RESUMO
Wilful movement requires neural control. Commonly, neural computations are thought to generate motor commands that bring the musculoskeletal system - that is, the plant - from its current physical state into a desired physical state. The current state can be estimated from past motor commands and from sensory information. Modelling movement on the basis of this concept of plant control strives to explain behaviour by identifying the computational principles for control signals that can reproduce the observed features of movements. From an alternative perspective, movements emerge in a dynamically coupled agent-environment system from the pursuit of subjective perceptual goals. Modelling movement on the basis of this concept of perceptual control aims to identify the controlled percepts and their coupling rules that can give rise to the observed characteristics of behaviour. In this Perspective, we discuss a broad spectrum of approaches to modelling human motor control and their notions of control signals, internal models, handling of sensory feedback delays and learning. We focus on the influence that the plant control and the perceptual control perspective may have on decisions when modelling empirical data, which may in turn shape our understanding of actions.
Assuntos
Aprendizagem , Movimento , HumanosRESUMO
As part of a long-term research project aiming at generating a biomechanical model of a fossil human tongue from a carefully designed 3D Finite Element mesh of a living human tongue, we present a computer-based method that optimally registers 3D CT images of the head and neck of the living human into similar images of another primate. We quantitatively evaluate the method on a baboon. The method generates a geometric deformation field which is used to build up a 3D Finite Element mesh of the baboon tongue. In order to assess the method's ability to generate a realistic tongue from bony structure information alone, as would be the case for fossil humans, its performance is evaluated and compared under two conditions in which different anatomical information is available: (1) combined information from soft-tissue and bony structures; (2) information from bony structures alone. An Uncertainty Quantification method is used to evaluate the sensitivity of the transformation to two crucial parameters, namely the resolution of the transformation grid and the weight of a smoothness constraint applied to the transformation, and to determine the best possible meshes. In both conditions the baboon tongue morphology is realistically predicted, evidencing that bony structures alone provide enough relevant information to generate soft tissue.
Assuntos
Hominidae , Animais , Humanos , Fósseis , Crânio/diagnóstico por imagem , Língua/diagnóstico por imagem , Papio , Análise de Elementos Finitos , Simulação por ComputadorRESUMO
In order to study the local interactions between facial soft-tissues and a Silhouette Soft® suspension suture, a CE marked medical device designed for the repositioning of soft tissues in the face and the neck, Finite element simulations were run, in which a model of the suture was embedded in a three-layer Finite Element structure that accounts for the local mechanical organization of human facial soft tissues. A 2D axisymmetric model of the local interactions was designed in ANSYS, in which the geometry of the tissue, the boundary conditions and the applied loadings were considered to locally mimic those of human face soft tissue constrained by the suture in facial tissue repositioning. The Silhouette Soft suture is composed of a knotted thread and sliding cones that are anchored in the tissue. Hence, simulating these interactions requires special attention for an accurate modelling of contact mechanics. As tissue is modelled as a hyper-elastic material, the displacement of the facial soft tissue changes in a nonlinear way with the intensity of stress induced by the suture and the number of the cones. Our simulations show that for a 4-cone suture a displacement of 4.35 mm for a 2.0 N external loading and of 7.6 mm for 4.0 N. Increasing the number of cones led to the decrease in the equivalent local strain (around 20%) and stress (around 60%) applied to the tissue. The simulated displacements are in general agreement with experimental observations.
Assuntos
Suturas , Humanos , Análise de Elementos Finitos , Cadáver , Fenômenos Biomecânicos , Estresse MecânicoRESUMO
Auditory speech perception enables listeners to access phonological categories from speech sounds. During speech production and speech motor learning, speakers' experience matched auditory and somatosensory input. Accordingly, access to phonetic units might also be provided by somatosensory information. The present study assessed whether humans can identify vowels using somatosensory feedback, without auditory feedback. A tongue-positioning task was used in which participants were required to achieve different tongue postures within the /e, ε, a/ articulatory range, in a procedure that was totally nonspeech like, involving distorted visual feedback of tongue shape. Tongue postures were measured using electromagnetic articulography. At the end of each tongue-positioning trial, subjects were required to whisper the corresponding vocal tract configuration with masked auditory feedback and to identify the vowel associated with the reached tongue posture. Masked auditory feedback ensured that vowel categorization was based on somatosensory feedback rather than auditory feedback. A separate group of subjects was required to auditorily classify the whispered sounds. In addition, we modeled the link between vowel categories and tongue postures in normal speech production with a Bayesian classifier based on the tongue postures recorded from the same speakers for several repetitions of the /e, ε, a/ vowels during a separate speech production task. Overall, our results indicate that vowel categorization is possible with somatosensory feedback alone, with an accuracy that is similar to the accuracy of the auditory perception of whispered sounds, and in congruence with normal speech articulation, as accounted for by the Bayesian classifier.
Assuntos
Retroalimentação Fisiológica , Fonética , Sensação/fisiologia , Percepção da Fala/fisiologia , Língua/fisiologia , Adulto , Feminino , Humanos , Masculino , Palato/fisiologia , Medida da Produção da Fala , Adulto JovemRESUMO
Recent studies on the remediation of speech disorders suggest that providing visual information of speech articulators may contribute to improve speech production. In this study, we evaluate the effectiveness of an illustration-based rehabilitation method on speech recovery of a patient with non-fluent chronic aphasia. The Ultraspeech-player software allowed visualization by the patient of reference tongue and lip movements recorded using ultrasound and video imaging. This method can improve the patient's awareness of their own lingual and labial movements, which can increase the ability to coordinate and combine articulatory gestures. The effects of this method were assessed by analyzing performance during speech tasks, the phonological processes identified in the errors made during the phoneme repetition task and the acoustic parameters derived from the speech signal. We also evaluated cognitive performance before and after rehabilitation. The integrity of visuospatial ability, short-term and working memory and some executive functions supports the effectiveness of the rehabilitation method. Our results showed that illustration-based rehabilitation technique had a beneficial effect on the patient's speech production, especially for stop and fricative consonants which are targeted (high visibility of speech articulator configurations) by the software, but also on reading abilities. Acoustic parameters indicated an improvement in the distinction between consonant categories: voiced and voiceless stops or alveolar, post-alveolar and labiodental fricatives. However, the patient showed little improvement for vowels. These results confirmed the advantage of using illustration-based rehabilitation technique and the necessity of detailed subjective and objective intra-speaker evaluation in speech production to fully evaluate speech abilities.
Assuntos
Afasia , Articuladores Dentários , Humanos , Fonética , Fala , Medida da Produção da Fala , FonoterapiaRESUMO
The human tongue is atypical as a motor system since its movement is determined by deforming its soft tissues via muscles that are in large part embedded in it (muscular hydrostats). However, the neurophysiological mechanisms enabling fine tongue motor control are not well understood. We investigated sensorimotor control mechanisms of the tongue through a perturbation experiment. A mechanical perturbation was applied to the tongue during the articulation of three vowels (/i/, /e/, /ε/) under conditions of voicing, whispering, and posturing. Tongue movements were measured at three surface locations in the sagittal plane using electromagnetic articulography. We found that the displacement induced by the external force was quickly compensated for. Individual sensors did not return to their original positions but went toward a position on the original tongue contour for that vowel. The amplitude of compensatory response at each tongue site varied systematically according to the articulatory condition. A mathematical simulation that included reflex mechanisms suggested that the observed compensatory response can be attributed to a reflex mechanism, rather than passive tissue properties. The results provide evidence for the existence of quick compensatory mechanisms in the tongue that may be dependent on tunable reflexes. The tongue posture for vowels could be regulated in relation to the shape of the tongue contour, rather than to specific positions for individual tissue points.NEW & NOTEWORTHY This study presents evidence of quick compensatory mechanisms in tongue motor control for speech production. The tongue posture is controlled not in relation to a specific tongue position, but to the shape of the tongue contour to achieve specific speech sounds. Modulation of compensatory responses due to task demands and mathematical simulations support the idea that the quick compensatory response is driven by a reflex mechanism.
Assuntos
Atividade Motora/fisiologia , Postura/fisiologia , Reflexo/fisiologia , Fala/fisiologia , Língua/fisiologia , Adolescente , Adulto , Feminino , Humanos , Masculino , Adulto JovemRESUMO
The hold phase of the stop consonants is crucial for a successful production of the release and the acoustic burst. Concurrently, it is also associated with weak acoustic energy and minimal movement, so that conventional acoustic and kinematic approaches are not relevant to investigate motor control. This paper presents an innovative experimental method to study speech motor control during this phase, based on meticulous measurement of the time variation of the mechanical pressure exerted by the tongue against the palate and also characterizing tongue-palate interaction. The concept is based on using miniature transducers with enhanced response characteristics inserted in different locations of the complete denture of edentulous subjects without perturbing the articulation. The study was done with a French-speaking adult whose maxillary denture was duplicated and mounted with six strain gauge transducers. The experiment was done with denti-alveolar and velar stop consonants with two vowel contexts. The results illustrate the potential of such device to analyse speech motor control when contact constrains tongue movements.
Assuntos
Idioma , Palato/fisiologia , Pressão , Língua/fisiologia , Fenômenos Biomecânicos , Dentaduras , França , Humanos , Masculino , Pessoa de Meia-Idade , TransdutoresRESUMO
Shifts in perceptual boundaries resulting from speech motor learning induced by perturbations of the auditory feedback were taken as evidence for the involvement of motor functions in auditory speech perception. Beyond this general statement, the precise mechanisms underlying this involvement are not yet fully understood. In this paper we propose a quantitative evaluation of some hypotheses concerning the motor and auditory updates that could result from motor learning, in the context of various assumptions about the roles of the auditory and somatosensory pathways in speech perception. This analysis was made possible thanks to the use of a Bayesian model that implements these hypotheses by expressing the relationships between speech production and speech perception in a joint probability distribution. The evaluation focuses on how the hypotheses can (1) predict the location of perceptual boundary shifts once the perturbation has been removed, (2) account for the magnitude of the compensation in presence of the perturbation, and (3) describe the correlation between these two behavioral characteristics. Experimental findings about changes in speech perception following adaptation to auditory feedback perturbations serve as reference. Simulations suggest that they are compatible with a framework in which motor adaptation updates both the auditory-motor internal model and the auditory characterization of the perturbed phoneme, and where perception involves both auditory and somatosensory pathways.
Assuntos
Teorema de Bayes , Percepção da Fala/fisiologia , Fala , Estimulação Acústica , Percepção Auditiva , Biologia Computacional , Simulação por Computador , Retroalimentação Sensorial , Audição , Humanos , Modelos Biológicos , Modelos Estatísticos , Destreza Motora , Distribuição Normal , Acústica da FalaRESUMO
Vowel reduction may involve phonetic reduction processes, with nonreached targets, and/or phonological processes in which a vowel target is changed for another target, possibly schwa. Coratino, a dialect of southern Italy, displays complex vowel reduction processes assumed to be phonological. We analyzed a corpus representative of vowel reduction in Coratino, based on a set of a hundred pairs of words contrasting a stressed and an unstressed version of a given vowel in a given consonant environment, produced by 10 speakers. We report vowelformants together with consonant-to-vowel formant trajectories and durations, and show that these data are rather in agreement with a change in vowel target from /i e É·É u/ to schwa when the vowel is a non-word-initial unstressed utterance, unless the vowel shares a place-of-articulation feature with the preceding or following consonant. Interestingly, it also appears that there are 2 targets for phonological reduction, differing in F1 values. A "higher schwa" - which could be considered as /ɨ/ - corresponds to reduction for high vowels /i u/ while a "lower schwa" - which could be considered as /É/ - corresponds to reduction for midhigh.
RESUMO
Direct touch finger interaction on a smartphone or a tablet is now ubiquitous. However, the latency inherent in digital computation produces an average feedback delay of ~ 75 ms between the action of the hand and its visible effect on digital content. This delay has been shown to affect users' performance, but it is unclear whether users adapt to this delay and whether it influences skill learning. Previous work studied adaptation to feedback delays but only for longer delays, with hidden hand or indirect devices. This paper addresses adaptation to touchscreen delay in two empirical studies involving the tracking of a target moving along an elliptical path. Participants were trained for the task either at the minimal delay the system allows (~ 9 ms) or at a longer delay equivalent to commercialized touch devices latencies (75 ms). After 10 training sessions over a minimum of 2 weeks (Experiment 1), participants adapt to the delay. They also display long-term retention 7 weeks after the last training session. This adaptation generalizes to a similar tracking path (e.g., infinity symbol). We also observed generalization of learning from the longer delay to the minimal-delay condition (Experiment 2). The delay thus does not prevent the learning of tracking skill, which suggests that delay adaptation and tracking skill could be two separate components of learning.
Assuntos
Adaptação Psicológica/fisiologia , Retroalimentação Sensorial/fisiologia , Tato/fisiologia , Visão Ocular/fisiologia , Adulto , Algoritmos , Feminino , Dedos/fisiologia , Generalização Psicológica , Humanos , Aprendizagem , Masculino , Pessoa de Meia-Idade , Destreza Motora/fisiologia , Desempenho Psicomotor/fisiologia , Tempo de ReaçãoRESUMO
The rehabilitation of speech disorders benefits from providing visual information which may improve speech motor plans in patients. We tested the proof of concept of a rehabilitation method (Sensori-Motor Fusion, SMF; Ultraspeech player) in one post-stroke patient presenting chronic non-fluent aphasia. SMF allows visualisation by the patient of target tongue and lips movements using high-speed ultrasound and video imaging. This can improve the patient's awareness of his/her own lingual and labial movements, which can, in turn, improve the representation of articulatory movements and increase the ability to coordinate and combine articulatory gestures. The auditory and oro-sensory feedback received by the patient as a result of his/her own pronunciation can be integrated with the target articulatory movements they watch. Thus, this method is founded on sensorimotor integration during speech. The SMF effect on this patient was assessed through qualitative comparison of language scores and quantitative analysis of acoustic parameters measured in a speech production task, before and after rehabilitation. We also investigated cerebral patterns of language reorganisation for rhyme detection and syllable repetition, to evaluate the influence of SMF on phonological-phonetic processes. Our results showed that SMF had a beneficial effect on this patient who qualitatively improved in naming, reading, word repetition and rhyme judgment tasks. Quantitative measurements of acoustic parameters indicate that the patient's production of vowels and syllables also improved. Compared with pre-SMF, the fMRI data in the post-SMF session revealed the activation of cerebral regions related to articulatory, auditory and somatosensory processes, which were expected to be recruited by SMF. We discuss neurocognitive and linguistic mechanisms which may explain speech improvement after SMF, as well as the advantages of using this speech rehabilitation method.
Assuntos
Afasia de Broca/terapia , Idioma , Plasticidade Neuronal , Fonoterapia/métodos , Fala/fisiologia , Retroalimentação Sensorial/fisiologia , Feminino , Humanos , Lábio , Imageamento por Ressonância Magnética , LínguaRESUMO
The nature of the speech goal in children was investigated in a study of compensation strategies for a lip-tube perturbation. Acoustic, articulatory, and perceptual analyses of the vowels /y/ and /u/ produced by ten 4-year-old French speakers and ten adult French speakers were conducted under two conditions: normal and with a large tube inserted between the lips. Ultrasound and acoustic recordings of isolated vowels were made in the normal condition before any perturbation, for each of the trials in the perturbed condition, and in the normal condition after the perturbed trials. Data revealed that adult participants moved their tongues in the perturbed condition more than children did. The perturbation was generally at least partly compensated for during the perturbed trials in adults, but children did not show a typical learning effect. In particular, unsystematic improvements were observed during the sequence of perturbed trials, and after-effects were not clear in the articulatory domain. This suggests that children may establish associative links between multisensory phonemic representations and articulatory maneuvers, but those links may mainly rely on trial-to-trial, error-based feedback correction mechanisms rather than on the internal model of the speech production apparatus, as they are in adults.
Assuntos
Acústica , Comportamento Infantil , Lábio/fisiologia , Movimento , Fonética , Acústica da Fala , Medida da Produção da Fala , Língua/fisiologia , Qualidade da Voz , Adulto , Fatores Etários , Pré-Escolar , Retroalimentação Sensorial , Feminino , Humanos , Aprendizagem , Lábio/diagnóstico por imagem , Masculino , Processamento de Sinais Assistido por Computador , Espectrografia do Som , Inteligibilidade da Fala , Língua/diagnóstico por imagem , Ultrassonografia , Adulto JovemRESUMO
The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.
Assuntos
Teorema de Bayes , Atividade Motora , Fala , Modelos TeóricosRESUMO
This article focuses on methodological issues related to quantitative assessments of speech quality after glossectomy. Acoustic and articulatory data were collected for 8 consonants from two patients. The acoustic analysis is based on spectral moments and the Klatt VOT. Lingual movements are recorded with ultrasound without calibration. The variations of acoustic and articulatory parameters across pre- and post-surgery conditions are analyzed in the light of perceptual evaluations of the stimuli. A parameter is considered to be relevant if its variation is congruent with perceptual ratings. The most relevant acoustic parameters are the skewness and the Center of Gravity. The Klatt VOT explains differences that could not be explained by spectral parameters. The SNTS ultrasound parameter provides information to describe impairments not accounted for by acoustical parameters. These results suggest that the combination of articulatory, perceptual and acoustic data provides comprehensive complementary information for a quantitative assessment of speech after glossectomy.
Assuntos
Transtornos da Articulação/reabilitação , Glossectomia/reabilitação , Testes de Articulação da Fala , Inteligibilidade da Fala , Medida da Produção da Fala , Neoplasias da Língua/cirurgia , Adulto , Transtornos da Articulação/diagnóstico , Feminino , Glossectomia/métodos , Humanos , Masculino , Pessoa de Meia-Idade , Esvaziamento Cervical/reabilitação , Fonética , Complicações Pós-Operatórias/diagnóstico , Complicações Pós-Operatórias/reabilitação , Espectrografia do Som , Acústica da Fala , UltrassonografiaRESUMO
A quick correction mechanism of the tongue has been formerly experimentally observed in speech posture stabilization in response to a sudden tongue stretch perturbation. Given its relatively short latency (< 150 ms), the response could be driven by somatosensory feedback alone. The current study assessed this hypothesis by examining whether this response is induced in the absence of auditory feedback. We compared the response under two auditory conditions: with normal versus masked auditory feedback. Eleven participants were tested. They were asked to whisper the vowel /e/ for a few seconds. The tongue was stretched horizontally with step patterns of force (1 N during 1 s) using a robotic device. The articulatory positions were recorded using electromagnetic articulography simultaneously with the produced sound. The tongue perturbation was randomly and unpredictably applied in one-fifth of trials. The two auditory conditions were tested in random order. A quick compensatory response was induced in a similar way to the previous study. We found that the amplitudes of the compensatory responses were not significantly different between the two auditory conditions, either for the tongue displacement or for the produced sounds. These results suggest that the observed quick correction mechanism is primarily based on somatosensory feedback. This correction mechanism could be learned in such a way as to maintain the auditory goal on the sole basis of somatosensory feedback.
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Although there is no doubt from an empirical viewpoint that reflex mechanisms can contribute to tongue motor control in humans, there is limited neurophysiological evidence to support this idea. Previous results failing to observe any tonic stretch reflex in the tongue had reduced the likelihood of a reflex contribution in tongue motor control. The current study presents experimental evidence of a human tongue reflex in response to a sudden stretch while holding a posture for speech. The latency was relatively long (50 ms), which is possibly mediated through cortical-arc. The activation peak in a speech task was greater than in a non-speech task while background activation levels were similar in both tasks, and the peak amplitude in a speech task was not modulated by the additional task to react voluntarily to the perturbation. Computer simulations with a simplified linear mass-spring-damper model showed that the recorded muscle activation response is suited for the generation of tongue movement responses that were observed in a previous study with the appropriate timing when taking into account a possible physiological delay between reflex muscle activation and the corresponding force. Our results evidenced clearly that reflex mechanisms contribute to tongue posture stabilization for speech production.
Assuntos
Reflexo , Fala , Humanos , Eletromiografia , Equilíbrio Postural , Língua , Músculo Esquelético/fisiologiaRESUMO
We present a calibration system called Dried Water Column (DWC). It applies pressure on a sensor with a latex finger filled with water, which pressure is controlled with a water column. This is intended to mimic the way the deformable tongue mechanically interacts with the hard palate. We show that, once some specificities of the elastic/plastic behavior of the latex finger are taken into account, namely the softening due to Mullins Effect and the non-elastic deformation occurring above a certain pressure level, the DWC provides a reliable measure of the linear relation between the pressure and the output voltage of the sensor within the limited pressure range [0, 2.5 kPa]. Such a precise calibration would not be possible with a rigid actuator, which position on the sensor can dramatically influence the measures. Extrapolating the linear relationship thus determined to a larger pressure range compatible with speech production and swallowing ([0, 35 kPa]), is possible once it has been verified that the behavior of the sensor is linear over this pressure range. This can be done with any rigid or semi rigid actuator. This reliable calibration procedure can be easily reproduced in any laboratory, and can be applied to any pressure sensor.
Assuntos
Látex , Palato Duro , Humanos , Água , Calibragem , Pressão , Língua , DeglutiçãoRESUMO
In a study of whether somatosensory feedback related to articulatory configuration is involved in speech perception, 30 French-speaking adults performed a speech discrimination task in which vowel pairs along the French /u/ (rounded vowel requiring a small lip area) to /Å/ (rounded vowel associated with larger lip area) continuum were used as stimuli. Listeners had to perform the test in two conditions: with a 2-cm-diameter lip-tube in place (mimicking /Å/) and without the lip-tube (neutral lip position). Results show that, in the lip-tube condition, listeners perceived more stimuli as /Å/, in line with the proposal that an auditory-somatosensory interaction exists.
Assuntos
Doenças Labiais , Percepção da Fala , Humanos , Fonética , IdiomaRESUMO
OBJECTIVES: The study aims to better understand the rhythmic abilities of people who stutter and to identify which processes potentially are impaired in this population: (1) beat perception and reproduction; (2) the execution of movements, in particular their initiation; (3) sensorimotor integration. MATERIAL AND METHOD: Finger tapping behavior of 16 adults who stutter (PWS) was compared with that of 16 matching controls (PNS) in five rhythmic tasks of various complexity: three synchronization tasks - a simple 1:1 isochronous pattern, a complex non-isochronous pattern, and a 4 tap:1 beat isochronous pattern -, a reaction task to an aperiodic and unpredictable pattern, and a reproduction task of an isochronous pattern after passively listening. RESULTS: PWS were able to reproduce an isochronous pattern on their own, without external auditory stimuli, with similar accuracy as PNS, but with increased variability. This group difference in variability was observed immediately after passive listening, without prior motor engagement, and was not enhanced or reduced after several seconds of tapping. Although PWS showed increased tapping variability in the reproduction task as well as in synchronization tasks, this timing variability did not correlate significantly with the variability in reaction times or tapping force. Compared to PNS, PWS exhibited larger negative mean asynchronies, and increased synchronization variability in synchronization tasks. These group differences were not affected by beat hierarchy (i.e., "strong" vs. "weak" beats), pattern complexity (non-isochronous vs. isochronous) or presence versus absence of external auditory stimulus (1:1 vs. 1:4 isochronous pattern). Differences between PWS and PNS were not enhanced or reduced with sensorimotor learning, over the first taps of a synchronization task. CONCLUSION: Our observations support the hypothesis of a deficit in neuronal oscillators coupling in production, but not in perception, of rhythmic patterns, and a larger delay in multi-modal feedback processing for PWS.
Assuntos
Percepção Auditiva , Gagueira , Humanos , Adulto , Percepção Auditiva/fisiologia , Movimento/fisiologia , Tempo de Reação , Auscultação , CogniçãoRESUMO
Skeletal muscle modeling has a vital role in movement studies and the development of therapeutic approaches. In the current study, a Huxley-based model for skeletal muscle is proposed, which demonstrates the impact of impairments in muscle characteristics. This model focuses on three identified ions: H+, inorganic phosphate Pi, and Ca2+. Modifications are made to actin-myosin attachment and detachment rates to study the effects of H+ and Pi. Additionally, an activation coefficient is included to represent the role of calcium ions interacting with troponin, highlighting the importance of Ca2+. It is found that maximum isometric muscle force decreases by 9.5% due to a reduction in pH from 7.4 to 6.5 and by 47.5% in case of the combination of a reduction in pH and an increase of Pi concentration up to 30 mM, respectively. Then the force decline caused by a fall in the active calcium ions is studied. When only 15% of the total calcium in the myofibrillar space is able to interact with troponin, up to 80% force drop is anticipated by the model. The proposed fatigued-injured muscle model is useful to study the effect of various shortening velocities and initial muscle-tendon lengths on muscle force; in addition, the benefits of the model go beyond predicting the force in different conditions as it can also predict muscle stiffness and power. The power and stiffness decrease by 40% and 6.5%, respectively, due to the pH reduction, and the simultaneous accumulation of H+ and Pi leads to a 50% and 18% drop in power and stiffness.