Integration of partially observed multimodal and multiscale neural signals for estimating a neural circuit using dynamic causal modeling

Abstract

Integrating multiscale, multimodal neuroimaging data is essential for a comprehensive understanding of neural circuits. However, this is challenging due to the inherent trade-offs between spatial coverage and resolution in each modality, necessitating a computational strategy that combines modality-specific information effectively. This study introduces a dynamic causal modeling (DCM) framework designed to address the challenge of combining partially observed, multiscale signals across a larger-scale neural circuit by employing a shared neural state model with modality-specific observation models. The proposed method achieves robust circuit inference by iteratively integrating parameter estimates from local microscale and global meso- or macroscale circuits, derived from signals across various scales and modalities. Parameters estimated from high-resolution data within specific regions inform global circuit estimation by constraining neural properties in unobserved regions, while large-scale circuit data help elucidate detailed local circuitry. Using a virtual ground truth system, we validated the method across diverse experimental settings, combining calcium imaging (CaI), voltage-sensitive dye imaging (VSDI), and blood-oxygen-level-dependent (BOLD) signals-each with distinct coverage and resolution. Our reciprocal and iterative parameter estimation approach markedly improves the accuracy of neural property and connectivity estimates compared to traditional one-step estimation methods. This iterative integration of local and global parameters presents a reliable approach to inferring extensive, complex neural circuits from partially observed, multimodal, and multiscale data, showcasing how information from different scales reciprocally enhances entire circuit parameter estimation.

Fig 1. Multimodal and multiscale signals and parameter estimation with mms-DCM.

A. Three neuroimaging modalities of CaI, VSDI, and BOLD (Y_CaI, Y_VSDI, and Y_BOLD), have different temporal and spatial resolutions in the current experimental setting. CaI measures activities within a neural population (n) with a middle temporal resolution (0.1 sec), VSDI measures activities among cortical columns (c) with high temporal resolution (1 msec), and BOLD measures activities of a region (r) composed of multitudes of neural columns with low temporal resolution (1 sec). B. In mms-DCM, a common neural state dynamics denoted as f generates CaI, VSDI, and BOLD (Y_CaI, Y_VSDI, and Y_BOLD) through corresponding observation model functions (g_CaI, g_VSDI, and g_BOLD). By fitting multimodal observed signals, Y = [Y_CaI,Y_VSDI,Y_BOLD] with model generated signals $\tilde{\mathit{Y}}=\left[{\tilde{\mathit{Y}}}_{\mathbf{C}\mathbf{a}\mathbf{I}},{\tilde{\mathit{Y}}}_{\mathbf{V}\mathbf{S}\mathbf{D}\mathbf{I}},{\tilde{\mathit{Y}}}_{\mathbf{B}\mathbf{O}\mathbf{L}\mathbf{D}}\right]$ mms-DCM estimates model parameters for the common neural state model f and each observation model function (g_CaI,g_VSDI, and g_BOLD). C. A schematic of convolution-based neural state model for two excitatory neural populations (1, 2) and one inhibitory neural population (3) is presented. For every connection from a source (m) to target (n) neural populations, an effective connectivity (A_nm)−weighted firing-rate transfer function of a membrane potential σ(x_m) of a source neural population is convoluted with the synaptic kernel (h(t)) to affect the membrane potential of the target neural population (x_nm).

Fig 2. The ground truth foundational model for mms-DCM experiments.

The ground truth foundational model for mms-DCM experiments is constructed based on CaI signals from layer 2/3 (L2/3) of the mouse barrel cortex. For this model, we extracted 12 CaI signals corresponding to four subregions (denoted as columns in the current study), each comprising three neural populations: two excitatory and one inhibitory. A. The virtual circuit model, illustrating both intra-columnal and inter-columnal connections, is displayed. We assume identical connections across each column. B. The estimated effective connectivity is shown, highlighting the dynamic interactions between neural populations. C. The reproduction of CaI signals, based on the estimated circuit parameters, is depicted. Solid lines represent the generated signals, contrasting with the dotted lines, which correspond to the experimental data. The different colors—red, orange, and blue—represent the excitatory populations E#1, E#2, and the inhibitory population I#1, respectively, with ‘#’ indicating the column number.

Fig 3. Multimodal signal generation using a virtual neural circuit model.

We used a virtual neural circuit model to selectively generate multimodal signals. This model serves as a ground truth and features four columns alongside a hidden external region, each column designed with identical connection topologies that include two excitatory and one inhibitory neural population. To add complexity to the model, we allowed for slight variations in the strength of intra-regional intrinsic connectivity among these columns. The strengths of these connections were derived from experimental data, specifically CaI signals (refer to Fig 2). For our simulations, CaI signals were generated exclusively for neural populations in column 1, while four VSDI signals were produced for all four columns to demonstrate the broader spatial coverage of this modality. Additionally, the hidden external region, which contains both inhibitory and excitatory neural populations, is included in the model but omitted in subsequent figures for simplicity. This selective signal generation strategy aims to reflect the diverse imaging capabilities of each signal modality within the intricate neural circuitry of the virtual model.

Fig 4. Iterative parameter estimation of local and global circuit parameters for multimodal signals.

A. This figure outlines an iterative process for estimating neural circuits based on CaI and VSDI signals. Initially, local circuit parameters are estimated using available CaI signals from column 1. These estimated local parameters serve as expectations of prior distributions for parameters in other columns, facilitating the exploration of inter-regional interaction parameters (A_inter). The third step updates expectations of prior distributions for intra-regional connectivity parameters, while the final step precisely refines those of both global and local circuit parameters. B and C. Simulated signals from the ground truth (dotted lines) and from the estimated parameters (solid lines) are displayed. D and E. Comparisons between the ground truth parameters (θ^gt, x-axis) and the estimated parameters (θ*, y-axis) are presented for both iterative (D) and one-step (E) estimations. The results from the optimal model parameters in both iterative and one-step estimations are compared in (B) ~ (E).

Fig 5. Evaluation of global circuit parameter estimation using local circuit priors (Experiment 2a).

A. Three different methods, designated as Method 1, Method 2, and Method 3, are depicted schematically. B. Scatter plots show correlations between the estimated parameters (θ*) and the ground truth parameters (θ^gt). Method 1, which incorporates local circuit information into global circuit estimation, demonstrates the highest accuracy, showcasing the significant impact of utilizing local data to enhance global parameter estimation accuracy.

Fig 6. Utility of the global circuit information on local circuit estimation (Experiment 2b).

A. This experiment compares the local circuit of column 1 under two different evaluation contexts. In Method 1, the local circuit is evaluated in isolation (without global circuit information), focusing solely on its inherent dynamics. B. Estimated and ground truth CaI and VSDI signals of Method 1 are plotted. The solid lines in the plots are generated from the estimated parameters, reflecting the model’s interpretation of the neural activity. Conversely, the dotted lines represent the signals derived from the ground truth parameters, serving as a benchmark for evaluating the accuracy of the model’s estimations. C. Scatter plots of Method 1 show correlations between the estimated parameters (θ*) and the ground truth parameters (θ^gt) for Method 1. D. Method 2 evaluates the same local circuit within a broader global context, incorporating global circuit information to potentially enhance parameter estimation accuracy. E. CaI and VSDI signals of Method 2 are plotted. F. Scatter plot between the estimated parameters and the ground truth parameters of Method 2 is displayed.

Fig 7. Results of mms-DCM estimation with integrated multimodal data across replicated experiments (Experiment 3).

A. Two cases from the experiment are schematically displayed. In Case 1, CaI signals were obtained from a perturbed system, reflecting intentional variations in input parameters to simulate real-world data inconsistencies. B. Estimated and ground truth CaI and VSDI signals of Case 1 are plotted. The solid lines are generated from the estimated parameters, while the dotted lines depict signals derived from the ground truth parameters. C. Scatter plot of Case 1 shows correlations between the estimated parameters (θ*) and the ground truth parameters (θ^gt). D. In Case 2, we used perturbed VSDI signals, introducing similar variability. E. Estimated and ground truth CaI and VSDI signals of Case 2 are plotted. F. Scatter plot of the estimated and ground truth parameters of Case 2 is displayed.

Fig 8. Parameter estimation incorporating local and global circuit priors for multimodal observation signals; CaI, VSDI, and BOLD signals.

A. This outlines an iterative process for estimating neural circuits based on CaI, VSDI, and BOLD signals. The process begins by estimating the local circuit parameters using CaI signals available exclusively in column 1. These estimated local parameters then serve as prior expectations for parameters in other columns, facilitating the exploration of inter-regional interaction parameters (A_inter). The third step updates expectations of prior distributions for intra-regional connectivity parameters, and the final step meticulously refines those of both global and local circuit parameters, ensuring comprehensive integration of all data sources. B and C. Simulated signals (CaI, VSDI, and BOLD) from the ground truth (dotted lines) and the estimated parameters (solid lines) are displayed. D and E. Correlations between the ground truth parameters (θ^gt, x-axis) and the estimated parameters (θ*, y-axis) are presented for the iterative (D) and the one-step (E) estimation schemes. The simulation results with optimal model parameters obtained from the iterative and the one-step estimation schemes are compared in (B) ~ (E).

Fig 9. Results of iterative mms-DCM for extended system that consists of two Regions.

A. The estimation process for the extended system involves two interconnected Regions. Initially, we estimate the circuitry of the first Region by adhering to the methodology outlined in Experiment 4, as presented in Fig 8 of Section 4.4. Following this, we proceed with both local and global circuit estimations for the extended system, utilizing priors derived from the initial estimation step. B and C. Simulated signals (CaI, VSDI, and BOLD signals) from ground truth (dotted lines) and estimated parameters (solid lines) are displayed. D and E. Comparisons between the ground truth parameters (θ^gt, x-axis) and the estimated parameters (θ*, y-axis) are presented for the iterative (D) and the one-step (E) estimation schemes. The simulation results with optimal model parameters obtained from the iterative and the one-step estimation schemes are compared in (B) ~ (E).

Fig 10. Posterior shrinkages from prior distributions for each effective connectivity in experiment 5.

Posterior shrinkages (ρ_i) of each parameter i from prior distributions in iterative estimation (left) and one-step estimation (right) are displayed. Both panels use blue box plots for intra-regional (A_intra) and red for inter-regional (A_inter) connectivity, with significant differences marked by three asterisks (* and *** represents p < 0.01 and p < 0.0001, respectively). Statistical significance was assessed using the Kruskal-Wallis test since the groups have different variances, violating the homogeneity of variance assumption required for one-way ANOVA.