistent across both, but the intermediate trajectory is variable; and D3/D4 recordings warrant the scrutiny in Section 3.7. 3.3 Across-day depression reflects loss of within-session endurance, not capacity Separating the first-trial (M1M_1) from the session-mean response showed these behave very differently. First-trial magnitude was relatively preserved D1→D7D1→ D7 (552: ∼50,000→∼37,000 50,000→ 37,000 net spikes; 613: ∼46,000→∼42,000 46,000→ 42,000), whereas the session mean M¯=1K∑kMk M= 1K _kM_k collapsed (552: ∼32,000→∼8,500 32,000→ 8,500; 613: ∼15,000→∼10,500 15,000→ 10,500). The ratio M1/M¯M_1/ M grew from ∼1.5 1.5–3×3× early to ∼6× 6× by day 7. The network’s capacity to mount a strong initial daily response was largely preserved; however, the ability to sustain responses across the session was degraded. The control was consistent, as 612612 at day 7 had both the highest first-trial response (∼73,500 73,500) and a high session mean. 3.4 Within-session dynamics: magnitude depression and independent desynchronization Within sessions, the response typically depressed across the ten trials, most often a rapid drop after the first stimulus, and then a lower plateau (synaptic-depression-like). Significant negative within-session magnitude slopes (Eq. (21)) occurred in multiple recordings, including organoid 613613 on essentially every day and the control 612612 (steepest decline, despite no prior stimulation). Organoid 552552 showed clear within-session depression on day 1 but a noisier pattern otherwise. We further observed that synchrony depresses independently of magnitude. Treating kS_k (Eq. (18)) separately revealed a dissociation, i.e., in several recordings, the burst became progressively less synchronous across trials, not always tracking magnitude (e.g. 552552 day 7 desynchronized significantly with no magnitude trend). The stimulation-naïve control 612612 showed strong magnitude depression but no significant desynchronization, whereas the repeatedly-stimulated 613613 desynchronized, suggesting (hypothesis, given small n) that desynchronization is more associated with prior stimulation while magnitude depression is intrinsic. As the control shows clear within-session depression on its first-ever session, fast within-session depression does not require prior stimulation, and as a result, the slow across-day component is what accumulates with repeated daily stimulation, suggesting partly distinct mechanisms. 3.5 The responding network spatially contracts with repeated stimulation The size of the responsive population nrespn_resp (Eq. (20)) showed the clearest, most robust effect. Table 3: Responsive-electrode count and array fraction across days. Organoid D1 D2 D3 D4 D7 552 responsive 3852 4020 4037 4005 384 (% array) 94% 99% 99% 99% 9.5% 613 responsive 1711 2932 574 4048 486 (% array) 42% 72% 14% 100% 12% 612 control responsive — — — — 3788 (% array) — — — — 93% In both repeatedly-stimulated organoids the responding population collapsed from essentially the whole array to ∼10% 10\% by day 7 (552552: 384384; 613613: 486486), whereas the single-stimulation control responded on 93%93\% (37883788 electrodes). At matched age, a first stimulation engaged ∼3800 3800 electrodes versus ∼400 400 after five prior sessions, a ∼10 10-fold difference. The surviving day-7 responders in 552552 were also spatially contracted (Σ from ∼26 26 to ∼10 10, Eq. (24)), indicating contraction toward a smaller region rather than uniform thinning. It is worth highlighting that the coherence was preserved (retained PR/PC1 metric). The detrended population coherence PC1PC1 (Eq. (23)) stayed ∼0.4 0.4–0.60.6 across all conditions, including the small day-7 networks. Repeated stimulation predominantly removed electrodes from the responding pool rather than desynchronizing those that remain, such that the effect was on population size more than coherence. 3.6 Per-day connectivity graphs were evaluated but are not reliable at K=10K=10 We constructed the per-day functional graphs of Section 2.3 and computed their co-variation structure on the detrended responsive population, with edge significance from a trial-shuffle permutation null. At K=10K=10 trials (effectively K−1K-1 after detrending) the null distribution of |r||r| is broad, i.e., permutation thresholds approached |r|≈0.98|r|≈ 0.98, yielding near-empty thresholded graphs, and two detrending variants (linear detrend vs. drop-trial-1) disagreed substantially on derived measures (density, modularity, largest component). We therefore do not report edge-level graph statistics as primary results; and the robust network-level conclusions rest on nrespn_resp (Eq. (20)) and PC1PC1 (Eq. (23)). This is a limitation of trial count, not of the construction, as the graphs were built and evaluated for every organoid and day. 3.7 Data-quality considerations and limitations • Day-3/day-4 anomalies. Organoid 613613 showed an implausibly non-monotonic responsive trajectory (42→72→14→100→12%42→ 72→ 14→ 100→ 12\%). Day 3 had the lowest total spike count; and both day-4 recordings were truncated (88–99 usable trials). These are under separate diagnostic examination (activity level vs. threshold fragility vs. baseline elevation vs. truncation). • Mis-aligned vs. failed trials. Some apparent single-trial failures were detection mis-alignments (a small spontaneous burst selected instead of the true evoked burst), but selecting the dominant burst (Eq. (4)) recovered the true responses. • One silent stimulation electrode in 613613 (ID 14211421) recorded no spikes. • Low-trial limits. Edge-level connectivity is not reliably estimable at ten trials (Section 3.6). • Control replication. The single-stimulation control is one organoid, and additional controls would strengthen the dissociation of stimulation history from development. 3.8 Status of the original metric suite Table 4: Status of each originally-proposed metric under the empirical findings Metric Original role Status in this study BMP test (Deff≥dmaxD_eff\!≥\!d_ ), Eq. (2) Link propagation depth to integration Set aside — no propagation (slope ≈0≈ 0) EIC =Deff=D_eff, Eq. (11) Multi-hop integration depth Not applicable — synchronous burst RI, Eq. (12) Fraction of network reached Not informative — near-global, no structure SSI, Eq. (14) Stimulus-specific encoding Not estimated — single stimulation condition per organoid PR, Eq. (15) Effective # activity modes Retained — per-trial read-out & PC1 coherence CRI, Eq. (16) Plasticity across epochs Retained — across-day change in valid read-outs 4 Discussion We set out to test whether stimulus-evoked activity in human cortical organoids reflects structured, multi-hop signal propagation that could be quantified with a graph-computational framework, and to characterize how that activity is reshaped by repeated stimulation. Two results frame everything that follows. First, once acquisition timing was correctly recovered, the evoked response proved to be a fast, near-synchronous, network-wide burst rather than a spatially propagating wave, so the propagation/integration-depth machinery we had developed (Deff≥dmaxD_eff≥ d_ , EIC, RI) does not apply to these preparations. Second, and independently, repeated daily stimulation produced a reproducible, control-validated depression and spatial contraction of the evoked response. We discuss each in turn, then their mechanistic interpretation and limitations. 4.1 Relation to prior work and the contribution of a stimulation-naïve control Repeated stimulation alters organoid network activity, as optogenetic entrainment of connected cerebral organoids induces sustained changes in later responses [19], and two weeks of daily electrical stimulation on high-density arrays reshapes response patterns, spontaneous activity and functional connectivity [27]. What such longitudinal designs cannot settle is "why". Because every preparation is stimulated, the observed change is confounded with ordinary developmental maturation over the same interval, and maturation is not a minor alternative in organoid preparations, where network activity changes substantially across days in culture [10]. Our design breaks this confound directly. Organoid 612 was cultured alongside the others, recorded spontaneously at day 1, and stimulated for the first time only at day 7. At matched age it engaged 3788 electrodes (93%93\% of the array), while the two organoids with five prior sessions engaged 384 and 486 (≈10%≈\!10\%), an order-of-magnitude difference attributable to stimulation history rather than age. This control, rather than the depression itself, is the load-bearing element of our claim. Three further results follow from the reframed read-outs. First, the depression is not a loss of capacity but of endurance. The first evoked response of each day was largely preserved from day 1 to day 7 (552: ∼50,000→∼37,000 50,000→ 37,000 net spikes; 613: ∼46,000→∼42,000 46,000→ 42,000), whereas the session mean collapsed and the ratio M1/M¯M_1/ M grew from ∼1.5 1.5–3×3× to ∼6× 6×. What repeated stimulation degrades is the network’s ability to sustain responses across a session, not to mount one. Second, the effect is on population size rather than coherence. The responding population contracted spatially (Σ from ∼26 26 to ∼10 10) while its shared-variance structure was preserved (PC1≈0.4PC1≈ 0.4–0.60.6 throughout), indicating that electrodes drop out of the responsive pool rather than desynchronising within it. Third, we report a negative result of methodological consequence. With stimulus timing correctly recovered, the evoked response showed no latency–distance gradient, so propagation-based graph metrics, such as reachability, integration depth, and bounds of the Deff≥dmaxD_eff≥ d_ form quantify a process these preparations do not exhibit, and should be justified empirically before being applied. 4.2 Why the evoked response is near-synchronous rather than propagating The absence of a latency–distance gradient (peak-latency slope ≈0≈ 0) indicates that focal stimulation recruits the network essentially simultaneously rather than through sequential, distance-dependent recruitment. This is consistent with what is known about maturing three-dimensional neural cultures, in which dense recurrent excitatory connectivity and developing inhibition give rise to network-wide synchronized bursting [10]. In such a regime, once activity crosses a threshold anywhere in the recurrent network, it engages the whole connected population within a few tens of milliseconds, so the observable is the presence, size, and timing precision of a global burst rather than a traveling wavefront. This has a direct methodological implication that generalizes beyond our preparations, i.e., graph metrics premised on measurable multi-hop propagation, such as reachability depth, integration depth, and any lower bound of the Deff≥dmaxD_eff≥ d_ form are only meaningful when the evoked response actually exhibits distance-dependent latency structure. We recommend that such structure be verified empirically (as in our Section 3.1 propagation check) before propagation-based graph metrics are applied to organoid or culture data; otherwise these metrics quantify a process the tissue does not exhibit. We regard the transparent reporting of this negative result, alongside the framework that motivated it, as a contribution in its own right 4.3 Repeated stimulation depresses and spatially contracts the evoked response The central positive finding is that repeated daily stimulation progressively depressed the evoked response, culminating in a striking collapse of the responding electrode population, from essentially the whole array to ∼10% 10\% by day 7 in both repeatedly-stimulated organoids, while a developmentally-matched organoid receiving its first-ever stimulation at day 7 retained ∼93% 93\%. Because the control was the same age but stimulation-naïve, the collapse cannot be attributed to maturation, viability decline, or array degradation over the recording period; it is specifically associated with the history of repeated stimulation. Repeated stimulation has been shown to induce sustained changes in organoid network responses and functional connectivity [19, 27]. Our results extend this in two ways, firstly by including a developmentally-matched, stimulation-naïve control that separates stimulation history from maturation, and secondly by dissociating a preserved first-trial response capacity from a progressively degrading within-session endurance. We showed that by including a stimulation-naïve, developmentally-matched control, the change is a progressive depression and spatial contraction of the responding population. [11, 12, 19]. 4.4 Dissociating capacity from endurance: candidate mechanisms A key refinement is that the across-day depression did not reflect loss of the network’s maximal capacity. The first (“fresh”) evoked response of each day was relatively preserved from day 1 to day 7, whereas the session-averaged response collapsed, because within-session depression became progressively more severe on later days. In other words, repeated stimulation degrades the network’s ability to sustain responses across a session more than its ability to mount an initial one. Several non-exclusive mechanisms are consistent with this dissociation: • Short-term synaptic depression / vesicle-pool depletion. The rapid within-session drop after the first stimulus, followed by a lower plateau, is the classic signature of short-term synaptic depression through depletion of the readily-releasable vesicle pool and its incomplete recovery at the 30 s inter-stimulus interval [13, 20]. That the stimulation-naïve control showed the steepest within-session depression on its first-ever session indicates this fast component is intrinsic and history-independent. • Slow, accumulating homeostatic or metabolic change. The across-day component, the worsening of within-session sustainability and the contraction of the responding pool accumulate only with repeated daily stimulation. Candidates include homeostatic synaptic downscaling in response to repeated strong drive [14, 15], activity-dependent shifts in excitation–inhibition balance, and slower metabolic or excitotoxic costs of repeated large-scale synchronous bursting. • Spatial contraction without loss of coherence. That the responding population shrinks in size while its shared-variance coherence (PC1) is preserved suggests that repeated stimulation progressively removes electrodes/units from the responsive pool rather than degrading the synchrony of those that remain. This is more consistent with a loss of recruitable periphery, i.e., units near threshold dropping out as excitability or synaptic efficacy declines than with a global desynchronization of the core. 4.5 Independent desynchronization and a possible signature of stimulation history Treating synchrony as a read-out separate from magnitude revealed a dissociation. In several recordings, the evoked burst became progressively less temporally precise across trials, independently of whether its magnitude declined. Notably, the stimulation-naïve control showed strong magnitude depression but no significant desynchronization, whereas a repeatedly-stimulated organoid desynchronized. We advance, as a hypothesis to be tested with larger samples, that within-session magnitude depression is an intrinsic, history-independent property of these networks, whereas progressive desynchronization is more associated with a prior history of repeated stimulation, potentially reflecting an accumulating disruption of the inhibitory or gap-junctional mechanisms that sharpen population timing [10]. Given n=1n=1 control, this remains a hypothesis rather than a conclusion. 4.6 Methodological lessons Two methodological points have broad relevance for organoid HD-MEA studies. First, correct recovery of the acquisition sampling rate and of stimulus timing was decisive. An incorrect default rate rescaled spike times and misaligned them from stimulus onsets by up to tens of seconds, which alone can manufacture or destroy apparent latency structure. Data-driven recovery of stimulus onsets directly from the population-rate trace rather than reliance on nominal protocol times proved essential given session-to-session variation in stimulation start. Second, the number of stimulus repetitions imposes a hard statistical ceiling on what can be estimated. At ten trials, pairwise functional-connectivity graphs over thousands of electrodes were not reliably thresholdable (permutation thresholds approaching |r|≈0.98|r|≈ 0.98), whereas aggregate measures, responsive-population size and first-principal-component coherence were stable and interpretable. Studies intending to estimate edge-level connectivity from evoked responses should plan trial counts accordingly. 4.7 Limitations Our conclusions are tempered by several limitations, stated forthrightly. The design comprises two repeatedly-stimulated organoids and a single single-stimulation control; findings are therefore reproducible, control-supported observations rather than population-level statistical claims, and the control-based dissociation of stimulation history from maturation rests on one control organoid. The day-3 and day-4 recordings of one organoid seemed anomalous, as day-3 session had the lowest total activity of the dataset and both day-4 recordings were truncated to eight or nine usable trials, so the intermediate day-to-day trajectory of that organoid should be interpreted with caution even though the day-7 endpoint was consistent across both repeatedly-stimulated organoids. One stimulation electrode in one organoid recorded no spikes. Finally, because the evoked response is a near-synchronous burst, our study does not, and cannot, adjudicate whether organoids support structured multi-hop computation under other stimulation regimes. It establishes only that they do not exhibit measurable propagation under the focal, single-site protocol used here. 4.8 Future work Several directions would directly extend and strengthen these findings. • Increase sample size and add controls. The most important next step is to replicate the across-day depression and the single-stimulation control in a larger cohort of organoids, enabling population-level statistics and a properly powered test of the stimulation-history-versus-maturation dissociation, including multiple single-stimulation controls at several ages. • Resolve recovery dynamics and reversibility. Whether the day-7 depression recovers after a stimulation-free interval, and on what timescale, would distinguish a transient homeostatic adaptation from a durable reconfiguration [25]. A design interleaving stimulation and rest days, with recordings during recovery, would address this. • Vary the inter-stimulus interval and protocol. Because within-session depression likely reflects incomplete recovery between stimuli, systematically varying the inter-stimulus interval (and total stimulus number) would map the recovery time-constant of the fast depression and test whether longer intervals spare within-session endurance. • Multi-site stimulation to test encoding and separability. The stimulus separability index (SSI) requires at least two distinguishable stimulus conditions and could not be estimated here because each organoid received a single, fixed stimulation pattern (one electrode column, applied identically on every trial). Delivering two or more spatially distinct stimulation patterns, for example, columns at different array positions interleaved across trials would allow a direct test of whether organoids produce separable population responses to different inputs, and whether such separability is itself degraded by repeated stimulation. • Denser trial sampling for connectivity. Increasing the number of stimulus repetitions per session, at the cost of longer recordings or shorter intervals would raise the statistical ceiling enough to make edge-level functional-connectivity graphs reliably estimable, allowing the originally-intended graph-structural analyses (density, modularity, community structure) to be revisited on firmer ground [26]. • Mechanistic and pharmacological dissection. Targeted manipulations, blocking specific receptors or transporters, or perturbing inhibition during the repeated-stimulation paradigm would help adjudicate among the candidate mechanisms (vesicle-pool depletion, homeostatic downscaling, excitation–inhibition shifts, metabolic cost) proposed above, and connect the network-level phenomenology to cellular substrates. • Cross-scale validation. Complementary read-outs, such as calcium imaging for single-cell spatial resolution, or molecular/transcriptomic profiling before and after repeated stimulation would test whether the electrophysiological contraction of the responding population corresponds to identifiable cellular or molecular changes. 5 Conclusions We set out to quantify multi-hop computational integration in stimulated cortical organoids using a graph-constrained dynamical framework and a biological message-passing theorem (Theorem 1), and we carried this program out in full, i.e., graph construction (Eqs. (6)–(7)), dynamical modeling (Eqs. (8)–(10)), the complete metric suite (Eqs. (11)–(16)), and per-day connectivity graphs. On evaluating these on longitudinal HD-MEA data, the evoked response was found not to propagate outward in a measurable multi-hop fashion but to engage the network near-synchronously, so the propagation/integration-depth components do not apply to these preparations. Reframing around synchrony, response-population size, and shared variability revealed a robust, control-validated phenomenon. Repeated daily stimulation progressively depresses the evoked response and spatially contracts the responding network, sparing the network’s fresh first-trial capacity while degrading its within-session endurance, with a developmentally-matched single-stimulation control establishing that the effect is driven by stimulation history rather than maturation. We report the original framework, its full empirical test, and the redirected findings together, as a transparent account of how the data reshaped the question. References [1] Bullmore, E., & Sporns, O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience 10(3), 186–198. https://doi.org/10.1038/nrn2575 [2] Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x [3] Kipf, T.N., & Welling, M. (2017). Semi-Supervised Classification with Graph Convolutional Networks. 5th International Conference on Learning Representations (ICLR). arXiv:1609.02907. [4] Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., & Dahl, G.E. (2017). Neural Message Passing for Quantum Chemistry. Proceedings of the 34th International Conference on Machine Learning (ICML), PMLR 70, 1263–1272. [5] Berdondini, L., Imfeld, K., Maccione, A., Tedesco, M., Neukom, S., Koudelka-Hep, M., & Martinoia, S. (2009). Active pixel sensor array for high spatio-temporal resolution electrophysiological recordings from single cell to large scale neuronal networks. Lab on a Chip 9(18), 2644–2651. https://doi.org/10.1039/b907394a [6] Amin, H., Maccione, A., Marinaro, F., Zordan, S., Nieus, T., & Berdondini, L. (2016). Electrical responses and spontaneous activity of human iPS-derived neuronal networks characterized for 3-month culture with 4096-electrode arrays. Frontiers in Neuroscience 10, 121. https://doi.org/10.3389/fnins.2016.00121 [7] Litwin-Kumar, A., Harris, K.D., Axel, R., Sompolinsky, H., & Abbott, L.F. (2017). Optimal Degrees of Synaptic Connectivity. Neuron 93(5), 1153–1164.e7. https://doi.org/10.1016/j.neuron.2017.01.030 [8] Gao, P., Trautmann, E., Yu, B.M., Santhanam, G., Ryu, S., Shenoy, K., & Ganguli, S. (2017). A theory of multineuronal dimensionality, dynamics and measurement. bioRxiv 214262. https://doi.org/10.1101/214262 [9] Mazzucato, L., Fontanini, A., & La Camera, G. (2016). Stimuli Reduce the Dimensionality of Cortical Activity. Frontiers in Systems Neuroscience 10, 11. https://doi.org/10.3389/fnsys.2016.00011 [10] Trujillo, C.A., Gao, R., Negraes, P.D., Gu, J., Buchanan, J., Preissl, S., Wang, A., Wu, W., Haddad, G.G., Chaim, I.A., Domissy, A., Vandenberghe, M., Devor, A., Yeo, G.W., Voytek, B., & Muotri, A.R. (2019). Complex Oscillatory Waves Emerging from Cortical Organoids Model Early Human Brain Network Development. Cell Stem Cell 25(4), 558–569.e7. https://doi.org/10.1016/j.stem.2019.08.002 [11] Cai, H., Ao, Z., Tian, C., Wu, Z., Liu, H., Tchieu, J., Gu, M., Mackie, K., & Guo, F. (2023). Brain organoid reservoir computing for artificial intelligence. Nature Electronics 6, 1032–1039. https://doi.org/10.1038/s41928-023-01069-w [12] Kagan, B.J., Kitchen, A.C., Tran, N.T., Habibollahi, F., Khajehnejad, M., Parker, B.J., Bhat, A., Rollo, B., Razi, A., & Friston, K.J. (2022). In vitro neurons learn and exhibit sentience when embodied in a simulated game-world. Neuron 110(23), 3952–3969.e8. https://doi.org/10.1016/j.neuron.2022.09.001 [13] Zucker, R.S., & Regehr, W.G. (2002). Short-Term Synaptic Plasticity. Annual Review of Physiology 64, 355–405. https://doi.org/10.1146/annurev.physiol.64.092501.114547 [14] Turrigiano, G.G., Leslie, K.R., Desai, N.S., Rutherford, L.C., & Nelson, S.B. (1998). Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature 391(6670), 892–896. https://doi.org/10.1038/36103 [15] Turrigiano, G.G., & Nelson, S.B. (2004). Homeostatic plasticity in the developing nervous system. Nature Reviews Neuroscience 5(2), 97–107. https://doi.org/10.1038/nrn1327 [16] Poli, D., Pastore, V.P., & Massobrio, P. (2015). Functional connectivity in in vitro neuronal assemblies. Frontiers in Neural Circuits 9, 57. https://doi.org/10.3389/fncir.2015.00057 [17] Benjamini, Y., & Hochberg, Y. (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society: Series B (Methodological) 57(1), 289–300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x [18] Sen, P.K. (1968). Estimates of the Regression Coefficient Based on Kendall’s Tau. Journal of the American Statistical Association 63(324), 1379–1389. https://doi.org/10.1080/01621459.1968.10480934 [19] Osaki, T., Duenki, T., Chow, S.Y.A., Ikegami, Y., Beaubois, R., Levi, T., Nakagawa-Tamagawa, N., Hirano, Y., & Ikeuchi, Y. (2024). Complex activity and short-term plasticity of human cerebral organoids reciprocally connected with axons. Nature Communications 15, 2945. https://doi.org/10.1038/s41467-024-46787-7 [20] Alam El Din, D.-M., Moenkemoeller, L., Loeffler, A., Habibollahi, F., Schenkman, J., Mitra, A., van der Molen, T., Ding, L., Laird, J., Schenke, M., Johnson, E.C., Kagan, B.J., Hartung, T., & Smirnova, L. (2025). Human neural organoid microphysiological systems show the building blocks necessary for basic learning and memory. Communications Biology 8, 1237. https://doi.org/10.1038/s42003-025-08632-5 [21] Sharf, T., van der Molen, T., Glasauer, S.M.K., Guzman, E., Buccino, A.P., Luna, G., Cheng, Z., Audouard, M., Ranasinghe, K.G., Kudo, K., Nagarajan, S.S., Tovar, K.R., Petzold, L.R., Hierlemann, A., Hansma, P.K., & Kosik, K.S. (2022). Functional neuronal circuitry and oscillatory dynamics in human brain organoids. Nature Communications 13, 4403. https://doi.org/10.1038/s41467-022-32115-4 [22] Smirnova, L., Caffo, B.S., Gracias, D.H., Huang, Q., Morales Pantoja, I.E., Tang, B., Zack, D.J., Berlinicke, C.A., Boyd, J.L., Harris, T.D., Johnson, E.C., Kagan, B.J., Kahn, J., Muotri, A.R., Paulhamus, B.L., Schwamborn, J.C., Plotkin, J., Szalay, A.S., Vogelstein, J.T., Worley, P.F., & Hartung, T. (2023). Organoid intelligence (OI): the new frontier in biocomputing and intelligence-in-a-dish. Frontiers in Science 1, 1017235. https://doi.org/10.3389/fsci.2023.1017235 [23] Smirnova, L. (2024). Biocomputing with organoid intelligence. Nature Reviews Bioengineering. https://doi.org/10.1038/s44222-024-00200-6 [24] Brown, P., & Varghese, S. (2026). Computing inspired by the brain: a journey from algorithms to organoids. Nature Computational Science 6(7), 686–696. https://doi.org/10.1038/s43588-026-01012-x [25] Robbins, A., Schweiger, H.E., Hernandez, S., Spaeth, A., Voitiuk, K., Parks, D.F., van der Molen, T., Geng, J., Cline, I., Kosik, K.S., Salama, S.R., Sharf, T., Mostajo-Radji, M.A., Haussler, D., & Teodorescu, M. (2026). Goal-directed learning in cortical organoids. Cell Reports 45, 116984. https://doi.org/10.1016/j.celrep.2026.116984 [26] Duenki, T., & Ikeuchi, Y. (2026). Multi-organoid loop cerebral connectoids exhibit enhanced neuronal network dynamics and sequence-specific entrainment. Communications Biology 9, 302. https://doi.org/10.1038/s42003-026-09589-9 [27] Chow, S.Y.A., Hu, H., Duenki, T., et al. (2025). Repetitive stimulation modifies network characteristics of neural organoid circuits. bioRxiv 2025.01.16.633310. https://doi.org/10.1101/2025.01.16.633310 [28] Schröter, M., et al. (2025). Advances in large-scale electrophysiology with high-density microelectrode arrays. Lab on a Chip 25, 4844–4885. https://doi.org/10.1039/D5LC00058K