Movement Coordination Research Articles

Collaborative Multi-Dynamic Pattern Modeling for Human Motion Prediction

The dynamic information of the joints, such as the movement amplitude, is critical for forecasting precise human joint trajectories. Existing methods adopt global modeling in which all joints are treated as a whole to extract features for movement coordination. Though global modeling can exploit hidden relationships between joints, it also inevitably introduces undesired trajectory dependencies, which weakens the dynamic information effects and simplifies the constraints and kinetics model of joints. Therefore, we propose a dynamic pattern-based collaborative modeling framework (DPnet) that contains a keyframe enhanced module (KEM) and multi-channel feature extractor blocks (MFE-block). The KEM tackles the discontinuity between the last frame of observation and the first predicted one by duplicating the decisive frame. The MFE-block utilizes a multi-channel graph structure to enrich the dynamic information effects and recessive constraints of joints. To distinguish the dynamic information of each joint, we calculate the movement amplitude of the joints and propose three dynamic patterns, including active, inactive, and static patterns. We also propose a dynamic pattern-guided feature extractor (DP-FE) to alleviate the trajectory dependencies between joints with different dynamic patterns. We evaluate our approach on three standard benchmark datasets, including H3.6M [8], CMU-Mocap [44], and 3DPW [45]. Our approach achieves impressive results in both short-term and long-term predictions, confirming its effectiveness and efficiency.

Analysis of motion characteristics of lower limb exoskeleton robot

To address the issue of motion coordination in lower limb exoskeleton rehabilitation robots, and to meet the basic characteristics of ergonomics and human kinematics, a humanoid design was adopted to design a lower limb exoskeleton rehabilitation robot. The Denavit- Hartenberg (D-H) mathematical model of the lower limb exoskeleton rehabilitation robot was established, and the motion characteristics of each joint were analyzed to obtain the D-H parameters during the motion process. The motion characteristics were analyzed from the perspectives of forward kinematics and inverse kinematics. The variation law of motion parameters during the motion process was obtained, and simulation analysis of the motion characteristics was performed. The results show that the maximum center of mass velocity is 0.45 m/s, which is reached within 0.8 seconds. After that, the velocity decreases, with a range of approximately -0.2 m/s to 0.55 m/s. It can be seen that the displacement and velocity changes of the exoskeleton robot legs are relatively stable, which meets the design requirements.

A case of pure apraxia of speech after left hemisphere stroke: behavioral findings and neural correlates.

Apraxia of speech (AOS) is a motor speech disorder impairing the coordination of complex articulatory movements needed to produce speech. AOS typically co-occurs with a non-fluent aphasia, or language disorder, making it challenging to determine the specific brain structures that cause AOS. Cases of pure AOS without aphasia are rare but offer the best window into the neural correlates that support articulatory planning. The goal of the current study was to explore patterns of apraxic speech errors and their underlying neural correlates in a case of pure AOS. A 67-year-old right-handed man presented with severe AOS resulting from a fronto-insular lesion caused by an ischemic stroke. The participant's speech and language were evaluated at 1-, 3- and 12-months post-onset. High resolution structural MRI, including diffusion weighted imaging, was acquired at 12 months post-onset. At the first assessment, the participant made minor errors on the Comprehensive Aphasia Test, demonstrating mild deficits in writing, auditory comprehension, and repetition. By the second assessment, he no longer had aphasia. On the Motor Speech Evaluation, the severity of his AOS was initially rated as 5 (out of 7) and improved to a score of 4 by the second visit, likely due to training by his SLP at the time to slow his speech. Structural MRI data showed a fronto-insular lesion encompassing the superior precentral gyrus of the insula and portions of the inferior and middle frontal gyri and precentral gyrus. Tractography derived from diffusion MRI showed partial damage to the frontal aslant tract and arcuate fasciculus along the white matter projections to the insula. This pure case of severe AOS without aphasia affords a unique window into the behavioral and neural mechanisms of this motor speech disorder. The current findings support previous observations that AOS and aphasia are dissociable and confirm a role for the precentral gyrus of the insula and BA44, as well as underlying white matter in supporting the coordination of complex articulatory movements. Additionally, other regions including the precentral gyrus, Broca's area, and Area 55b are discussed regarding their potential role in successful speech production.

Motion from Shape Change

We consider motion effected by shape change. Such motions are ubiquitous in nature and the human made environment, ranging from single cells to platform divers and jellyfish. The shapes may be immersed in various media ranging from the very viscous to air and nearly inviscid fluids. In the absence of external forces these settings are characterized by constant momentum. We exploit this in an algorithm which takes a sequence of changing shapes, say, as modeled by an animator, as input and produces corresponding motion in world coordinates. Our method is based on the geometry of shape change and an appropriate variational principle. The corresponding Euler-Lagrange equations are first order ODEs in the unknown rotations and translations and the resulting time stepping algorithm applies to all these settings without modification as we demonstrate with a broad set of examples.

Quantum Dynamical Investigation of Dihydrogen-Hydride Exchange in a Transition-Metal Polyhydride Complex.

The ongoing shift toward clean, sustainable energy is a primary driving force behind hydrogen fuel research. Safe and effective storage of hydrogen is a major challenge (particularly for mobile applications) and requires a detailed understanding of the atomic level interactions of hydrogen with its host materials. The light mass of hydrogen, however, implies that quantum effects are important, so a quantum dynamical treatment is required to properly account for these effects in computational simulations. As one such example, we describe herein the hydrogen exchange dynamics between a hydride and a dihydrogen ligand in the [FeH(H2)(PH3)4]+ model complex. A global three-dimensional (3D) potential energy surface (PES) was constructed by fitting to and interpolating from a discrete set of grid points computed using density functional theory; exact quantum dynamical calculations were then carried out on the 3D PES using discrete variable representation basis sets. Energy levels and their quantum tunneling splittings were computed up to 3000 cm-1 above the ground state. Within that energy range, all three fundamentals have been identified using wave function plots, as well as the first three overtones of the exchange (reaction coordinate) motion and several of its combination bands. From the tunneling splittings, the Boltzmann-averaged tunneling rates were computed. The Arrhenius plot of the total exchange rate shows a clear transition around 150 K, below which the activation energy is essentially zero and above which it is less than half of the electronic structure barrier. This indicates that exchange rates are governed by quantum tunneling throughout the relevant temperature range with the low-temperature regime dominated by a single quantum (ground) state. This work is the first-ever fully quantum dynamical study to investigate the hydrogen exchange dynamics between hydride and dihydrogen ligands coordinated to a transition-metal complex.

Asymmetrical distribution of roof microseismicity and its application to roof control of a deep longwall panel

Deep mining is widely carried out across the world. Due to large cover depth, both stress magnitude and fracture development are greatly enlarged, increasing the complexity in mining conditions. Correspondingly, a series of ground control problems emerge in deep coal mines, such as face collapsing, roof falling and support jamming. This study mainly focusses on the variation in roof activity along face length direction, which helps to strengthen roof control of a deep longwall panel. Geological radar detection reveals that the development of mining-induced fractures present an increasing trend from the maingate to tailgate side, implying the variation in roof activity along face length direction. Microseismic (MS) monitoring is moreover conducted, with which both spatial distribution and dynamic evolution of MS events in roof strata are thoroughly analyzed. Due to stronger influence provided by fault structures, the concentration of MS number mainly occurs to the tailgate section. Thus, roof microseismicity is brisker in the referred section, accounting for 63.7% of the total events. The sensitivity of MS energy to fault structures is weaker than that of MS number. Energy concentration can be observed in the whole panel width. In the maingate section, the energy proportion reaches 44.1%, indicating stronger roof microseismicity. Such asymmetrical distribution in roof microseismicity is sensitive to fault activation, fracture influence and mining disturbance. The location of fault structures, spatial variation in fracture parameters and the difference in stress rotation characteristics contribute to asymmetrical distribution in roof microseismicity on two sides of the target panel. Based on MS characteristics, a coordinative movement method is innovatively proposed for hydraulic supports, which weakens cyclic disturbance of support movement on roof strata at the face area. The method is proved to be effective by the improvement in roof stability and mining efficiency.

Вікові особливості функціонування вестибулярного аналізатора

The main importance of the vestibular system is to maintain the vertical position of a person and ensure the coordination of movements. The peculiarity of the structure of the vestibular apparatus prompts it to be constantly in a state of spontaneous activity. This is due to the effect on it of afferent impulses that come from the labyrinths to the vestibular centers. With proper excitability, this information indicates the normal course of physiological reactions. In this regard, persons with normal vestibular sensitivity have not experience symptoms of impaired vestibular function. However, in cases where this spontaneous impulse changes due to the influence of external and internal factors, and the inhibition mechanisms are not sufficiently activated, symptoms appear that indicate the insufficiency of vestibular afferentation compensation processes and are manifestations of increased excitability of the vestibular analyzer. It is known from literary sources that increased sensitivity of the vestibular analyzer is widespread among the population. At the same time, there is a tendency to increase the prevalence of increased sensitivity of the vestibular analyzer among people of different ages. The review presents modern views on the peculiarities of the functional activity of the vestibular analyzer in different age periods. We are describe features of development, structure and reflex activity to ensure the vital activity of the organism from the beginning of intrauterine development to old age. We considered functions of ensuring a sense of position and movement of the body in space, maintaining both a posture at rest and during movement in different age periods. We also analyzed data on the frequency of symptoms of a vestibular analyzer disorder.

Premotor function in interpersonal bimanual coordination: Neural responses to varying frequencies and spatio–temporal relationships

BackgroundInterpersonal movement coordination is an important aspect of daily life. Behavioral studies have found that rhythmic bimanual coordination of movement is mainly influenced by two factors, spatio–temporal relationship and frequency of movements. How these factors affect action coordination at the neural level needs further exploration. The current study used a factor design to investigate the brain basis of movement coordination under various spatiotemporal relationships and frequencies, as well as their intricate interaction. MethodsParticipants were asked to perform symmetric or alternating hand movements under conditions of different spatio–temporal relationships (symmetric, alternating) and frequencies. A multi–channel, continuous wave, functional near–infrared spectral (fNIRS) imaging instrument was used to monitor hemodynamic activity while 16 pairs of volunteers performed the task. ResultsBehaviorally, as indexed by phase locking value, movements were more stable in symmetric mode than in alternate mode. With increasing frequency, symmetric mode became more unstable; in contrast, alternating mode became more stable at higher frequencies, suggesting phase transition. Activation in brain regions of interest was much stronger in symmetric mode as compared with alternate mode. In alternate mode, but not symmetric mode, [HbO] varied with frequency. ConclusionInterpersonal bimanual coordination involves activity in premotor areas (premotor cortex, supplementary motor area, and frontal eye fields). More oxygen is consumed in these regions in alternating mode than in symmetric mode.

Inhibiting cholinergic signalling in the cerebellar interpositus nucleus impairs motor behaviour.

The role of neuromodulators in the cerebellum is not well understood. In particular, the behavioural significance of the cholinergic system in the cerebellum is unknown. To investigate the importance of cerebellar cholinergic signalling in behaviour, we infused acetylcholine receptor antagonists, scopolamine and mecamylamine, bilaterally into the rat cerebellum (centred on interpositus nucleus) and observed the motor effects through a battery of behavioural tests. These tests included unrewarded behaviour during open field exploration and a horizontal ladder walking task and reward-based beam walking and pellet reaching tasks. Infusion of a mix of the antagonists did not impair motor learning in the horizontal ladder walking or the reaching task but reduced spontaneous movement during open field exploration, impaired coordination during beam walking and ladder walking, led to fewer reaches in the pellet reaching task, slowed goal-directed reaching behaviour and reduced reward pellet consumption in a free access to food task. Infusion of the muscarinic antagonist scopolamine on its own resulted in deficits in motor performance and a reduction in the number of reward pellets consumed in the free access to food task. By contrast, infusion of the nicotinic antagonist mecamylamine on its own had no significant effect on any task, except beam walking traversal time, which was reduced. Together, these data suggest that acetylcholine in the cerebellar interpositus nucleus is important for the execution and coordination of voluntary movements mainly via muscarinic receptor signalling, especially in relation to reward-related behaviour.

Light and Affordable Vision System for Mouth Opening–Closing Movement Deviation Assessment in Women with Mild Temporomandibular Joint Disorder

(1) Background: This paper aims to demonstrate a novel and, in terms of application, universal method of the qualitative and quantitative assessment of mandibular movement. (2) Methods: Mandibular movements are recorded by a mono-vision system where a digital camera is fixed on a special extension arm attached to the patient’s head. The described method was used to check lateral deviations in 25 women with mild temporomandibular joint disorder (TMD) and in 25 women from the control group. The maximum deviation (MAX) and mean deviation (MSE) parameters were examined. In addition, the occurrence of parafunctions and joint clicking in the temporomandibular joints was checked in the examined individuals. (3) Results: Among the women with mild TMD, a significantly higher MSE parameter was found compared to the control group. Joint clicking also occurred significantly more frequently. The parameter of MAX did not differ significantly between the examined groups. (4) Conclusions: In women with mild TMD, a lack of movement coordination between the right and left joints can be observed. The method’s high availability combined with simple use makes it a valuable tool for experts in different fields who diagnose and treat stomatognathic system disorders.

Optimal Geometry and Motion Coordination for Multisensor Target Tracking with Bearings-Only Measurements.

This paper focuses on the optimal geometry and motion coordination problem of mobile bearings-only sensors for improving target tracking performance. A general optimal sensor-target geometry is derived with uniform sensor-target distance using D-optimality for arbitrary n (n≥2) bearings-only sensors. The optimal geometry is characterized by the partition cases dividing n into the sum of integers no less than two. Then, a motion coordination method is developed to steer the sensors to reach the circular radius orbit (CRO) around the target with a minimum sensor-target distance and move with a circular formation. The sensors are first driven to approach the target directly when outside the CRO. When the sensor reaches the CRO, they are then allocated to different subsets according to the partition cases through matching the optimal geometry. The sensor motion is optimized under constraints to achieve the matched optimal geometry by minimizing the sum of the distance traveled by the sensors. Finally, two illustrative examples are used to demonstrate the effectiveness of the proposed approach.

Measuring upper limb active joint position sense: Introducing a new clinical tool - The Upper Limb Proprioception Reaching Test

BackgroundProprioception is our sense of body awareness, including the sub-category of active joint position sense (AJPS). AJPS is fundamental to joint stability and movement coordination. Despite its importance, there remain few confident ways to measure upper limb AJPS in a clinic. ObjectiveTo assess a new AJPS clinical tool, the Upper Limb Proprioception Reaching Test (PRO-Reach; seven targets), for discriminant validity, intra-rater and absolute reliability. DesignCross-sectional measurement study. MethodsSeventy-five healthy participants took part in a single session with 2 consecutive evaluations (E1 and E2) (within-day reliability). Twenty participants were randomly selected to perform a dominant shoulder fatigue protocol (discriminant validity), whereafter a third evaluation was repeated (E3). The PRO-Reach was analyzed with paired t tests (discriminant validity), intra-class correlation coefficients (ICCs) and minimal detectable change [MDC]) (intra-rater: within-day and between-trial relative and absolute reliability). ResultsThe PRO-Reach supports moderate (mostly superior targets) to excellent (mostly inferior targets) reliability. Between-trial ICCs (T1/T2/T3) varied between 0.72 and 0.90, and within-day (E1/E2) ICCs between 0.45 and 0.72, with associated MDC95 values (3.9–5.0 cm). The overall scores (seven targets) supported the strongest within-day reliability (ICC = 0.77). The inferior targets demonstrated the highest between-trial and within-day reliability (ICCs = 0.90 and 0.72). A fatigue effect was found with the superior and superior-lateral targets (P < .05). ConclusionsThe inferior targets and overall scores demonstrate the strongest reliability. The use of the PRO-Reach tool may be suitable for clinical use upon further psychometric testing amongst pathological populations. Level of evidenceLevel III cross-sectional study.

Learning to manipulate a whip with simple primitive actions – A simulation study

This simulation study investigated whether a 4-degrees-of-freedom (DOF) arm could strike a target with a 50-DOF whip using a motion profile similar to discrete human movements. The interactive dynamics of the multi-joint arm was modeled as a constant joint-space mechanical impedance, with values derived from experimental measurement. Targets at various locations could be hit with a single maximally smooth motion in joint-space coordinates. The arm movements that hit the targets were identified with fewer than 250 iterations. The optimal actions were essentially planar arm motions in extrinsic task-space coordinates, predominantly oriented along the most compliant direction of both task-space and joint-space mechanical impedances. Of the optimal movement parameters, striking a target was most sensitive to movement duration. This result suggests that the elementary actions observed in human motor behavior may support efficient motor control in interaction with a dynamically complex object.

Geometric framework for statistical analysis of eye tracking heat maps, with application to a tobacco waterpipe study

Health warning labels have been found to increase awareness of the harmful effects of tobacco products. An eye tracking study was conducted to determine the optimal placement and type of a health warning label on tobacco waterpipes. Participants viewed images that contained one of (1) four waterpipes, (2) three different types of warning labels, (3) placed in three locations. Typically, statistical analysis of eye tracking data is conducted based on summary statistics such as total dwell time, duration score, and number of visits to an area of interest. However, these summary statistics fail to capture the complete variability in a participant's eye movement. Instead, we propose to estimate heat maps defined on the entire image domain using the raw two-dimensional coordinates of eye movement via kernel density estimation. For statistical analysis of heat maps, we adopt the Fisher–Rao Riemannian geometric framework, which enables computationally efficient comparisons of heat maps, statistical summarization and exploration of variability in a sample of heat maps, and metric-based hierarchical clustering. We apply this framework to eye tracking data from the tobacco waterpipe study and comment on the results in the context of the optimal placement and type of health warning labels on tobacco waterpipes.

IDENTIFICATION AND QUANTITATION OF FEXOFENADINE HYDROCHLORIDE IN MODEL ORAL DROPS

Relevance. Fexofenadine hydrochloride is a representative of the III generation of histamine H1 receptor blockers, therefore, it is not characterized by the disadvantages of antihistamines, such as: suppression of the central nervous system, cardiotoxic effect, headache, impaired coordination of movements, photosensitivity. Analysis of fexofenadine hydrochloride was performed using UV spectroscopy. The purpose of the study – development of a new analytical method for the qualitative and quantitative identification of fixofenadine in drops for in-ternal use. Material and methods. The study used: fexofenadine, sodium hydroxide, water for injection, UV spectrophotometer type SF-104. Results and conclusions. A method for the qualitative and quantitative determination of fexofenadine hydrochloride in model drops for internal use by the SPS method has been proposed. This method meets the requirements of OFS 1.1.0012.15 Validation of analytical methods, in terms of indica-tors: linearity and analytical area, correctness, precision.

Pearls & Oy-sters: Cognitive and Affective Dysfunction Caused by a Small Cerebellar Hemangioblastoma.

The primary function of the cerebellum is the coordination and regulation of movement; therefore, cerebellar tumors usually present with ataxia, dysarthria, and vertigo. Large tumors also cause elevated intracranial pressure that may lead to a disturbance of consciousness. Furthermore, it has become increasingly evident that the cerebellum plays a substantial role in cognitive and affective processing. A 44-year-old female patient presented with one-month history of depression and flat affect. She had no cerebellar symptoms including no coordination dysfunction or dysarthria. Cognitive function tests revealed impairments in attention, execution, and processing speed. Hamilton Depression Scale and Hospital Anxiety Depression Scale indicated moderate-to-severe depression. Magnetic resonance (MR) imaging revealed a 7-mm enhancing lesion in the culmen of the cerebellar vermis with surrounding edema. Technetium-99m ethyl cysteinate dimer single-photon emission tomography (SPECT) showed hypoperfusion in the left frontal lobe. Although she was initially treated with corticosteroids for presumed sero-negative autoimmune encephalitis, her symptoms persisted. She then underwent cerebellar lesion resection. The histological diagnosis was hemangioblastoma. The patient's symptoms dramatically improved within 1 week of resection, including improved batteries for cognitive function and depression. Complete regression of cerebellar edema and left frontal lobe hypoperfusion were observed on MR and SPECT images, respectively. This case reiterates the crucial influence of the cerebellum on cognitive and affective function. Moreover, cognitive dysfunction may be masked in cases with focal cerebellar symptoms or elevated intracranial pressure, and consequently, not adequately evaluated.

THE INFLUENCE OF AGILITY INDICATORS ON FORMATION OF VOCATIONAL READINESS IN LAW ENFORCEMENT OFFICERS

The experience of warfare in Ukraine proves the importance of increasing the degree of psychophysical readiness in law enforcement officers. The aim - to determine the significance of the main components of physical readiness of law enforcement officers for productive work performing. Material and methods: Servicemen (n=368) of the National Guard of Ukraine were interviewed. Spearman's rank correlation analysis of indicators` interrelation was carried out. The opinions of experts and beginners reliably differed on a number of indicators. Coordination of movements was significantly correlated with relatively the largest number of indicators of physical readiness, as well as psychological performance of servicemen. It has been established that agility is related to concentration, endurance, span and switching of attention. Conclusions: For the successful professional growth of the students of educational institutions of the National Guard of Ukraine, it is necessary to develop their agility, and especially coordination of movements. It is associated with improving the speed and strength of the officers of the National Guard of Ukraine, as well as attention and logical thinking.

PECULIARITIES OF FORENSIC HANDWRITING EXAMINATION OF SIGNATURES MADE BY PERSONS OF ALL AGES UNDER THE INFLUENCE OF CONFOUNDING FACTORS

The article is devoted to the features of forensic handwriting examination of signatures made by persons of different ages under the influence of confounding factors. The classification of confounding factors and their influence on signs of handwriting and signatures of a person is considered. The peculiarities of signatures and samples of different age groups were studied, namely: transcription of the signature, degree of coordination, complexity and coherence of movements, the pace of writing, size, inclination, arrangement and acceleration of elements, degree and character of pressure and direction of the baseline of the signature. It is shown that three classes of tasks are distinguished in the forensic handwriting examination: identification (establishing the identity of the executor of the object of handwriting), diagnostic (resolving questions about the conditions of execution of the handwritten text, record or signature), classification (related to the assignment of the executor of the handwriting to certain groups, in particular by gender and age). A comparative analysis of the results of signature studies by different age groups was carried out. It is noted that the stability of signs of handwriting and signatures is relative. A person’s handwriting can undergo changes depending on various reasons, including those caused by the ageing of the body. In addition, the persistence of characteristic features is also influenced by diseases that are characteristic of the elderly and senile.

The role of ipsilateral motor network in upper limb movement.

The execution of voluntary movements is primarily governed by the cerebral hemisphere contralateral to the moving limb. Previous research indicates that the ipsilateral motor network, comprising the primary motor cortex (M1), supplementary motor area (SMA), and premotor cortex (PM), plays a crucial role in the planning and execution of limb movements. However, the precise functions of this network and its interplay in different task contexts have yet to be fully understood. Twenty healthy right-handed participants (10 females, mean age 26.1 ± 4.6years) underwent functional MRI scans while performing biceps brachii representations such as bilateral, unilateral flexion, and bilateral flexion-extension. Ipsilateral motor evoked potentials (iMEPs) were obtained from the identical set of participants in a prior study using transcranial magnetic stimulation (TMS) targeting M1 while employing the same motor tasks. The voxel time series was extracted based on the region of interest (M1, SMA, ventral PM and dorsal PM). Directed functinal connectivity was derived from the extracted time series using time-resolved partial directed coherence. We found increased connectivity from left-PMv to both sides M1, as well as right-PMv to both sides SMA, in unilateral flexion compared to bilateral flexion. Connectivity from left M1 to left-PMv, and left-SMA to right-PMd, also increased in both unilateral flexion and bilateral flexion-extension compared to bilateral flexion. However, connectivity between PMv and right-M1 to left-PMd decreased during bilateral flexion-extension compared to unilateral flexion. Additionally, during bilateral flexion-extension, the connectivity from right-M1 to right-SMA had a negative relationship with the area ratio of iMEP in the dominant side. Our results provide corroborating evidence for prior research suggesting that the ipsilateral motor network is implicated in the voluntary movements and underscores its involvement in cognitive processes such as movement planning and coordination. Moreover, ipsilateral connectivity from M1 to SMA on the dominant side can modulate the degree of ipsilateral M1 activation during bilateral antagonistic contraction.

Fine-Grained Complexity Analysis of Multi-Agent Path Finding on 2D Grids

Multi-Agent Path Finding (MAPF) is a fundamental motion coordination problem arising in multi-agent systems with a wide range of applications. The problem's intractability has led to extensive research on improving the scalability of solvers for it. Since optimal solvers can struggle to scale, a major challenge that arises is understanding what makes MAPF hard. We tackle this challenge through a fine-grained complexity analysis of time-optimal MAPF on 2D grids, thereby closing two gaps and identifying a new tractability frontier. First, we show that 2-colored MAPF, i.e., where the agents are divided into two teams, each with its own set of targets, remains NP-hard. Second, for the flowtime objective (also called sum-of-costs), we show that it remains NP-hard to find a solution in which agents have an individually optimal cost, which we call an individually optimal solution. The previously tightest results for these MAPF variants are for (non-grid) planar graphs. We use a single hardness construction that replaces, strengthens, and unifies previous proofs. We believe that it is also simpler than previous proofs for the planar case as it employs minimal gadgets that enable its full visualization in one figure. Finally, for the flowtime objective, we establish a tractability frontier based on the number of directions agents can move in. Namely, we complement our hardness result, which holds for three directions, with an efficient algorithm for finding an individually optimal solution if only two directions are allowed. This result sheds new light on the structure of optimal solutions, which may help guide algorithm design for the general problem.