Gait asymmetry and symptom laterality in Parkinson's disease: two of a kind?

BACKGROUND: The laterality of motor symptoms is considered a key feature of Parkinson's disease (PD). Here, we investigated whether gait and turning asymmetry coincided with symptom laterality as determined by the MDS-UPRDS part III and whether it was increased compared to healthy controls (HC). METHODS: We analyzed the asymmetry of gait and turning with and without a cognitive dual task (DT) using motion capture systems and wearable sensors in 97 PD patients mostly from Hoehn & Yahr stage II and III and 36 age-matched HC. We also assessed motor symptom asymmetry using the bilateral sub-items of the MDS-UPDRS-III. Finally, we examined the strength of the association between gait asymmetry and symptom laterality. RESULTS: Participants with PD had increased gait but not more turning asymmetry compared to HC (p < 0.05). Only 53.7% of patients had a shorter step length on the more affected body side as determined by the MDS-UPDRS-III. Also, 54% took more time and 29% more steps during turns toward the more affected side. The degree of asymmetry in the different domains did not correlate with each other and was not influenced by DT-load. CONCLUSIONS: We found a striking mismatch between the side and the degree of asymmetry in different motor domains, i.e., in gait, turning, and distal symptom severity in individuals with PD. We speculate that motor execution in different body parts relies on different neural control mechanisms. Our findings warrant further investigation to understand the complexity of gait asymmetry in PD.

Deep brain stimulation of the subthalamic nucleus restores spatial reversal learning in patients with Parkinson's disease.

Spatial learning and navigation are supported by distinct memory systems in the human brain such as the hippocampus-based navigational system and the striatum-cortex-based system involved in motor sequence, habit and reversal learning. Here, we studied the role of subthalamic circuits in hippocampus-associated spatial memory and striatal-associated spatial reversal learning formation in patients with Parkinson's disease, who underwent a deep brain stimulation of the subthalamic nucleus. Deep brain stimulation patients (Parkinson's disease-subthalamic nucleus: n = 26) and healthy subjects (n = 15) were tested in a novel experimental spatial memory task based on the Morris water maze that assesses both hippocampal place memory as well as spatial reversal learning. All subjects were trained to navigate to a distinct spatial location hidden within the virtual environment during 16 learning trials in a subthalamic nucleus Stim-On condition. Patients were then randomized into two groups with either a deep brain stimulation On or Off condition. Four hours later, subjects were retested in a delayed recall and reversal learning condition. The reversal learning was realized with a new hidden location that should be memorized during six consecutive trials. The performance was measured by means of an index indicating the improvement during the reversal learning. In the delayed recall condition, neither patients, healthy subjects nor the deep brain stimulation On- versus Off groups showed a difference in place memory performance of the former trained location. In the reversal learning condition, healthy subjects (reversal index 2.0) and patients in the deep brain stimulation On condition (reversal index 1.6) showed a significant improvement. However, patients in the deep brain stimulation Off condition (reversal index 1.1) performed significantly worse and did not improve. There were no differences between all groups in a final visual guided navigation task with a visible target. These results suggest that deep brain stimulation of subthalamic nucleus restores spatial reversal learning in a virtual navigation task in patients with Parkinson's disease and gives insight into the neuromodulation effects on cognition of subthalamic circuits in Parkinson's disease.

Effect of Thalamic versus Pallidal Deep Brain Stimulation on Head Tremor in Dystonic and Essential Tremor Patients-A Retrospective Video-Blinded Study.

BACKGROUND: Head tremor is common in dystonia syndromes and difficult to treat. Deep brain stimulation (DBS) is a therapeutic option in medically-refractory cases. In most DBS-centers, the globus pallidus internus (GPi) is targeted in patients with predominant dystonia and the ventrointermediate nucleus of the thalamus (Vim) in predominant tremor. The aim of the study was to evaluate the effect of GPi- versus Vim-DBS in dystonic or essential head tremor. METHODS: All patients with dystonia or essential tremor (ET) (n = 381) who underwent DBS surgery at our institution between 1999 and 2020 were screened for head tremor in our database according to predefined selection criteria. Of the 33 patients meeting inclusion criteria tremor and dystonia severity were assessed at baseline, short- (mean 10 months) and long-term follow-up (41 months) by two blinded video-raters. RESULTS: Twenty-two patients with dystonic head tremor received either GPi- (n = 12) or Vim-stimulation (n = 10), according to the prevailing clinical phenotype. These two groups were compared with 11 patients with ET, treated with Vim-stimulation. The reduction in head tremor from baseline to short- and long-term follow-up was 60-70% and did not differ significantly between the three groups. CONCLUSIONS: GPi-DBS effectively and sustainably reduced head tremor in idiopathic dystonia. The effect was comparable to the effect of Vim-DBS on head tremor in dystonia patients with predominant limb tremor and to the effect of Vim-DBS on head tremor in ET.

Towards a better understanding of anticipatory postural adjustments in people with Parkinson's disease.

INTRODUCTION: Previous studies have shown that anticipatory postural adjustments (APAs) are altered in people with Parkinson's disease but its meaning for locomotion is less understood. This study aims to investigate the association between APAs and gait initiation, gait and freezing of gait and how a dynamic postural control challenging training may induce changes in these features. METHODS: Gait initiation was quantified using wearable sensors and subsequent straight walking was assessed via marker-based motion capture. Additionally, turning and FOG-related outcomes were measured with wearable sensors. Assessments were conducted one week before (Pre), one week after (Post) and 4 weeks after (Follow-up) completion of a training intervention (split-belt treadmill training or regular treadmill training), under single task and dual task (DT) conditions. Statistical analysis included a linear mixed model for training effects and correlation analysis between APAs and the other outcomes for Pre and Post-Pre delta. RESULTS: 52 participants with Parkinson's disease (22 freezers) were assessed. We found that APA size in the medio-lateral direction during DT was positively associated with gait speed (p<0.001) and stride length (p<0.001) under DT conditions at Pre. The training effect was largest for first step range of motion and was similar for both training modes. For the associations between changes after the training (pooled sample) medio-lateral APA size showed a significant positive correlation with first step range of motion (p = 0.033) only in the DT condition and for the non-freezers only. CONCLUSIONS: The findings of this work revealed new insights into how APAs were not associated with first step characteristics and freezing and only baseline APAs during DT were related with DT gait characteristics. Training-induced changes in the size of APAs were related to training benefits in the first step ROM only in non-freezers. Based on the presented results increasing APA size through interventions might not be the ideal target for overall improvement of locomotion.

Re-emergent Tremor in Parkinson's Disease: Evidence of Pathologic ß and Prokinetic γ Activity.

BACKGROUND: Re-emergent tremor is characterized as a continuation of resting tremor and is often highly therapy refractory. This study examines variations in brain activity and oscillatory responses between resting and re-emergent tremors in Parkinson's disease. METHODS: Forty patients with Parkinson's disease (25 males, mean age, 66.78 ± 5.03 years) and 40 age- and sex-matched healthy controls were included in the study. Electroencephalogram and electromyography signals were simultaneously recorded during resting and re-emergent tremors in levodopa on and off states for patients and mimicked by healthy controls. Brain activity was localized using the beamforming technique, and information flow between sources was estimated using effective connectivity. Cross-frequency coupling was used to assess neuronal oscillations between tremor frequency and canonical frequency oscillations. RESULTS: During levodopa on, differences in brain activity were observed in the premotor cortex and cerebellum in both the patient and control groups. However, Parkinson's disease patients also exhibited additional activity in the primary sensorimotor cortex. On withdrawal of levodopa, different source patterns were observed in the supplementary motor area and basal ganglia area. Additionally, levodopa was found to suppress the strength of connectivity (P < 0.001) between the identified sources and influence the tremor frequency-related coupling, leading to a decrease in ß (P < 0.001) and an increase in γ frequency coupling (P < 0.001). CONCLUSIONS: Distinct variations in cortical-subcortical brain activity are evident in tremor phenotypes. The primary sensorimotor cortex plays a crucial role in the generation of re-emergent tremor. Moreover, oscillatory neuronal responses in pathological ß and prokinetic γ activity are specific to tremor phenotypes. © 2024 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

How to Use the New European Academy of Neurology/Movement Disorder Society European Section Guideline for Invasive Therapies in Parkinson's Disease.

BACKGROUND: The decision to choose invasive treatments for Parkinson's disease (PD) is complex and needs careful consideration. OBJECTIVES: Although the recommendations of the European Academy of Neurology/Movement Disorder Society European Section guideline for invasive therapies of PD are useful, the different clinical profiles of people with PD who seek advice for possible invasive therapy need further attention. METHODS AND RESULTS: Here we describe 8 clinical standard situations of people with PD unsatisfied with their current oral treatment where invasive therapies may be considered. These are PD patients presenting with the following symptoms: (1) severe motor fluctuations, (2) beginning of levodopa-responsive fluctuations, severe tremor at (3) young or (4) advanced age, (5) impulse control disorders and related behavioral disorders, (6) hallucinations and psychosis, (7) minimal cognitive impairment or mild dementia, and (8) patients in need of palliative care. For some of these conditions, evidence at lower level or simple clinical considerations exist. CONCLUSIONS: There are no one-fits-all answers, but physician and patient should discuss each option carefully considering symptom profile, psychosocial context, availability of therapy alternatives, and many other factors. The current paper outlines our proposed approach to these circumstances.

Management of Impulse Control and Related Disorders in Parkinson's Disease: An Expert Consensus.

BACKGROUND: Impulse-control and related behavioral disorders (ICBDs) significantly impact the lives of Parkinson's disease (PD) patients and caregivers, with lasting consequences if undiagnosed and untreated. While ICBD pathophysiology and risk factors are well-studied, a standardized severity definition and treatment evidence remain elusive. OBJECTIVE: This work aimed to establish international expert consensus on ICBD treatment strategies. To comprehensively address diverse treatment availabilities, experts from various continents were included. METHODS: From 2021 to 2023, global movement disorders specialists engaged in a Delphi process. A core expert group initiated surveys, involving a larger panel in three iterations, leading to refined severity definitions and treatment pathways. RESULTS: Experts achieved consensus on defining ICBD severity, emphasizing regular PD patient screenings for early detection. General treatment recommendations focused on continuous monitoring, collaboration with significant others, and seeking specialist advice for legal or financial challenges. For mild to severe ICBDs, gradual reduction in dopamine agonists was endorsed, followed by reductions in other PD medications. Second-line treatment strategies included diverse approaches like reversing the last medication change, cognitive behavior therapy, subthalamic nucleus deep brain stimulation, and specific medications like quetiapine, clozapine, and antidepressants. The panel reached consensus on distinct treatment pathways for punding and dopamine dysregulation syndrome, formulating therapy recommendations. Comprehensive discussions addressed management strategies for the exacerbation of either motor or non-motor symptoms following the proposed treatments. CONCLUSION: The consensus offers in-depth insights into ICBD management, presenting clear severity criteria and expert consensus treatment recommendations. The study highlights the critical need for further research to enhance ICBD management. © 2024 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

The role of the motor thalamus in deep brain stimulation for essential tremor.

The advent of next-generation technology has significantly advanced the implementation and delivery of Deep Brain Stimulation (DBS) for Essential Tremor (ET), yet controversies persist regarding optimal targets and networks responsible for tremor genesis and suppression. This review consolidates key insights from anatomy, neurology, electrophysiology, and radiology to summarize the current state-of-the-art in DBS for ET. We explore the role of the thalamus in motor function and describe how differences in parcellations and nomenclature have shaped our understanding of the neuroanatomical substrates associated with optimal outcomes. Subsequently, we discuss how seminal studies have propagated the ventral intermediate nucleus (Vim)-centric view of DBS effects and shaped the ongoing debate over thalamic DBS versus stimulation in the posterior subthalamic area (PSA) in ET. We then describe probabilistic- and network-mapping studies instrumental in identifying the local and network substrates subserving tremor control, which suggest that the PSA is the optimal DBS target for tremor suppression in ET. Taken together, DBS offers promising outcomes for ET, with the PSA emerging as a better target for suppression of tremor symptoms. While advanced imaging techniques have substantially improved the identification of anatomical targets within this region, uncertainties persist regarding the distinct anatomical substrates involved in optimal tremor control. Inconsistent subdivisions and nomenclature of motor areas and other subdivisions in the thalamus further obfuscate the interpretation of stimulation results. While loss of benefit and habituation to DBS remain challenging in some patients, refined DBS techniques and closed-loop paradigms may eventually overcome these limitations.

The Challenge of Choosing the Right Stimulation Target for Dystonic Tremor-A Series of Instructive Cases.

Background: Thalamic deep brain stimulation (DBS) is established for medically refractory tremor syndromes and globus pallidus stimulation (GPi-DBS) for medically refractory dystonia syndromes. For combined tremor and dystonia syndromes, the best target is unclear. Objectives: We present four patients with two different profiles whose clinical course demonstrates that our current analysis of clinical symptomatology is not a sufficient predictor of surgical success. Methods: Outcome parameters were assessed with observer-blinded video ratings and included the Fahn-Tolosa-Marin-Tremor Rating Scale (FTM-TRS) and the Unified Dystonia Rating Scale (UDRS). Results: Two patients with "predominant lateralized action tremor" of the hands and mild cervical dystonia showed no relevant tremor improvement after GPi-DBS, but UDRS improved (mean, 45%). Rescue ventral intermediate nucleus of the thalamus (Vim)-DBS electrodes were implanted and both patients benefited significantly with a mean tremor reduction of 51%.Two other patients with "axial-predominant action tremor of the trunk and head" associated with cervical dystonia underwent bilateral Vim-DBS implantation with little effect on tremor (24% reduction in mean FTM-TRS total score) and no effect on dystonic symptoms. GPi rescue DBS was implanted and showed a significant effect on tremor (63% reduction in mean FTM-TRS) and dystonia (49% reduction in UDRS). Conclusions: The diagnosis of dystonic tremor alone is not a sufficient predictor to establish the differential indication of GPi- or Vim-DBS. Further criteria (eg, proximal-distal distribution of tremor/dystonia) are needed to avoid rescue surgery in the future. On the other hand, the course of our patients encourages rescue surgery in such severely disabled patients if the first target fails.

The Clinical Profile of Tremor in Parkinson's Disease.

Background: Tremor is one of the most troublesome manifestations of Parkinson's Disease (PD) and its response to dopaminergic medication is variable; an evidence-based framework of PD tremor is lacking yet needed to inform future investigations. Objective: To perform a comprehensive longitudinal analysis on the clinical characteristics, course and response to dopaminergic medication of tremor in de-novo PD. Methods: Three hundred ninety-seven participants were recruited in the Parkinson Progressive Markers Initiative, a prospective observational cohort study in early de-novo PD. Rest, postural and kinetic tremor scores were extracted from the Movement Disorders Society-Unified Parkinson's Disease Rating Scale. Progression from baseline to 7-year follow-up of rest, postural and kinetic tremor scores, and their response to in-clinic dopaminergic medication were analyzed through linear mixed-effects models adjusted for age, sex and disease duration at enrollment. A sensitivity analysis was conducted through subgroup and imputation analyses. Results: 382 (96.2%) participants showed tremor and 346 (87.2%) showed rest tremor in at least one assessment over 7 years. Off-state rest, postural and kinetic tremor scores increased significantly over time, coupled with a significant effect of dopaminergic medication in reducing tremor scores. However, at each assessment, tremor was unresponsive to in-clinic dopaminergic medication in at least 20% of participants for rest, 30% for postural and 38% for kinetic tremor. Conclusions: PD tremor is a troublesome manifestation, with increasing severity and variable response to medications. This analysis details the current clinical natural history of tremor in early-to-mid stage PD, outlining an evidence-based framework for future pathophysiological and interventional studies.

Development and Validation of a Prognostic Model to Predict Overall Survival in Multiple System Atrophy.

Background: Multiple system atrophy (MSA) is a devastating disease characterized by a variable combination of motor and autonomic symptoms. Previous studies identified numerous clinical factors to be associated with shorter survival. Objective: To enable personalized patient counseling, we aimed at developing a risk model of survival based on baseline clinical symptoms. Methods: MSA patients referred to the Movement Disorders Unit in Innsbruck, Austria, between 1999 and 2016 were retrospectively analyzed. Kaplan-Meier curves and multivariate Cox regression analysis with least absolute shrinkage and selection operator penalty for variable selection were performed to identify prognostic factors. A nomogram was developed to estimate the 7 years overall survival probability. The performance of the predictive model was validated and calibrated internally using bootstrap resampling and externally using data from the prospective European MSA Study Group Natural History Study. Results: A total of 210 MSA patients were included in this analysis, of which 124 patients died. The median survival was 7 years. The following clinical variables were found to significantly affect overall survival and were included in the nomogram: age at symptom onset, falls within 3 years of onset, early autonomic failure including orthostatic hypotension and urogenital failure, and lacking levodopa response. The time-dependent area under curve for internal and external validation was >0.7 within the first 7 years of the disease course. The model was well calibrated showing good overlap between predicted and actual survival probability at 7 years. Conclusion: The nomogram is a simple tool to predict survival on an individual basis and may help to improve counseling and treatment of MSA patients.

The Role of Levodopa Challenge in Predicting the Outcome of Subthalamic Deep Brain Stimulation.

Background: Deep brain stimulation of the subthalamic nucleus (STN-DBS) is an effective and evidence-based treatment for idiopathic Parkinson's disease (iPD). A minority of patients does not sufficiently benefit from STN-DBS. Objective: The predictive validity of the levodopa challenge for individual patients is analyzed. Methods: Data from patients assessed with a preoperative Levodopa-test and a follow-up examination (mean ± standard deviation: 9.15 months ±3.39) from Kiel (n = 253), Berlin (n = 78) and Toronto (n = 98) were studied. Insufficient DBS outcome was defined as an overall UPDRS-III reduction <33% compared to UPDRS-III in med-off at baseline or alternatively if the minimal clinically important improvement of 5 points was not reached. Single UPDRS-items and sub-scores were dichotomized. Following exploratory analysis, we trained supervised regression- and classification models for outcome prediction. Results: Data analysis confirmed significant correlation between the absolute UPDRS-III reduction during Levodopa challenge and after stimulation. But individual improvement was inaccurately predicted with a large range of up to 30 UPDRS III points. Further analysis identified preoperative UPDRS-III/med-off-scores and preoperative Levodopa-improvement as most influential factors. The models for UPDRS-III and sub-scores improvement achieved comparably low accuracy. Conclusions: With large prediction intervals, the Levodopa challenge use for patient counseling is limited, though remains important for excluding non-responders to Levodopa. Despite these deficiencies, the current practice of patient selection is highly successful and builds not only on the Levodopa challenge. However, more specific motor tasks and further paraclinical tools for prediction need to be developed.

Characterizing Camptocormia in Parkinson's Disease Using Muscle Ultrasonography.

BACKGROUND: Camptocormia (CC) is the forward-bending of the spine of more than 30 degrees that can be found in Parkinson's disease (PD) as a disabling complication. Detection of changes in paraspinal lumbar musculature in CC is of value for choosing treatment strategies. OBJECTIVE: To investigate whether these changes can be detected using muscle ultrasonography (mUSG). METHODS: Age and sex-matched groups comprised 17 PD patients with CC (seven acute, PD-aCC; 10 chronic PD-cCC), 19 PD patients with no CC, and 18 healthy controls (HC). Lumbar paravertebral muscles (LPM) on both sides were assessed using mUSG by two different raters blinded to the group assignment. Groups were compared with regard to the linear measurements of the muscle thickness as well as semi-quantitative and quantitative (grayscale) analyses of muscle echogenicity using a univariate general linear model. RESULTS: All assessments showed substantial interrater reliability. The PD-cCC group had significantly thinner LPM compared to groups with no CC (PD and HC). Groups of PD-aCC and PD-cCC differed from the groups of no CC in quantitative and semi-quantitative analyses of LPM echogenicity, respectively. CONCLUSION: Assessment of LPM in PD patients with CC can be reliably performed using mUSG. Also, mUSG may be used as a screening tool to detect CC-related changes in thickness and echogenicity of the LPM in patients with PD.

Worsening of Parkinson's Disease After Termination of COVID-19 Quarantine Cannot Be Reversed Despite Resumption of Physiotherapy.

In a retrospective analysis, we recently reported findings on the detrimental motor effects of interrupted physiotherapy following the COVID-19 pandemic in parkinsonian patients. Using an extended follow-up period, we investigated the beneficial effect of reinstated physiotherapy on patients' disease severity and reversal of interruption-induced motor deterioration. Compared to before the COVID-19 outbreak, we observed persistence of motor disease worsening despite full resumption of state-of-the-art physical therapy suggesting that motor deterioration after discontinuation of physical therapy could not be compensated for. Therefore, and considering possible future crises, establishing means to safeguard continuation of physical therapy and to foster remote provision of care should be major goals.

Intravenous thrombolysis and mechanical recanalization for acute ischemic stroke in deep brain stimulation patients: a case series.

BACKGROUND: Intravenous thrombolysis (IVT) and endovascular mechanical thrombectomy therapy (MT) are well established in the treatment of acute ischemic stroke. It is currently unclear whether these treatments can be applied in patients with previous deep brain stimulation (DBS) surgery and how long the interval to the DBS operation should be. METHODS: Four patients with ischemic stroke and IVT or MT were included in this retrospective case series. Data on demographics, genesis, severity and course of the stroke and the DBS indication were extracted and evaluated. Furthermore, a literature review was conducted. Outcomes and hemorrhagic complications after IVT, MT or intra-arterial thrombolysis in patients with prior deep brain stimulation surgery and intracranial surgery were analyzed. RESULTS: Four patients with acute ischaemic stroke and previous DBS surgery were treated with IVT (2 patients), MT (1) or a combined therapy of IVT and MT (1). The time interval to the previous DBS surgery was between 6 and 135 months. In these four patients, no bleeding complications occurred. The literature review revealed four publications with a total of 18 patients, who were treated with IVT, MT or intra-arterial thrombolysis. Of these 18 patients, only 1 had undergone deep brain stimulation surgery, the other 17 patients had received brain surgery for other reasons. Bleeding complications occurred in four of the 18 reported patients, but not in the DBS case. All four patients with bleeding complications were reported to have died as a result. In three of the four patients with fatal outcome, surgery was less than 90 days before the onset of stroke. CONCLUSION: IVT and MT were tolerated by four patients with ischemic stroke more than 6 months after DBS surgery without bleeding complications.

Grey matter correlates of dystonic soft signs in essential tremor.

BACKGROUND: Questionable signs of dystonia are a common finding in patients with essential tremor (ET). Brain structural alterations in ET patients plus dystonic soft signs (ET + ds) in comparison to ET patients without dystonic soft signs (ET-ds) or patients with tremor associated with manifest dystonia (TAWD) have not been examined yet. Therefore, our study aims to explore alterations of brain grey matter in patients with ET + ds. METHODS: A total of 68 elderly patients with ET-ds (n = 32), ET + ds (n = 20) or idiopathic cervical dystonia with dystonia associated action tremor of the upper limbs (TAWD, n = 16) and 42 age-matched healthy controls underwent a clinical and electrophysiological assessment and 3T MRI. For grey matter alterations T1 MRI images were analysed by voxel-based morphometry. Additionally, regression analyses with clinical parameters (tremor frequency, severity and disease duration) were performed. RESULTS: VBM showed a significant increase of grey matter in the right lentiform nucleus in ET + ds and TAWD compared to HC and ET-ds. Further, an increase of cortical grey matter in the middle frontal gyrus in ET + ds was shown. The hypertrophy of the lentiform nucleus in ET + ds was correlated with disease severity and duration. CONCLUSION: Patients with ET + ds showed grey matter brain structural alterations similar to TAWD. Our findings suggest an involvement of the basal ganglia-cortical loop in ET + ds which may indicate a pathophysiological similarity with TAWD rather than ET.

Three-Dimensional Mesh Recovery from Common 2-Dimensional Pictures for Automated Assessment of Body Posture in Camptocormia.

Background: Three-dimensional (3D) human body estimation from common photographs is an evolving method in the field of computer vision. It has not yet been evaluated on postural disorders. We generated 3D models from 2-dimensional pictures of camptocormia patients to measure the bending angle of the trunk according to recommendations in the literature. Methods: We used the Part Attention Regressor algorithm to generate 3D models from photographs of camptocormia patients' posture and validated the resulting angles against the gold standard. A total of 2 virtual human models with camptocormia were generated to evaluate the performance depending on the camera angle. Results: The bending angle assessment using the 3D mesh correlated highly with the gold standard (R = 0.97, P < 0.05) and is robust to deviations of the camera angle. Conclusions: The generation of 3D models offers a new method for assessing postural disorders. It is automated and robust to nonperfect pictures, and the result offers a comprehensive analysis beyond the bending angle.