Synergistic effects of neuroprotective drugs with intravenous recombinant tissue plasminogen activator in acute ischemic stroke: A Bayesian network meta-analysis

Where is the protocol for this located so stroke survivors can inform their stroke medcal 'professionals' about using this?  Oh, you didn't create one, did you? YOU'RE FIRED!

You'll have to ask your competent? doctor why the hell edaravone is approved in Japan since 2001 but not the US.

Has your stroke hospital done anything with edaravone in the last decade?

 

• edaravone (12 posts to November 2011)

The latest here:

 Synergistic effects of neuroprotective drugs with intravenous recombinant tissue
plasminogen activator in acute ischemic stroke: A Bayesian network meta-analysis

RESEARCH ARTICLE
Synergistic effects of neuroprotective drugs
with intravenous recombinant tissue
plasminogen activator in acute ischemic
stroke: A Bayesian network meta-analysis
Chun DangID1, Qinxuan Wang2, Yijia Zhuang2, Qian Li3, Yaoheng LuID4☯*,
Ying XiongID1☯*, Li Feng5☯*
1 Department of Periodical Press/Chinese Evidence-Based Medicine Center, West China Hospital, Sichuan
University, Chengdu, China, 2 West China Hospital, West China School of Medicine, Sichuan University,
Chengdu, China, 3 Department of Neurology, The Second Affiliated Hospital of Harbin Medical University,
Harbin, China, 4 Department of General Surgery, Chengdu Integrated Traditional Chinese Medicine and
Western Medicine Hospital, Chengdu, China, 5 Department of General Surgery and Regenerative Medicine
Research Center, West China Hospital, Sichuan University, Chengdu, China
☯ These authors contributed equally to this work.
* fengli@scu.edu.cn (LF); 61711445@qq.com (YX); lyh93@cdutcm.edu.cn (YL)

Abstract

Neuroprotective drugs as adjunctive therapy for adults with acute ischemic stroke (AIS)
remains contentious. This study summarizes the latest evidence regarding the benefits of
neuroprotective agents combined with intravenous recombinant tissue plasminogen activa-
tor (rt-PA) intravenous thrombolysis. This study conducted a structured search of PubMed,
the Cochrane Library, EMBASE, Wanfang Data, and CNKI databases from their inception
to March 2024. Grey literature was also searched. The outcomes included efficacy (National
Institutes of Health Stroke Scale (NIHSS) score and Barthel Index (BI) score) and safety
(rate of adverse reactions). A total of 70 randomized controlled trials were selected for this
network meta-analysis (NMA), encompassing 4,140 patients with AIS treated using different
neuroprotective agents plus RT-PA, while 4,012 patients with AIS were in control groups.
The top three treatments for NIHSS scores at the 2-week follow-up were Edaravone Dex-
borneo with 0.9 mg/kg rt-PA, Edaravone with 0.9 mg/kg rt-PA, and HUK with 0.9 mg/kg rt-
PA. HUK with 0.9 mg/kg rt-PA, Dl-3n-butylphthalide with 0.9 mg/kg rt-PA, and Edaravone
Dexborneo with 0.9 mg/kg rt-PA were ranked the top three for BI scores at the 2-week fol-
low-up. The top three treatments with the lowest adverse effect rates were 0.6 mg/kg rt-PA,
HUK with 0.9 mg/kg rt-PA, and Edaravone Dexborneo with 0.9 mg/kg rt-PA due to their
excellent safety profiles. Compared to rt-PA alone, the combination treatments of Edara-
vone+rt-PA, Edaravone Dexborneol+rt-PA, HUK+rt-PA, Dl-3n-butylphthalide+rt-PA, and
Ganglioside GM1+rt-PA have shown superior efficacy. This NMA suggest that combination
therapies of neuroprotective agents and rt-PA can offer better outcomes for patients with
AIS. The results support the potential integration of these combination therapies into stan-
dard AIS treatment, aiming for improved patient outcomes and personalized therapeutic
approaches.

Comparative efficacy and safety of various mechanical thrombectomy strategies for patients with acute ischemic stroke: a Bayesian network meta-analysis

Do you not care about getting survivors 100% recovered?  With no measurement of 100% recovery, it's obvious you don't belong in stroke research. 

“What's measured, improves.” So said management legend and author Peter F. Drucker 

The latest here:

Comparative efficacy and safety of various mechanical thrombectomy strategies for patients with acute ischemic stroke: a Bayesian network meta-analysis

Jiahao Meng, Zeya Yan, […], and Gang Chen+9View all authors and affiliations

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https://doi.org/10.1177/17562864231181180

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• • Abstract
  • Introduction
  • Methods
  • Results
  • Discussion
  • Conclusion
  • Acknowledgments
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Abstract

Background:

Stent retriever, contact aspiration, and combined treatment are crucial mechanical thrombectomy strategies for patients with acute ischemic stroke (AIS).

Objectives:

The aim of this study was to compare and rank three different mechanical thrombectomy strategies for AIS due to large vessel occlusion by means of a Bayesian network meta-analysis.

Design:

A systematic review and Bayesian network meta-analysis based on PRISMA guidelines.

Data sources and methods:

Relevant randomized controlled trials (RCTs) were identified in Embase, MEDLINE, the Cochrane Library database, and Clinicaltrials.gov from inception to 15 March 2022. We used random effect models to estimate corresponding odds ratios (ORs) and rank probabilities using pairwise and Bayesian network meta-analysis. We applied the grading of recommendations assessment, development, and evaluation (GRADE) methodology to rate the certainty of evidence.

Results:

We identified 10 RCTs enrolling 2098 participants. As for modified Rankin Scale (mRS) 0–2, moderate certainty evidence established all mechanical thrombectomy strategies that were more effective than standard medical treatment [combined: log OR 0.9288, 95% credibility intervals (CrI) 0.1268–1.7246; contact aspiration: log OR 0.9507, 95% CrI 0.3361–1.5688; stent retriever: log OR 1.0919, 95% CrI 0.6127–1.5702]. The same applied to mRS 0–3 (combined: log OR 0.9603, 95% CrI 0.2122–1.7157; contact aspiration: log OR 0.7554, 95% CrI 0.1769–1.3279; stent retriever: log OR 1.0046, 95% CrI 0.6001–1.4789). Combined treatment was superior to stent retriever in substantial reperfusion (log OR 0.8921, 95% CrI 0.2105–1.5907, high certainty). Stent retriever had the highest probability of being optimal for mRS 0–2 and mRS 0–3. Standard medical treatment had the lowest risk of subarachnoid hemorrhage. For all other outcomes, combined treatment was most likely the best treatment.

Conclusion:

Our results indicated that, with the exception of functional outcome, combined treatment might be the outstanding strategy. Apart from subarachnoid hemorrhage, all three mechanical thrombectomy strategies proved better strategies than standard medical treatment.

Registration:

PROSPERO (CRD42022351878).

Introduction

Stroke is one of the leading causes of death and disability globally.¹ Meanwhile, it is the most significant contributor to neurological disability-adjusted life-years.² Acute ischemic stroke (AIS) accounts for approximately 90% of strokes per year.³ Until now, recanalization treatment involving intravenous thrombolysis and mechanical thrombectomy has been supported by class I level A recommendation as treatment strategies for AIS.⁴

Previous research demonstrates that mechanical thrombectomy can significantly reduce disability and improve clinical outcomes for patients with AIS compared with standard medical treatment.^5,6 Even the guidelines have recommended mechanical thrombectomy for large vessel occlusion in the anterior circulation up to 24 h from symptom onset.^4,7 Nevertheless, the benefits of successful revascularization using various mechanical thrombectomy strategies as the first-line therapy approach remain uncertain to date. For mechanical thrombectomy, previous guidelines recommended a stent retriever as the first-line approach.⁷ Meanwhile, contact aspiration has gained growing acceptance. In the 2019 updated guidelines, contact aspiration and stent retriever are considered as equally crucial.⁴ Contact aspiration is also proposed to shorten the time for successful reperfusion and reduce the total cost of hospitalization.⁸ However, three randomized controlled trials (RCTs), including ASTER,⁹ COMPASS,¹⁰ and a study by Tsang et al.,¹¹ confirmed that stent retriever compared with contact aspiration did not result in a greater functional outcome or higher successful revascularization rate. In accordance with several retrospective studies, contact aspiration combined with stent retriever can boost revascularization rate and may have a synergistic effect.^12,13 Nogueira et al.¹⁴ observed combined treatment versus contact aspiration alone did not significantly improve efficacy and safety outcomes. Furthermore, the ASTER2 trial revealed that stent retriever was non-inferior to combined treatment.¹⁵

As a result, clinicians and patients were perplexed by the selection of treatment strategies. Few RCTs directly compared multiple mechanical thrombectomy strategies to our knowledge. Moreover, previous researches were either conventional pairwise meta-analysis¹⁶ or network meta-analysis¹⁷ that excluded combined treatment and were published early. In this study, we systematically evaluated three different mechanical thrombectomy strategies. We conducted the pairwise meta-analysis and first Bayesian network meta-analysis to, directly and indirectly, compare their efficacy and safety as the first-line approach for the treatment of patients with AIS.

 

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Long-term forecasting of a motor outcome following rehabilitation in chronic stroke via a hierarchical bayesian dynamic model

You do realize predicting failure to recover doesn't do a damn bit of good in getting survivors recovered? Or are you that fucking clueless? Survivors want recovery, do the research that gets there!

 

Long-term forecasting of a motor outcome following rehabilitation in chronic stroke via a hierarchical bayesian dynamic model

• Nicolas Schweighofer,
• Dongze Ye,
• Haipeng Luo,
• David Z. D’Argenio &
• Carolee Winstein 

Journal of NeuroEngineering and Rehabilitation volume 20, Article number: 83 (2023) Cite this article

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Abstract

Background

Given the heterogeneity of stroke, it is important to determine the best course of motor therapy for each patient, i.e., to personalize rehabilitation based on predictions of long-term outcomes. Here, we propose a hierarchical Bayesian dynamic (i.e., state-space) model (HBDM) to forecast long-term changes in a motor outcome due to rehabilitation in the chronic phase post-stroke.

Methods

The model incorporates the effects of clinician-supervised training, self-training, and forgetting. In addition, to improve forecasting early in rehabilitation, when data are sparse or unavailable, we use the Bayesian hierarchical modeling technique to incorporate prior information from similar patients. We use HBDM to re-analyze the Motor Activity Log (MAL) data of participants with chronic stroke included in two clinical trials: (1) the DOSE trial, in which participants were assigned to a 0, 15, 30, or 60-h dose condition (data of 40 participants analyzed), and (2) the EXCITE trial, in which participants were assigned a 60-h dose, in either an immediate or a delayed condition (95 participants analyzed).

Results

For both datasets, HBDM accounts well for individual dynamics in the MAL during and outside of training: mean RMSE = 0.28 for all 40 DOSE participants (participant-level RMSE 0.26 ± 0.19—95% CI) and mean RMSE = 0.325 for all 95 EXCITE participants (participant-level RMSE 0.32 ± 0.31), which are small compared to the 0-5 range of the MAL. Bayesian leave-one-out cross-validation shows that the model has better predictive accuracy than static regression models and simpler dynamic models that do not account for the effect of supervised training, self-training, or forgetting. We then showcase model’s ability to forecast the MAL of “new” participants up to 8 months ahead. The mean RMSE at 6 months post-training was 1.36 using only the baseline MAL and then decreased to 0.91, 0.79, and 0.69 (respectively) with the MAL following the 1st, 2nd, and 3rd bouts of training. In addition, hierarchical modeling improves prediction for a patient early in training. Finally, we verify that this model, despite its simplicity, can reproduce previous findings of the DOSE trial on the efficiency, efficacy, and retention of motor therapy.

Conclusions

In future work, such forecasting models can be used to simulate different stages of recovery, dosages, and training schedules to optimize rehabilitation for each person.

Trial registration This study contains a re-analysis of data from the DOSE clinical trial ID NCT01749358 and the EXCITE clinical trial ID NCT00057018

Introduction

Recent modeling work has sought to predict the long-term spontaneous recovery of individuals post-stroke from baseline clinical or neural data, e.g., [1,2,3,4]. Whereas such predictions are useful for clinical and research stratification, the neurorehabilitation clinician needs to accurately predict the long-term changes in motor outcomes in response to specific treatments. With the predicted responses, the clinician could then determine the best course of motor therapy for each patient, i.e., personalize rehabilitation [5].

A difficulty is that stroke is heterogeneous and exhibits considerable variability, including in response to motor therapy [6]. It is known that the integrity of the corticospinal tract predicts gains in functional outcomes due to rehabilitation, e.g., [4, 7, 8]. However, multiple other factors are also likely to affect these gains, as well as the retention of these gains following rehabilitation. For instance, we have previously shown that the integrity of visuospatial working memory modulated the effect of blocked, but not distributed, training schedules in chronic stroke [9]. In addition, in re-analyses of the data of the EXCITE [10] and DOSE [11] trials, we have shown that approximately one-fourth of participants continued to see improvements in upper extremity (UE) function following training; conversely, another fourth lost most gains in UE function that resulted from therapy [12, 13].

Given this variability in response to therapy, we need a paradigm shift in predictive modeling in neurorehabilitation that, in addition to clinical and lesion data, incorporates repeated measurements of motor outcomes as soon as they become available during motor therapy. Predictive models that primarily consider such repeated measurements indexed in time order (i.e., time-series) are forecasting models. For example, a recent model can more accurately forecast spontaneous recovery 6 months post-stroke when incorporating repeated measurements than only baseline data [14]. Here, we extend such an approach to forecast the effect of rehabilitation in chronic stroke.

What should be the form of forecasting models in neurorehabilitation? Since neurorehabilitation is based on the premise that sensorimotor activity improves motor recovery via brain plasticity, i.e., “changeability”, the models need to account for the changes in outcomes both during movement therapy, when an increase in performance is expected, and outside of therapy, when both a decrease in performance due to forgetting and an increase in performance are possible. Previously, we proposed a piece-wise linear model of changes in a motor outcome in the DOSE clinical trial, in which the periods of therapy marked the limit between the different linear segments [13]. Although this model well accounted for positive and negative changes both during and following therapy, a model of this type cannot generalize to other datasets because it depends on the timing of training and measurements.

We propose a state-space modeling approach to predict motor outcomes during and following rehabilitation post-stroke. The model has a compact representation and an adjustable time resolution, allowing generalization to different data sets and even to different schedules of therapy for individual patients. The model extends a previous non-linear, first-order state-space model that explained the long-term changes, and the variability in these changes, in arm use following training in the EXCITE trial [12]. This previous model uses a retention term to account for the performance decay often observed post-training, at least in subgroups of patients [12, 13] and a “self-training” term to account for the change in spontaneous use of the paretic limb outside of training when UE function is above a threshold post-therapy [12, 13, 15, 16], which further increases future use and function. In the present model, we further account for the response to therapy via an input term proportional to the dose of motor training, as in our previous piece-wise model [13]. Indeed, animal studies, meta-analyses, and recent clinical trials with large doses, including the DOSE trial, showed that large training doses improve UE function, e.g., [11, 17,18,19].

Previous models in neurorehabilitation typically predict the mean of the future outcome, e.g., [8, 20, 21]. However, such point estimation of a future outcome is insufficient for clinical decision-making in neurorehabilitation because clinicians need to account for the uncertainty of the forecast when assessing different treatment options.^{Footnote 1} To provide interval estimation, we utilize the Bayesian approach, which extends our previous work [12], as Bayesian models naturally deal with uncertainties by focusing on the probability distributions of all parameters.

A final difficulty for accurate long-term forecasting in neurorehabilitation, however, is that for each new patient, there is initially no or little data on the effect of motor therapy. A hierarchical Bayesian model [22] can, in theory, refine the initial predictions by incorporating prior information from similar patients, via “hyper-parameters.” Crucially, these hyper-parameters can be used as individual prior parameters when predicting the response of a new individual when little outcome data are available, i.e., early in therapy.

Here, we therefore propose and test a novel hierarchical Bayesian dynamic modeling (HBDM) framework that can accurately forecast a clinical measure following rehabilitation in chronic stroke. As a testbed of our model, we use the Motor Activity Log (MAL) data from both the DOSE trial [11] and the EXCITE trial [10]. We test whether a minimal model with three terms, accounting for retention, response to external training, and self-learning, respectively, can better predict the MAL than reduced dynamical models and non-dynamical regression models for these two datasets. Then, using the DOSE data, we simulate the model to forecast the MAL of “new” patients up to 8 months ahead and study the change in the long-term accuracy of the forecasts as additional training data becomes available. We compare the prediction accuracy for models with and without a hierarchical structure for different ranges of forecasting. Finally, we validate the model by testing whether it can account for our previous results on the DOSE dataset on the efficacy, efficiency, and retention of motor training in chronic stroke.

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Comparative efficacy of 5 non-pharmacological therapies for adults with post-stroke cognitive impairment: A Bayesian network analysis based on 55 randomized controlled trials

So further research required. Will never occur, there is NO STROKE LEADERSHIP to contact to get it done.

Comparative efficacy of 5 non-pharmacological therapies for adults with post-stroke cognitive impairment: A Bayesian network analysis based on 55 randomized controlled trials

Zhendong Li¹, Lei Yang¹, Hangjian Qiu², Xiaoqian Wang², Chengcheng Zhang¹ and Yuejuan Zhang^1*

• ¹Department of Nursing, The First Affiliated Hospital of Hunan University of Chinese Medicine, Changsha, China
• ²School of Nursing, Hunan University of Chinese Medicine, Changsha, China

Background: As a common sequela after stroke, cognitive impairment negatively impacts patients' activities of daily living and overall rehabilitation. Non-pharmacological therapies have recently drawn widespread attention for their potential in improving cognitive function. However, the optimal choice of non-pharmacological therapies for post-stroke cognitive impairment (PSCI) is still unclear. Hence, in this study, we compared and ranked 5 non-pharmacological therapies for PSCI with a Bayesian Network Meta-analysis (NMA), to offer a foundation for clinical treatment decision-making.

Methods: PubMed, EMBASE, Web of Science, Cochrane Central Register of Controlled Trials, Chinese Biomedical Medicine, China National Knowledge Infrastructure, Wangfang Database, and China Science and Technology Journal Database were searched from database inception to December 31, 2021, to collect Randomized Controlled Trials for PSCI. All of the studies were assessed (according to Cochrane Handbook for Systematic Reviews) and then data were extracted by two researchers separately. Pairwise meta-analysis for direct comparisons was performed using Revman. NMA of Bayesian hierarchical model was performed by WinBUGS and ADDIS. STATA was used to construct network evidence plots and funnel plots.

Results: A total of 55 trials (53 Two-arm trials and 2 Three-arm trials) with 3,092 individuals were included in this study. In the pair-wise meta-analysis, Transcranial Magnetic Stimulation (TMS), Virtual Reality Exposure Therapy (VR), Computer-assisted cognitive rehabilitation (CA), Transcranial Direct Current Stimulation (tDCS), and Acupuncture were superior to normal cognition training in terms of MoCA, MMSE, and BI outcomes. Bayesian NMA showed that the MoCA outcome ranked Acupuncture (84.7%) as the best therapy and TMS (79.7%) as the second. The MMSE outcome ranked TMS (76.1%) as the best therapy and Acupuncture as the second (72.1%). For BI outcome, TMS (89.1%) ranked the best.

Conclusions: TMS and Acupuncture had a better effect on improving cognitive function in post-stroke patients according to our Bayesian NMA. However, this conclusion still needs to be confirmed with large sample size and high-quality randomized controlled trials.

Registration: https://inplasy.com (No. INPLASY202260036).

Introduction

Post-stroke cognitive impairment (PSCI) is a common comorbidity of stroke, and the prevalence of it varies enormously across studies (17.6–83%), depending on the time of assessment, the study environment, the demographic variables, and the numerous cognitive tests and cut-offs that were utilized (1). PSCI is defined as a clinical syndrome characterized by any sort of cognitive neurodegeneration after stroke, ranging from mild impairment to a more severe form: post-stroke dementia (2, 3). Disruptions in advanced brain functions such as attention, language, memory, executive, and visuospatial function are the most common symptoms of PSCI, which not only have a negative impact on patients' activities of daily living and overall rehabilitation (4–6) but also linked closely to a higher risk of recurrent ischemic stroke (7) and a lower 5-year survival rate (2). In addition, the ongoing care and support needs required by PSCI patients are closely related to the increased physical and psychological burden of family caregivers (8) and the medical and economic burden on society (9). To sum up, PSCI has become a major public health concern that has to be addressed promptly as the great burden of stroke continues to climb (10, 11).

Currently, pharmaceutical interventions such as Acetylcholinesterase inhibitors, memantine, galantamine, etc., which are mainly approved for use in Alzheimer's disease have shown some clinical benefits in vascular dementia (12, 13). Unfortunately, a recent study revealed that little evidence demonstrates they helped symptoms or slowed dementia progression down in PSCI patients (14). On the contrary, side effects and adverse reactions such as gastrointestinal issues (diarrhea or constipation), headaches, dizziness, and so on, do exist in pharmaceutical interventions (15). Therefore, non-pharmacological therapies such as Transcranial Magnetic Stimulation (TMS) (16), Transcranial Direct Current Stimulation (tDCS) (17), Computer-assisted cognitive rehabilitation (CA) (18), Virtual Reality Exposure Therapy (VR) (19), and Acupuncture (20), which have been found have a positive impact on cognitive function of PSCI patients in several systematic review and meta-analysis, have gradually aroused people's attention (21).

However, due to a lack of manpower and resources, most studies to date have only compared individual therapy to traditional cognition training or, at most, two therapies. Direct comparisons provide little useful information for determining which therapy is more appropriate for PSCI patients. It is obvious that a deeper exploration to assess the relative value between different interventions will be greatly helpful for medical decisions and the rehabilitation of PSCI patients. Network meta-analysis is an extension of pairwise meta-analysis that allows data from multiple clinical trials evaluating at least two treatments to be pooled. The incorporation of both direct and indirect information strengthens inferences about each treatment's relative efficacy (22, 23).

Therefore, in the present study, we included 55 RCTs and used Bayesian Network Meta-analysis (NMA) to assess and rank the efficacy of the 5 different alternative strategies listed above, in order to find the best treatment plan for PSCI patients and to provide an evidence-based foundation for clinical treatments decision-making.

Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

We need this for stroke survivors so we can objectively determine what our muscle problems are. Knowing that we can objectively assign EXACT STROKE PROTOCOLS to fix those problems. At least that is what smart competent people would be doing. But no one in stroke  leadership or the stroke medical world seems to be smart or competent.

Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

• Russell T. Johnson,
• Daniel Lakeland &
• James M. Finley 

Journal of NeuroEngineering and Rehabilitation volume 19, Article number: 34 (2022) Cite this article

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Abstract

Background

Musculoskeletal modeling is currently a preferred method for estimating the muscle forces that underlie observed movements. However, these estimates are sensitive to a variety of assumptions and uncertainties, which creates difficulty when trying to interpret the muscle forces from musculoskeletal simulations. Here, we describe an approach that uses Bayesian inference to identify plausible ranges of muscle forces for a simple motion while representing uncertainty in the measurement of the motion and the objective function used to solve the muscle redundancy problem.

Methods

We generated a reference elbow flexion–extension motion and computed a set of reference forces that would produce the motion while minimizing muscle excitations cubed via OpenSim Moco. We then used a Markov Chain Monte Carlo (MCMC) algorithm to sample from a posterior probability distribution of muscle excitations that would result in the reference elbow motion. We constructed a prior over the excitation parameters which down-weighted regions of the parameter space with greater muscle excitations. We used muscle excitations to find the corresponding kinematics using OpenSim, where the error in position and velocity trajectories (likelihood function) was combined with the sum of the cubed muscle excitations integrated over time (prior function) to compute the posterior probability density.

Results

We evaluated the muscle forces that resulted from the set of excitations that were visited in the MCMC chain (seven parallel chains, 500,000 iterations per chain). The estimated muscle forces compared favorably with the reference forces generated with OpenSim Moco, while the elbow angle and velocity from MCMC matched closely with the reference (average RMSE for elbow angle = 2°; and angular velocity = 32°/s). However, our rank plot analyses and potential scale reduction statistics, which we used to evaluate convergence of the algorithm, indicated that the chains did not fully mix.

Conclusions

While the results from this process are a promising step towards characterizing uncertainty in muscle force estimation, the computational time required to search the solution space with, and the lack of MCMC convergence indicates that further developments in MCMC algorithms are necessary for this process to become feasible for larger-scale models.

Background

Movement scientists are often interested in quantifying the timing and magnitude of muscle forces during motions like walking or reaching to understand causal links between muscle mechanics and movement. Accurately and reliably estimating individual muscle forces has implications for how well researchers can evaluate muscle function to help guide surgical interventions, inform the design of prosthetics and orthotics, and estimate other clinically relevant outputs (e.g., joint contact forces) [1,2,3,4,5,6]. Measuring muscle forces in vivo is difficult to do, except on a limited scale (e.g., triceps surae forces [7]), but most often the methodology is far too invasive to use with human participants. Instead, researchers often use experimental data combined with musculoskeletal modeling to estimate muscle forces during a movement [8,9,10,11]. Several methods have been developed to estimate individual muscle forces during a motion, including static optimization, computed muscle control, as well as direct collocation or simulated annealing methods to solve for muscle forces [e.g., [12,13,14,15]]. Typically, these methods result in a single force trajectory for each muscle that optimizes a chosen objective function for a given musculoskeletal model and experimental motion. However, accurately solving for muscle forces remains difficult because the musculoskeletal system is redundant (an infinite combination of muscle forces can often give rise to the same joint moment) [16], and simulations of movement depend on experimental data and a variety of parameters that are prone to uncertainties [17, 18].

The uncertainty associated with muscle force estimation can arise from the uncertainty with which we mathematically represent how the central nervous system distributes muscle forces amongst agonist muscles [8, 12], errors in marker placement and skin movement relative to anatomical landmarks [19, 20], and modeling assumptions related to muscle parameters [21, 22]. Typical representations of motor control assume that the central nervous system attempts to minimize some objective function (e.g., minimize muscle fatigue or metabolic energy cost [8, 17, 23]). Choosing an appropriate objective function for a particular motion is difficult because it is not known exactly how the nervous system distributes forces across muscles. In reality, the nervous system is unlikely to generate an “optimal” motion under any hypothesis represented by a simple objective function, as biological systems may find “good-enough” solutions to movement objectives, but these may not necessarily be optimal behavior as defined in trajectory optimization problems [24]. The unknowns associated with choosing an appropriate objective function for musculoskeletal simulations are problematic because muscle force estimates are sensitive to the objective function chosen [17, 23, 25,26,27]. There are other aspects of musculoskeletal modeling that can lead to uncertainty in muscle force estimation, such as variability in marker placement, movement artifact, and unknown model parameters which can also play a role in impacting the computed muscle forces [18,19,20,21, 28,29,30]. With uncertainties in the motor control model, the measured data, and the musculoskeletal model, the single solutions typically obtained from standard optimizations conceal the inherent uncertainty we have about the predicted muscle forces. By better quantifying the uncertainty in muscle force estimation, researchers can evaluate experimental design approaches capable of reducing uncertainty and better predict whether a designed intervention would lead to meaningful changes in muscle force production.

One approach to quantifying uncertainty in musculoskeletal modeling is to treat the objective function as unknown while keeping the other model parameters fixed. There have been a few different methods developed to try to capture some of the uncertainty associated with choosing an objective function and how it would affect the estimated muscle forces for a given model or motion [31,32,33]. These approaches have used mathematical mappings between joint torques and muscle activations to compute upper and lower bounds on the muscle forces for each muscle over time. Instead of choosing an explicit objective function to solve the muscle redundancy problem, these methods instead solve for the upper and lower bounds then assume the muscle forces lie somewhere in between. However, these ranges include solutions that would only be possible with extreme co-activation of agonist and antagonist muscles. Extreme co-activation is unlikely to occur in most healthy human sub-maximal movements, especially if muscle forces are distributed in a way that is sensitive to the physiological load (or effort) across individual muscles [23] or reduces metabolic cost. One previous study used EMG data as a way to provide some bounds on the range of possible muscle forces [31], however the remaining muscles without EMG data were left unbounded and therefore still had vast ranges of possible muscle forces. Additionally, there are other limitations to directly using EMG data for this approach, such as uncertainty about how to normalize EMG, resolving forces from EMG, and collecting EMG from deep muscles [34,35,36,37]. Therefore, there is a critical gap in the field of musculoskeletal modeling and simulation between (a) solving for muscle forces with an explicit, but uncertain, objective function (or subset of them) and (b) solving for the broad range of possible muscle forces that include muscle force combinations that are not realistic without extreme co-activation of agonist muscle groups.

Bayesian inference methods are well suited for problems where we want to constrain the set of plausible solutions based on prior evidence and knowledge of the musculoskeletal system. This evidence could include information about physiology, measurement errors, and model-based uncertainties. Bayesian inference problems are defined with a prior function (a set of plausible assumptions about the problem), a likelihood function (provided by observed data about a set of parameters), and a posterior function (a quantification of the plausible values of a set of parameters) [38]. The logarithmic forms of these functions (log Prior, log Likelihood, and log Posterior) are preferred for a Bayesian inference problem because it is computationally more stable and effective.

One common way to sample from the solution space is to use a Markov Chain Monte Carlo (MCMC), which is a computer-driven sampling method that allows us to characterize a posterior distribution without knowing all of the distribution’s properties. The MCMC analysis generates the random samples (or proposals) from a multi-dimensional parameter space via a sequential process according to rules that compare consecutive proposals, and this generates a ‘chain’ of proposals [39, 40]. One unique property of a MCMC chain is that new proposals are based on the previous proposal, but do not depend on any proposal prior to the previous one [38]. Then, as the MCMC algorithm is iterated, the set of visited locations is used as a sample from the Bayesian posterior distribution of the unknown parameters [40, 41], which numerically represents a set of equally plausible parameter vectors that could produce a result that is similar to the observed data.

Our aim is to evaluate the feasibility of using Bayesian inference methods to quantify the plausible range of muscle forces for human motion. For this initial feasibility assessment, we developed a prior based on a commonly used objective function (integrated muscle excitation cubed), while keeping other musculoskeletal model parameters constant throughout the study (e.g., peak isometric muscle forces, tendon slack lengths). Our prior was based on physiological hypotheses that muscle forces are distributed amongst agonist muscles and that co-activation of agonist and antagonist muscles is typically low for healthy human motions [23, 42]. We used an MCMC sampling algorithm in MATLAB and simulated an elbow flexion–extension task (reference motion) using OpenSim to explore the plausible excitations that could give rise to the reference joint trajectory. We then compared the excitations from MCMC to the known original simulation that generated the reference motion. Our aim for this paper is to present a workflow for building a Bayesian model and performing MCMC analysis to sample plausible muscle forces for a measured motion with a musculoskeletal model. Ultimately, we hope that this workflow will allow movement scientists to appropriately account for uncertainties in measurement, model structure, model parameters, and assumed cost functions in musculoskeletal simulations.

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