A task-general connectivity model reveals variation in convergence of cortical inputs to functional regions of the cerebellum

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1. 

   Version published to 10.7554/elife.81511 on eLife

   Apr 21, 2023
2. 

   eLife

   Jan 3, 2023

   Author Response

   Reviewer #1 (Public Review):

   King et al. provide an interesting reanalysis of existing fMRI data with a novel functional connectivity modeling approach. Three connectivity models accounting for the relationship between cortical and cerebellar regions are compared, each representing a hypothesis. Evidence is presented that - contrary to a prominent theoretical account in the literature - cortical connectivity converges on cerebellar regions, such that the cerebellum likely integrates information from the cortex (rather than forming parallel loops with the cortex). If true, this would have large implications for understanding the likely computational role of the cerebellum in influencing cortical functions. Further, this paper provides a unique and potentially groundbreaking set of methods for testing alternate …

   Author Response

   Reviewer #1 (Public Review):

   King et al. provide an interesting reanalysis of existing fMRI data with a novel functional connectivity modeling approach. Three connectivity models accounting for the relationship between cortical and cerebellar regions are compared, each representing a hypothesis. Evidence is presented that - contrary to a prominent theoretical account in the literature - cortical connectivity converges on cerebellar regions, such that the cerebellum likely integrates information from the cortex (rather than forming parallel loops with the cortex). If true, this would have large implications for understanding the likely computational role of the cerebellum in influencing cortical functions. Further, this paper provides a unique and potentially groundbreaking set of methods for testing alternate connectivity hypotheses in the human brain. However, it appears that insufficient details were provided to properly evaluate these methods and their implications, as described below.

   Strengths:

   • Use of a large task battery performed by every participant, increasing confidence in the generality ofthe results across a variety of cognitive functions.

   • Multiple regression was used to reduce the chance of confounding (false connections driven by a thirdregion) in the functional connectivity estimates.

   • A focus on the function and connectivity of the cerebellum is important, given that it is clearly essentialfor a wide variety of cognitive processes but is studied much less often than the cortex.

   • The focus on clear connectivity-based hypotheses and clear descriptions of what would be expectedin the results if different hypotheses were true.

   • Generalization of models to a completely held-out dataset further increases confidence in thegeneralizability of the models.

   Concerns:

   1. The main conclusion of the paper (including in the title) involves a directional inference, and yet it is notoriously difficult to make directional inferences with fMRI. The term "input" into the cerebellum is repeatedly used to describe the prediction of cerebellar activity based on cortical activity, and yet the cerebellum is known to form loops with the cortex. With the slow temporal resolution of fMRI it is typically unclear what is the "input" versus the "output" in the kinds of predictions used in the present study. Critically, this may mean that a cerebellar region could receive input from a single cortical region (i.e., the alternate hypothesis supposedly ruled out by the present study), then output to multiple cortical regions, likely resulting (using the fMRI-based approach used here) in a faulty inference that convergent signals from cortex drove the results. On pg. 4 it is stated: "We chose this direction of prediction, as the cerebellar BOLD signal overwhelmingly reflects mossy-fiber input, with minimal contribution from cerebellar output neurons, the Purkinje cells (Mathiesen et al., 2000; Thomsen et al., 2004)." First, it would be good to know how certain this is in 2022, given the older references and ongoing progress in understanding the relationship between neuronal activity and the BOLD signal (e.g., Drew 2019). Second, given that it's likely that activity in the mossy-fiber inputs has an impact on Purkinje cell outputs, and that some cortical activity supposedly reflects cerebellar output, it is possible that FC could also reflect the opposite direction (cerebellumcortex). It would seem important to consider these possibilities in the interpretation of the results.

   We agree that making directional inferences with fMRI BOLD signals is difficult. We also note that because of the low temporal resolution of fMRI BOLD signals, we have not tried to extract directional information based on temporal lags. Rather, we emphasize that the relationship between neural activity and BOLD differs between the neocortex and cerebellum. In the cerebellum, mossy fiber activity releases glutamate which activates granule cells and the release of Nitric oxide (NO). NO is mostly released by granule cells and stellate cells. The release of NO increases the diameter of capillaries which in turn causes changes in blood flow and blood volume, two major contributors to BOLD signal changes (Alahmadi et al. 2016; Alahmadi et al. 2015; Drew 2019; Mapelli et al. 2017; Gagliano et al. 2022). Importantly, there is a negligible contribution of NO from the Purkinje cells. Taken together, these data make a strong case that the BOLD signal in the cerebellar cortex reflects activity at the input stage. We acknowledge that the references cited in our initial submission were somewhat dated. We have now provided additional references (which are in agreement with the findings from the earlier papers).. Based on this evidence, we chose to predict cerebellar activity from cortical activity.

   References: Alahmadi, A. A., Samson, R. S., Gasston, D., Pardini, M., Friston, K. J., D’Angelo, E., ... & Wheeler-Kingshott, C. A. (2016). Complex motor task associated with non-linear BOLD responses in cerebro-cortical areas and cerebellum. Brain Structure and Function, 221(5), 2443-2458.

   Alahmadi, A. A., Pardini, M., Samson, R. S., D'Angelo, E., Friston, K. J., Toosy, A. T., & Gandini Wheeler‐Kingshott, C. A. (2015). Differential involvement of cortical and cerebellar areas using dominant and nondominant hands: an FMRI study. Human brain mapping, 36(12), 5079-5100.

   Mapelli, L., Gagliano, G., Soda, T., Laforenza, U., Moccia, F., & D'Angelo, E. U. (2017). Granular layer neurons control cerebellar neurovascular coupling through an NMDA receptor/NO-dependent system. Journal of Neuroscience, 37(5), 1340-1351.

   Gagliano, G., Monteverdi, A., Casali, S., Laforenza, U., Gandini Wheeler-Kingshott, C. A., D’Angelo, E., & Mapelli, L. (2022). Non-Linear Frequency Dependence of Neurovascular Coupling in the Cerebellar Cortex Implies Vasodilation–Vasoconstriction Competition. Cells, 11(6), 1047.

   Drew, P. J. (2019). Vascular and neural basis of the BOLD signal. Current Opinion in Neurobiology, 58, 61–69.

   1. It would be helpful to have more details included in the "Connectivity Models" sub-section of the Methods section. The GLM-based connectivity approach is highly non-standard, such that more details on the logic behind it and any validation of the approach would be helpful. More specifically, it would be helpful to have clarity on how this form of functional connectivity relates to more standard forms, such as Pearson correlation and perhaps less standard multiple regression (or partial correlation) approaches. If I understand this approach correctly, each cortical parcel's time series is modulated (up or down) using that parcel's task-evoked beta weights, then "normalized" by the standard deviation of that parcel's time series, with the resulting time series then used in a multiple regression model to explain variance in a given cerebellar voxel's time series. It would be helpful if each of these steps were better explained and justified. For example, it is unclear what modulation of the cortical parcel time series by task-related beta weights does to the functional connectivity estimates, and thus how they should be interpreted.

   All of the models are multiple regression models. The independent variables (X) are the fitted (task-evoked) time series of the cortical parcels and the dependent variables (Y) are the fitted time series of each cerebellar voxel. Coefficients from multiple regression are identical to partial correlation coefficients if the cortical and cerebellar time series are z-standardized (SD=1). Here we only standardized the cortical time series. This only retains the weighting of the different cerebellar voxels (a cerebellar voxel that has a strong task-related signal should contribute more to the overall evaluation than a voxel where the task-related signal is weak); beyond this, the conclusions will be the same as that obtained with a partial correlation analysis.

   Because the number of predictors (#cortical parcels) approaches or outstrips the number of available observations (#task-related regressors), the ordinary-least-squares (OLS) solution to the multiple regression problem is not unique. We thus compared 3 common ways of regularizing a multiple regression problem: a) Picking only the most important regressor (a form of feature selection or optimal subspace selection), Ridge regression (L2 regularization) or Lasso regression (L1 regularization). Each method biases the solution in a particular way: The winner-take-all solution is obviously very sparse, the Lasso solution somewhat less sparse, and the Ridge solution quite dispersed. Here we exploited these differences in inductive bias, reasoning that the method with the bias that best matches the structure of the data-generating process will lead to better prediction performance on independent data.

   The results clearly favored a distributed input to each cerebellar voxel from the cortical parcels. We have rewritten the method section on connectivity models to better communicate the main idea.

   1. It appears that task-related functional connectivity is used in the present study, and yet the potential for task-evoked activations to distort such connectivity estimates does not appear to be accounted for (Norman-Haignere et al. 2012; Cole et al. 2019). For example, voxel A may respond to just the left hemifield of visual space while voxel B may respond to just the right hemifield of visual space, yet their correlation will be inflated due to task-evoked activity for any centrally presented visual stimuli. There are multiple methods for accounting for the confounding effect of task-evoked activations, none of which appear to be applied here. For example, the following publications include some options for reducing this confounding bias: (Cole et al. 2019; Norman-Haignere et al. 2012; Ito et al. 2020; Rissman, Gazzaley, and D'Esposito 2004; Al-Aidroos, Said, and Turk-Browne 2012). If this concern does not apply in the current context it would be important to explain/show why.

   The papers cited by the reviewer focus on the problem of how to remove task-evoked activity to estimate the correlation of spontaneous (task-independent) fluctuations. Here we are doing the opposite. We removed almost all spontaneous fluctuations and noise by averaging across trials and runs in order to fit the task-evoked activity. Additionally, we used a crossed approach as a way to control for the influence of task-independent fluctuations on the regression models: Within each task set, cerebellar activity from one half of the runs was predicted from cortical activity from the other half of the runs. Returning to the papers cited by the reviewer, these are designed to look at connectivity not related to task-evoked activity. We briefly summarize each below:

   ● Cole et al. (2019): Demonstrates that the removal of mean task-evoked activations while preserving task-evoked response shape is an important preprocessing step for validating task-based FC.

   ● Ito et al. (2020): Addressed the issue of shared variability between brain regions during task-evoked activity by estimating time series variance. They removed task-evoked activity from the time series in order to get a direct measure of neural-to-neural correlations (e.g., “background connectivity”) rather than task-to-neural associations.

   ● Al-Aidroos et al. (2012): Confronted with a similar problem of interpreting intrinsic correlations related to a goal (e.g., attending to scenes) from correlations related to synchronized stimulus-evoked responses. To mitigate this confound, they removed stimulus-evoked responses from the data resulting in “background connectivity” which was then used to assess inter-region coupling.

   ● Rissman et al. (2004): Introduced a new approach to characterize inter-region correlations during event-related activity by allowing inter-regional interactions to be assessed independent of activity at individual stages of a task.

   ● Norman-Haignere et al. (2012): To assess inter-region interactions (between fusiform gyrus and parahippocampal cortex), the authors removed the mean stimulus-evoked response and examined the correlations that occurred in the background of stimulus-locked changes (e.g., background connectivity).

   1. It is stated (pg. 21): "To reduce the influence of these noise correlations, we used a "crossed" approach to train the models: The cerebellar time series for the first session was predicted by the cortical time series from the second session, and vice-versa (see Figure 1). This procedure effectively negates the influence of noise processes, given that noise processes are uncorrelated across sessions." However, this does not appear to be strictly true, given that the task design (parts of which repeat across sessions) could interact with sources of noise. For example, task instruction cues (regardless of the specific task) likely increase arousal, which likely increases breathing and heart rates known to impact global fMRI BOLD signals. The current approach likely reduces the impact of noise relative to other approaches, but such strong certainty that noise processes are uncorrelated across sessions appears to be unwarranted.

   We completely agree. What we meant to say is that the procedure “negates the influence of any noise process that is uncorrelated with the tasks.” If we can predict the cerebellar activity patterns in session 2 by the cortical activity patterns measured in session 1, we can conclude that this prediction must be based on task-related signal changes given that the sequence of tasks is randomized. However, we do not know whether these task-related signals are caused directly by neural processes or indirectly by physiological processes (for example increased heart-rate in some conditions). The procedure only removes the influence of noise processes that are unrelated to the tasks. In our experience, these noise correlations can be quite strong and methods to remove them can introduce biases. For task-related noise processes we relied on high-pass filtering, a standard approach in task-based GLM approaches (see Methods).

   1. It appears possible that the sparse cerebellar model does worse simply because there are fewer predictors than the alternate models. It would be helpful to verify that the methods used, such as cross-validation, rule out (or at least reduce the chance) that this result is a trivial consequence of just having a different number of predictors across the tested models. It appears that the "model recovery" simulations may rule this out, but it is unclear how these simulations were conducted. Additional details in the Methods section would be important for evaluating this portion of the study.

   Our methods ensure full correction for model complexity (see response to major comment #2). Note that the sparse methods select regressors from all available cortical parcels; as such, “model complexity” is not well summarized by the number of non-zero regressors. We have now clarified these issues in the Methods section and have also revised the paper to better describe our model recovery simulations designed to address the issue of possible biases caused by different degrees of collinearity between cortical regressors.

   Reviewer #2 (Public Review):

   The human cerebellum likely has a significant but understudied contribution to cognition and behavior beyond the motor domain. Clarifying its functional relationship with the cerebral cortex is a critical detail necessary for understanding cerebellar functions. This paper addresses this challenge by testing three simple but intuitive models: winner-take-all, one-to-one model versus two converging input models. Results showed that the convergence model outperformed the one-to-one mapping model, indicating that cerebellar regions received multiple converging inputs from the different cortical regions. Overall the paper is well-written, and the results are clean and interesting. The methodological rigor of using cross-validation and generalization is also a strength of this paper.

   1. The authors concluded that some cerebellar regions receive converging inputs from multiple cortical regions because the Ridge and Lasso models outperformed the WTA model. The WTA model has a fixed diagonal pattern, in contrast, Ridge/Lasso models included more weights in the connectivity matrix. Considering what's being estimated in this matrix, then perhaps the findings are not surprising because even after penalizing and regularization, the ridge regression models are still more complex than the WTA model (more elements are allowed to vary). In other words, Lasso/Ridge models allow more variables from the X side to explain variances in Y, similar to how throwing in more regressors can always improve the R square. I am unsure if cross-validation mitigates this issue. It would be more straightforward for the authors to compare model performance in a way that controls for the number of variables in the Ridge/Lasso models.

   We now recognize that we could have done a better job in explaining our approach on this issue in the original submission. The models (including connectivity weights and regularization parameter) are trained solely on data from Task set A. They are tested on 2 independent datasets: 1) Data from the same participants performing novel tasks; 2) Data from new participants performing novel tasks. This allows us to compare models of different structure and complexity.

   1. The authors did an excellent job reviewing the anatomical relationship between the cerebral cortex and the cerebellum. There are several issues that the authors should address in the introduction or discussion. First, if the anatomical relationship between the cerebellum and the cortex is closed-loop as suggested in the intro, then how convergence can arise from multiple cortical inputs given there is no physical cross-talk? Second, there are multiple synapses connecting a cerebellar region and the cortex, and therefore could integration occur at other sites but not the cerebellum? For example, the caudate, the thalamus, or even the cortex (integrating inputs before sending to the cerebellum)?

   We agree that the correlation structure of BOLD signals in the neocortex and cerebellum is shaped by the closed-loop (bi-directional) interactions between the two structures. As such, some of the observed convergence could be caused by divergence of cerebellar output. We have added a new section to the discussion on the directionality of the model (Page 18).

   That said, there are strong reasons to believe that our results are mainly determined by how the neocortex sends signals to the cerebellum, and not vice versa. An increasing body of physiological studies (and this includes newer papers, see response to reviewer #1, comment #1 for details) show that cerebellar blood flow is determined by signal transmission from mossy fibers to granule cells and parallel fibers, followed by Nitric oxide signaling from molecular layer interneurons. Importantly, it is clear that Purkinje cells, the only output cell of the cerebellar cortex, are not reflected in the BOLD signal from the cerebellar cortex. (We also note that increases in the firing rate of inhibitory Purkinje cells means less activation of the neocortex). Thus, while we acknowledge that cerebellar-cortical connectivity likely plays a role in the correlations we observed, we cannot use fMRI observations from the cerebellar cortex and neocortex to draw conclusions about cerebellar-cortical connectivity. To do so we would need to measure activity in the deep cerebellar nuclei (and likely thalamus).

   The situation is different when considering the other direction (cortico-cerebellar connections). Here we have the advantage that the cerebellar BOLD signal is mostly determined by the mossy fiber input which, at least for the human cerebellum, comes overwhelmingly from cortical sources. On the neocortical side, the story is admittedly less clear: The cortical BOLD signal is likely determined by a mixture of incoming signals from the thalamus (which mixes inputs from the basal ganglia and cerebellum), subcortex, other cortical areas, and local cortical inputs (e.g., across layers). While the cortical BOLD signal (in contrast to the cerebellum) also reflects the firing rate of output cells, not all output cells will send collaterals to the pontine nuclei. These caveats are now clearly expressed in the discussion section2.

   On balance, there is an asymmetry: Cerebellar BOLD signal is dominated by neocortical input without contribution from the output (Purkinje) cells. Neocortical BOLD signal reflects a mixture of many inputs (with the cerebellar input making a small contribution) and cortical output firing. This asymmetry means that the observed correlation structure between cortical and cerebellar BOLD activity (the determinant of the estimated connectivity weights) will be determined more directly by cortico-cerebellar connections than by cerebellar-cortical connections. Given this, we have left the title and abstract largely the same, but have tempered the strength of the claim by discussing the influence of connectivity in the opposite direction.

   1. The dispersion metric quantifying the spread level in cortical inputs is interesting. Could the authors expand this finding and show anatomically what the physical spread is like in cortical space? The metric is novel but hard to interpret. A figure demonstrating the physical spread in the cortex should help readers interpret this result.

   Figure 3 (previously Figure 4) was included to provide examples of differences in the spatial spread of cortical inputs. For example, regions 1 and 2 are explained by a more restricted and spatially contiguous set of cortical inputs (e.g., primary motor cortices) whereas regions 7 & 8 are explained by a set of spatially disparate regions (e.g., angular gyrus, superior and middle frontal cortices, and superior temporal gyrus). Prompted by this comment, we have opted to reverse the order of Figures 3 and 4 to give the reader a chance to visualize differences in physical spread of cortical regions before we walk through the quantitative analysis.

   1. At the end of the discussion section, the authors discussed how results are more likely driven by cortical inputs to the cerebellum but not the other way around. This interpretation is likely overstated given the hemodynamic blurring and low temporal resolution of BOLD. Without a faster imaging sequence and accurate models that account for differences in hemodynamic properties, the more parsimonious interpretation is results are driven by bidirectional cortico-cerebellar interactions. The results are still very interesting without this added nuisance.

   Our analyses do not rely on the exact time course or delays between neocortical and cerebellar activation, but only on the activity profiles across a wide range of tasks. In terms of bidirectionality, please see our response above. We have added a dedicated section in the revised Discussion on this issue.

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3. 

   eLife

   Jan 3, 2023

   eLife assessment

   This paper should be a high priority for neuroscientists interested in the role of connectivity in generating cognitive functions, especially with respect to the cerebellum (which has more neurons than any other part of the human brain). This study makes a compelling case for convergent connectivity from cortex to cerebellum supporting a variety of cognitive functions in the cerebellum. However, insufficient details were provided for proper evaluation of claims, and some of the claims (such as directionality of cortico-cerebellar inferences) may not be supported by the analyses.

   Read the original source
4. 

   eLife

   Jan 3, 2023

   Reviewer #1 (Public Review):

   King et al. provide an interesting reanalysis of existing fMRI data with a novel functional connectivity modeling approach. Three connectivity models accounting for the relationship between cortical and cerebellar regions are compared, each representing a hypothesis. Evidence is presented that - contrary to a prominent theoretical account in the literature - cortical connectivity converges on cerebellar regions, such that the cerebellum likely integrates information from the cortex (rather than forming parallel loops with the cortex). If true, this would have large implications for understanding the likely computational role of the cerebellum in influencing cortical functions. Further, this paper provides a unique and potentially groundbreaking set of methods for testing alternate connectivity hypotheses in …

   Reviewer #1 (Public Review):

   King et al. provide an interesting reanalysis of existing fMRI data with a novel functional connectivity modeling approach. Three connectivity models accounting for the relationship between cortical and cerebellar regions are compared, each representing a hypothesis. Evidence is presented that - contrary to a prominent theoretical account in the literature - cortical connectivity converges on cerebellar regions, such that the cerebellum likely integrates information from the cortex (rather than forming parallel loops with the cortex). If true, this would have large implications for understanding the likely computational role of the cerebellum in influencing cortical functions. Further, this paper provides a unique and potentially groundbreaking set of methods for testing alternate connectivity hypotheses in the human brain. However, it appears that insufficient details were provided to properly evaluate these methods and their implications, as described below.

   Strengths:
   • Use of a large task battery performed by every participant, increasing confidence in the generality of the results across a variety of cognitive functions.
   • Multiple regression was used to reduce the chance of confounding (false connections driven by a third region) in the functional connectivity estimates.
   • A focus on the function and connectivity of the cerebellum is important, given that it is clearly essential for a wide variety of cognitive processes but is studied much less often than the cortex.
   • The focus on clear connectivity-based hypotheses and clear descriptions of what would be expected in the results if different hypotheses were true.
   • Generalization of models to a completely held-out dataset further increases confidence in the generalizability of the models.

   Concerns:
   • The main conclusion of the paper (including in the title) involves a directional inference, and yet it is notoriously difficult to make directional inferences with fMRI. The term "input" into the cerebellum is repeatedly used to describe the prediction of cerebellar activity based on cortical activity, and yet the cerebellum is known to form loops with the cortex. With the slow temporal resolution of fMRI it is typically unclear what is the "input" versus the "output" in the kinds of predictions used in the present study. Critically, this may mean that a cerebellar region could receive input from a single cortical region (i.e., the alternate hypothesis supposedly ruled out by the present study), then output to multiple cortical regions, likely resulting (using the fMRI-based approach used here) in a faulty inference that convergent signals from cortex drove the results. On pg. 4 it is stated: "We chose this direction of prediction, as the cerebellar BOLD signal overwhelmingly reflects mossy-fiber input, with minimal contribution from cerebellar output neurons, the Purkinje cells (Mathiesen et al., 2000; Thomsen et al., 2004)." First, it would be good to know how certain this is in 2022, given the older references and ongoing progress in understanding the relationship between neuronal activity and the BOLD signal (e.g., Drew 2019). Second, given that it's likely that activity in the mossy-fiber inputs has an impact on Purkinje cell outputs, and that some cortical activity supposedly reflects cerebellar output, it is possible that FC could also reflect the opposite direction (cerebellumcortex). It would seem important to consider these possibilities in the interpretation of the results.
   • It would be helpful to have more details included in the "Connectivity Models" sub-section of the Methods section. The GLM-based connectivity approach is highly non-standard, such that more details on the logic behind it and any validation of the approach would be helpful. More specifically, it would be helpful to have clarity on how this form of functional connectivity relates to more standard forms, such as Pearson correlation and perhaps less standard multiple regression (or partial correlation) approaches. If I understand this approach correctly, each cortical parcel's time series is modulated (up or down) using that parcel's task-evoked beta weights, then "normalized" by the standard deviation of that parcel's time series, with the resulting time series then used in a multiple regression model to explain variance in a given cerebellar voxel's time series. It would be helpful if each of these steps were better explained and justified. For example, it is unclear what modulation of the cortical parcel time series by task-related beta weights does to the functional connectivity estimates, and thus how they should be interpreted.
   • It appears that task-related functional connectivity is used in the present study, and yet the potential for task-evoked activations to distort such connectivity estimates does not appear to be accounted for (Norman-Haignere et al. 2012; Cole et al. 2019). For example, voxel A may respond to just the left hemifield of visual space while voxel B may respond to just the right hemifield of visual space, yet their correlation will be inflated due to task-evoked activity for any centrally presented visual stimuli. There are multiple methods for accounting for the confounding effect of task-evoked activations, none of which appear to be applied here. For example, the following publications include some options for reducing this confounding bias: (Cole et al. 2019; Norman-Haignere et al. 2012; Ito et al. 2020; Rissman, Gazzaley, and D'Esposito 2004; Al-Aidroos, Said, and Turk-Browne 2012). If this concern does not apply in the current context it would be important to explain/show why.
   • It is stated (pg. 21): "To reduce the influence of these noise correlations, we used a "crossed" approach to train the models: The cerebellar time series for the first session was predicted by the cortical time series from the second session, and vice-versa (see Figure 1). This procedure effectively negates the influence of noise processes, given that noise processes are uncorrelated across sessions." However, this does not appear to be strictly true, given that the task design (parts of which repeat across sessions) could interact with sources of noise. For example, task instruction cues (regardless of the specific task) likely increase arousal, which likely increases breathing and heart rates known to impact global fMRI BOLD signals. The current approach likely reduces the impact of noise relative to other approaches, but such strong certainty that noise processes are uncorrelated across sessions appears to be unwarranted.
   • It appears possible that the sparse cerebellar model does worse simply because there are fewer predictors than the alternate models. It would be helpful to verify that the methods used, such as cross-validation, rule out (or at least reduce the chance) that this result is a trivial consequence of just having a different number of predictors across the tested models. It appears that the "model recovery" simulations may rule this out, but it is unclear how these simulations were conducted. Additional details in the Methods section would be important for evaluating this portion of the study.

   References:

   Al-Aidroos, Naseem, Christopher P. Said, and Nicholas B. Turk-Browne. 2012. "Top-down Attention Switches Coupling between Low-Level and High-Level Areas of Human Visual Cortex." Proceedings of the National Academy of Sciences of the United States of America 109 (36): 14675-80.
   Cole, Michael W., Takuya Ito, Douglas Schultz, Ravi Mill, Richard Chen, and Carrisa Cocuzza. 2019. "Task Activations Produce Spurious but Systematic Inflation of Task Functional Connectivity Estimates." NeuroImage 189 (April): 1-18.
   Drew, Patrick J. 2019. "Vascular and Neural Basis of the BOLD Signal." Current Opinion in Neurobiology 58 (October): 61-69.
   Ito, Takuya, Scott L. Brincat, Markus Siegel, Ravi D. Mill, Biyu J. He, Earl K. Miller, Horacio G. Rotstein, and Michael W. Cole. 2020. "Task-Evoked Activity Quenches Neural Correlations and Variability in Large-Scale Brain Systems." PLoS Computational Biology. https://doi.org/10.1101/560730.
   Norman-Haignere, S. V., G. McCarthy, M. M. Chun, and N. B. Turk-Browne. 2012. "Category-Selective Background Connectivity in Ventral Visual Cortex." Cerebral Cortex 22 (2): 391-402.
   Rissman, Jesse, Adam Gazzaley, and Mark D'Esposito. 2004. "Measuring Functional Connectivity during Distinct Stages of a Cognitive Task." NeuroImage 23 (2): 752-63.

   Read the original source
5. 

   eLife

   Jan 3, 2023

   Reviewer #2 (Public Review):

   The human cerebellum likely has a significant but understudied contribution to cognition and behavior beyond the motor domain. Clarifying its functional relationship with the cerebral cortex is a critical detail necessary for understanding cerebellar functions. This paper addresses this challenge by testing three simple but intuitive models: winner-take-all, one-to-one model versus two converging input models. Results showed that the convergence model outperformed the one-to-one mapping model, indicating that cerebellar regions received multiple converging inputs from the different cortical regions. Overall the paper is well-written, and the results are clean and interesting. The methodological rigor of using cross-validation and generalization is also a strength of this paper.

   The authors concluded that …

   Reviewer #2 (Public Review):

   The human cerebellum likely has a significant but understudied contribution to cognition and behavior beyond the motor domain. Clarifying its functional relationship with the cerebral cortex is a critical detail necessary for understanding cerebellar functions. This paper addresses this challenge by testing three simple but intuitive models: winner-take-all, one-to-one model versus two converging input models. Results showed that the convergence model outperformed the one-to-one mapping model, indicating that cerebellar regions received multiple converging inputs from the different cortical regions. Overall the paper is well-written, and the results are clean and interesting. The methodological rigor of using cross-validation and generalization is also a strength of this paper.

   The authors concluded that some cerebellar regions receive converging inputs from multiple cortical regions because the Ridge and Lasso models outperformed the WTA model. The WTA model has a fixed diagonal pattern, in contrast, Ridge/Lasso models included more weights in the connectivity matrix. Considering what's being estimated in this matrix, then perhaps the findings are not surprising because even after penalizing and regularization, the ridge regression models are still more complex than the WTA model (more elements are allowed to vary). In other words, Lasso/Ridge models allow more variables from the X side to explain variances in Y, similar to how throwing in more regressors can always improve the R square. I am unsure if cross-validation mitigates this issue. It would be more straightforward for the authors to compare model performance in a way that controls for the number of variables in the Ridge/Lasso models.

   The authors did an excellent job reviewing the anatomical relationship between the cerebral cortex and the cerebellum. There are several issues that the authors should address in the introduction or discussion. First, if the anatomical relationship between the cerebellum and the cortex is closed-loop as suggested in the intro, then how convergence can arise from multiple cortical inputs given there is no physical cross-talk? Second, there are multiple synapses connecting a cerebellar region and the cortex, and therefore could integration occur at other sites but not the cerebellum? For example, the caudate, the thalamus, or even the cortex (integrating inputs before sending to the cerebellum)?

   The dispersion metric quantifying the spread level in cortical inputs is interesting. Could the authors expand this finding and show anatomically what the physical spread is like in cortical space? The metric is novel but hard to interpret. A figure demonstrating the physical spread in the cortex should help readers interpret this result.

   At the end of the discussion section, the authors discussed how results are more likely driven by cortical inputs to the cerebellum but not the other way around. This interpretation is likely overstated given the hemodynamic blurring and low temporal resolution of BOLD. Without a faster imaging sequence and accurate models that account for differences in hemodynamic properties, the more parsimonious interpretation is results are driven by bidirectional cortico-cerebellar interactions. The results are still very interesting without this added nuisance.

   Read the original source
6. 

   eLife

   Jan 3, 2023

   Reviewer #3 (Public Review):

   Resting stage fMRI studies have revealed functional associations between cerebral cortical networks and cerebellar regions. However, it remains unknown whether specific regions of the cerebellar cortex integrate information from functionally related areas of the cerebral cortex. Here, the authors used a task-based fMRI approach to infer the degree of convergence of cerebral cortical inputs at the level of the cerebellar cortex. Models that allow for integration of cerebral cortical inputs, rather than one-to-one relationships between cerebral cortical and cerebellar regions best explained cerebellar task-related activity. A higher degree of convergence was needed to explain activity in non-motor cerebellar regions.

   Strengths:
   - Innovative task-based approach to assess the level of cerebral cortical inputs to …

   Reviewer #3 (Public Review):

   Resting stage fMRI studies have revealed functional associations between cerebral cortical networks and cerebellar regions. However, it remains unknown whether specific regions of the cerebellar cortex integrate information from functionally related areas of the cerebral cortex. Here, the authors used a task-based fMRI approach to infer the degree of convergence of cerebral cortical inputs at the level of the cerebellar cortex. Models that allow for integration of cerebral cortical inputs, rather than one-to-one relationships between cerebral cortical and cerebellar regions best explained cerebellar task-related activity. A higher degree of convergence was needed to explain activity in non-motor cerebellar regions.

   Strengths:
   - Innovative task-based approach to assess the level of cerebral cortical inputs to the cerebellar cortex.
   - Used a large multi-domain battery of fMRI tasks.
   - Multiple models of interactions between the cerebral cortex and cerebellum were assessed.
   - Predictive accuracy of models was assessed across multiple parcellations of the cerebral cortex.
   - Connectivity models can be useful in predicting new cerebellar functional data in new participants.

   Weaknesses:
   - One limitation of the approach that is not discussed is that the motor responses that can be performed in the scanner are inherently simple, whereas non-motor tasks can be more varied and have a higher degree of complexity. Thus, it is unclear if the types of tasks used in multi-domain batteries are sufficient to substantiate the finding that there is less functional integration in non-motor regions of the cerebellar cortex.

   Likely impact and utility:
   - The study provides insightful evidence that regions of the cerebellar cortex may integrate inputs from different regions of the cerebral cortex. This finding is useful for theories of cerebellar function and for guiding future studies of how integration may occur at the level of the cerebellar cortex.

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7. 

   Version published to 10.1101/2022.05.07.490946v2 on bioRxiv

   Dec 30, 2022
8. 

   Version published to 10.1101/2022.05.07.490946v1 on bioRxiv

   May 8, 2022