ABSTRACT
The genetic blueprint for the essential functions of life is encoded in DNA, which is translated into proteins-the engines driving most of our metabolic processes. Recent advancements in genome sequencing have unveiled a vast diversity of protein families, but compared with the massive search space of all possible amino acid sequences, the set of known functional families is minimal. One could say nature has a limited protein "vocabulary." A major question for computational biologists, therefore, is whether this vocabulary can be expanded to include useful proteins that went extinct long ago or have never evolved (yet). By merging evolutionary algorithms, machine learning, and bioinformatics, we can develop highly customized "designer proteins." We dub the new subfield of computational evolution, which employs evolutionary algorithms with DNA string representations, biologically accurate molecular evolution, and bioinformatics-informed fitness functions, Evolutionary Algorithms Simulating Molecular Evolution.
Subject(s)
Algorithms , Computational Biology , Evolution, Molecular , Computational Biology/methods , Proteins/genetics , Proteins/chemistry , Proteins/metabolism , Computer SimulationABSTRACT
Incidental bone lesions are encountered frequently in day-to-day practice. Many of these lesions are indeterminate requiring referral to specialist centres for further characterisation with or without biopsy; however, as biopsy has its own drawbacks, not all lesions can be subjected to biopsy. The primary role of a radiologist in these situations is to characterise these lesions based on their imaging appearances into aggressive lesions requiring biopsy and non-aggressive lesions that do not require a biopsy. The term "do-not-touch lesion" is used to describe a lesion with typical radiographic appearances that can be characterised based on radiographic appearances alone without needing a biopsy. With recent advances in imaging, many incidental lesions can be characterised into do-not-touch lesions based on their imaging appearances alone using a single imaging technique or using a combination of imaging techniques and, less frequently, with the additional help of serological investigations, without the need for biopsy. Hence, the definition of do-not-touch lesions of bone needs a revisit. In this article, we attempt to redefine do-not-touch lesions of bone and propose an imaging-based classification for characterisation of these lesions.
Subject(s)
Bone Diseases/diagnostic imaging , Bone and Bones/injuries , Biopsy/adverse effects , Bone Diseases/classification , Bone Diseases/pathology , Bone and Bones/diagnostic imaging , Bone and Bones/pathology , Humans , Incidental Findings , Magnetic Resonance Imaging , Osteitis Deformans/diagnostic imaging , Positron Emission Tomography Computed Tomography , Radiography , Tomography, Emission-Computed, Single-Photon , Tomography, X-Ray ComputedABSTRACT
Lesions of the tibial tuberosity are very rare but often present a diagnostic dilemma due to their unusual location and appearances. Although some pathologies affecting this region are commonly seen elsewhere in the skeleton, they may have atypical imaging appearances and morphological characteristics when present at the tibial tuberosity. The present review describes the developmental stages of the tibial tuberosity, explaining why this area is prone to degenerative tractional changes and injury, and also highlights various pathologies including benign and malignant osseous lesions and trauma/degenerative related abnormalities.
Subject(s)
Bone Neoplasms/diagnostic imaging , Diagnostic Imaging/methods , Tibia/diagnostic imaging , Diagnosis, Differential , Humans , Magnetic Resonance Imaging , Radiography , Tomography, X-Ray ComputedABSTRACT
OBJECTIVE: To determine the value of chest and skeletal staging in patients with parosteal osteosarcoma (POS), and the incidence of late local and chest recurrence. MATERIALS AND METHODS: Retrospective review of patients across two institutions with histological confirmation of POS diagnosed between January 2007 and March 2020. Data collected included age, sex, skeletal location, results of chest CT and whole-body bone scintigraphy (WB-BSc) or whole-body MRI (WB-MRI) obtained at initial diagnosis. The histological tumour grade based on surgical resection specimens was classified as low-grade POS (LG-POS) and dedifferentiated POS (DD-POS). Findings of chest CT and skeletal staging were correlated with tumour grade. Follow-up chest CT and MRI studies were reviewed to determine the rate of late lung metastases and local recurrence. RESULTS: There were 27 males and 44 females, mean age 33 years (range 12-79 years). The femur (n = 43) and tibia (n = 14) were the most commonly involved bones. From surgical resection histology, 42 (59.2%) were LG-POS and 29 (40.8%) were DD-POS. WB-BSc/WB-MRI showed no skeletal metastases, while 1 case of DD-POS presented with bilateral calcified lung metastases. At follow-up, 7 patients (9.9%) developed lung metastases (mean of 18.9 months, range 10-48 months) from initial presentation, of which all were DD-POS. All but 1 patient who developed subsequent lung metastases had a local recurrence. CONCLUSIONS: Skeletal staging is unlikely to be of value in POS. Staging chest CT is very unlikely to demonstrate lung metastases in LG-POS and could be limited to DD-POS, particularly at the time of local recurrence.
Subject(s)
Bone Neoplasms , Osteosarcoma, Juxtacortical , Adolescent , Adult , Aged , Bone Neoplasms/diagnostic imaging , Child , Female , Humans , Male , Middle Aged , Neoplasm Recurrence, Local , Retrospective Studies , Whole Body Imaging , Young AdultABSTRACT
AIM: To retrospectively review a series of solitary central cartilage tumours (CCTs) of the proximal fibula and propose an imaging protocol for their management. MATERIALS AND METHODS: Over 11 years, 48 patients were identified with a CCT of the proximal fibula. The initial magnetic resonance imaging (MRI) and follow-up imaging were assessed for tumour length, endosteal scalloping, or aggressive/malignant features. Each case was categorised according to the Birmingham Atypical Cartilage Tumour Imaging Protocol (BACTIP). The final diagnosis and outcome were reviewed to establish an appropriate imaging protocol for the management of similar cases in the future. RESULTS: The final diagnosis based on imaging alone or imaging and histopathology was enchondroma in 46 cases (96%) and atypical cartilage tumour (ACT)/low-grade chondrosarcoma in two (4%). Using the BACTIP classification, the majority were type IC (48%) with type IA the second commonest (24%). Of 19 that underwent follow-up MRI, only two revealed any increase in length, neither of which was shown to be malignant. No cases re-presented later with evidence of malignant transformation. CONCLUSION: There has been a significant increase in the number of CCTs of the proximal fibula referred to Royal Orthopaedic Hospital, Birmingham, over the past decade. This can largely be attributed to the increased use of MRI. The majority were benign with only 4% classified as an ACT. A modified BACTIP, the Fibular Atypical Cartilage Tumour Imaging Protocol (FACTIP) is presented, indicating which cases would benefit from follow-up imaging and which require referral to a specialist orthopaedic oncology service.
Subject(s)
Bone Neoplasms/diagnosis , Chondrosarcoma/diagnosis , Disease Management , Fibula , Forecasting , Magnetic Resonance Imaging/methods , Diagnosis, Differential , Female , Follow-Up Studies , Humans , Male , Retrospective StudiesABSTRACT
The iliofemoral ligament is strongest ligament of the body. We review the magnetic resonance imaging (MRI) appearances of the iliofemoral ligament, and discuss the disease entities that may affect this region.
Subject(s)
Hip Joint/diagnostic imaging , Ligaments, Articular/diagnostic imaging , Magnetic Resonance Imaging , Hip Joint/anatomy & histology , Hip Joint/pathology , Humans , Ligaments, Articular/anatomy & histology , Ligaments, Articular/pathologyABSTRACT
AIM: To provide a diagnostic approach to pulmonary nodules in patients with chondrosarcoma. MATERIALS AND METHODS: A search of the oncology database at a specialist orthopaedic oncology referral centre was performed to identify all patients who were treated surgically for chondrosarcoma between January 2007 and December 2018. Reports from the computed tomography (CT) examinations of the thorax of these patients were reviewed. In patients who had pulmonary nodules/metastases identified on CT, data on the primary chondrosarcoma and pulmonary nodule characteristics were collected. RESULTS: Twenty point two percent of patients had a pulmonary nodule identified on either initial or follow-up staging CT of the thorax, of which 8.1% were pulmonary metastases. Patients with grade 3 and dedifferentiated chondrosarcoma were more likely to have pulmonary metastases than patients with grade 1/2 chondrosarcoma. The time interval to developing metastases was shorter in patients with grade 2/3 and dedifferentiated chondrosarcoma versus patients with grade 1 chondrosarcoma. A low proportion of patients with grade 1 chondrosarcoma developed metastases (12.5%), all of which were identified at the time of a local recurrence. Nodules ≥10mm, nodules with lobulate margins, nodules containing irregular or subtle calcification, and nodules seen bilaterally or both centrally and peripherally were more likely to represent pulmonary metastases than benign nodules. CONCLUSION: The diagnostic significance of pulmonary nodules (i.e., whether they represent pulmonary metastases or not) can be predicted by taking into account a number of factors, in particular, the histological grade of the patient's chondrosarcoma, the size and margins of the nodules, and the presence of subtle/irregular calcification.
Subject(s)
Bone Neoplasms/pathology , Chondrosarcoma/diagnostic imaging , Lung Neoplasms/diagnostic imaging , Multiple Pulmonary Nodules/diagnostic imaging , Tomography, X-Ray Computed , Adult , Aged , Aged, 80 and over , Chondrosarcoma/secondary , Female , Humans , Lung Neoplasms/secondary , Male , Middle Aged , Multiple Pulmonary Nodules/secondary , Neoplasm Grading , Radiography, ThoracicABSTRACT
AIM: To provide a diagnostic approach to distinguish osteochondroma-induced pseudoaneurysm from sarcoma on imaging and prevent biopsy which may be fatal. MATERIALS AND METHODS: A retrospective study of the orthopaedic oncology database was performed to identify all patients referred to specialist orthopaedic oncology service with a final diagnosis of osteochondroma-induced pseudoaneurysm. The demographics of the cohort, the anatomical location of the osteochondromas and pseudoaneurysms, and the imaging appearances were assessed. RESULTS: Seven contemporary and one historical case of osteochondroma-induced-pseudoaneurysm were identified. There were five patients with solitary osteochondroma and three cases of hereditary multiple exostosis. Five cases underwent magnetic resonance imaging (MRI) of which pulsation artefact was present in 40%. On MRI, all the present cases demonstrated a small central pseudoaneurysm surrounded by multiple eccentric layers of thrombus and haemorrhage, which was termed the "eccentric-whorl sign". CONCLUSION: Osteochondroma-induced pseudoaneurysms are often misdiagnosed as malignant transformation of an osteochondroma or a soft-tissue sarcoma and referred for urgent biopsy. This study presents the largest case series, which includes the first documented case diagnosed in 1934. Differentiating and characterising pseudoaneurysms from sarcomas is imperative in order to prevent a biopsy, which could be fatal.
Subject(s)
Aneurysm, False/diagnosis , Bone Neoplasms/complications , Magnetic Resonance Imaging/methods , Osteochondroma/complications , Popliteal Artery , Adolescent , Adult , Aneurysm, False/etiology , Bone Neoplasms/diagnosis , Child , Diagnosis, Differential , Female , Follow-Up Studies , Humans , Lower Extremity , Male , Osteochondroma/diagnosis , Retrospective Studies , Sarcoma/diagnosis , Soft Tissue Neoplasms/diagnosis , Young AdultABSTRACT
AIM: To investigate whether the long-held view that the hand is the commonest site for an enchondroma is actually correct in light of more sensitive imaging techniques that are able to demonstrate small enchondromas at other skeletal sites. MATERIALS AND METHODS: A two-part retrospective study was undertaken. Part 1 comprised a review of the hand radiographs obtained in two major teaching hospitals over a 10-year period to establish the incidence of enchondroma in the hand. Part 2 was a review of a series of enchondromas of the proximal humerus, distal femur, and proximal tibia <4 cm in length on magnetic resonance imaging (MRI) to see which cases were visible or not on corresponding radiographs. RESULTS: Part 1: 84 enchondromas were identified on 116,354 trauma radiographs to give an incidence of 0.07%. Part 2: 157 patients with an enchondroma on MRI <4 cm were reviewed. Only 17% of lesions <2 cm in length were visible on the contemporaneous radiographs. In lesions that were 2-2.9 and 3-3.9 cm the percentage visible on the radiographs increased to 58 and 77%, respectively. CONCLUSION: It is well recognised from existing studies that incidental enchondromas can be seen in approximately 2.5% of routine shoulder and knee MRI scans. This figure is 35 times higher than the incidence found in the series of hand trauma radiographs. This infers that the hand should no longer be considered as the commonest site for an enchondroma. This is because radiographs are relatively insensitive to the detection of small lesions in larger bones, such as the proximal humerus and around the knee, when compared with MRI.
Subject(s)
Bone Neoplasms/diagnostic imaging , Chondroma/diagnostic imaging , Hand Bones/diagnostic imaging , Adult , Humans , Humerus/diagnostic imaging , Magnetic Resonance Imaging , Radiography , Retrospective Studies , Tibia/diagnostic imagingABSTRACT
The ring-shaped meniscus (RSM) is a rare meniscal variant in which there is an intermeniscal bridge between the anterior and posterior horns of the meniscus, thus forming a complete ring. The lateral meniscus is more commonly involved than the medial meniscus. Distinguishing an RSM from a bucket handle tear (BHT) with a displaced fragment in the intercondylar notch is challenging and there are reports of negative arthroscopies for suspected BHTs. There are many reports of symptomatic and asymptomatic lateral RSMs diagnosed on MRI in the literature. We report a series of RSMs in six patients, which includes MRI descriptions of two cases of medial RSM and a case of bilateral lateral RSM, which were diagnosed on MRI and have never previously been reported. This study will also describe the various imaging features of a RSM that distinguish it from a displaced BHT. We will also discuss associated rare malformations encountered in our study, such as hypoplastic anterior cruciate ligament and the anomalous insertion of the popliteus tendon onto the posterior horn of a lateral RSM.
Subject(s)
Magnetic Resonance Imaging/methods , Tibial Meniscus Injuries/diagnostic imaging , Adolescent , Adult , Child , Female , Humans , Male , Menisci, Tibial/diagnostic imaging , Middle Aged , Retrospective Studies , Young AdultABSTRACT
OBJECTIVE: We describe a novel and efficient CT biopsy technique that we have termed 'skin adhesive and hand-aided biopsy technique', shortened to the acronym SAHNA. This technique is ideal for biopsying surface osseous lesions where there is a lack of subcutaneous fat. This avoids the need for the radiologist's hand to be in close proximity to the CT scanner beam at the time of intervention. METHODS: The SAHNA technique uses a plastic surgical forceps towel clamp to stabilise the biopsy needle just proximal to the lesion after piercing through the skin. The clamp itself is stabilised via a self-adhesive dressing which is stuck down to the skin at its shank. RESULTS: In our institution, we have already used the SAHNA technique successfully in over 5 cases. CONCLUSION: The SAHNA technique is a widely accessible and effective way of stabilising the CT biopsy needle in technically challenging superficial bony lesions.
Subject(s)
Biopsy, Needle/methods , Bone Diseases/pathology , Image-Guided Biopsy/methods , Tomography, X-Ray Computed , Adhesives , Biopsy, Needle/instrumentation , Equipment Design , Humans , Image-Guided Biopsy/instrumentationABSTRACT
BACKGROUND: Studies have demonstrated the presence of muscle atrophy around the hip in patients with hip osteoarthritis. Few studies have examined the psoas muscle or assessed it at a paraspinal level in patients post-total hip arthroplasty. The aim of this study was to determine if there is significant psoas muscle atrophy as indicated by muscle cross-sectional area and high degree of fat infiltration post-unilateral hip arthroplasty. METHODS: Retrospective analysis of 341 patients with unilateral hip implant and subsequent lumbar spine MRI over a 8-year period was performed. Fat infiltration and cross-sectional area of the psoas muscle at L3/4 level were measured by two musculoskeletal fellows (1 year experience in musculoskeletal radiology), and comparison made between the implant and non-operative sides was made. Fat infiltration was measured using the modified Goutallier grading. The degree of hip osteoarthritis in the non-operative side was measured using the Kellgren-Lawrence grading. The data was analysed using paired t test, ANOVA, unpaired t test, Pearson correlation and Jonckheere-Terpstra test. RESULTS: The cross-sectional area of the psoas muscle on the implant side was significantly less than the non-operative side. There was significance between the cross-sectional area difference and the fat grade of the implant side. CONCLUSION: Our results demonstrate psoas atrophy on the implant side compared to the non-operative side in post-unilateral implant patients. Post-operative hip implant rehabilitation may benefit from more focused psoas strengthening exercises to improve functional outcome.
Subject(s)
Arthroplasty, Replacement, Hip , Psoas Muscles , Arthroplasty, Replacement, Hip/adverse effects , Humans , Lumbar Vertebrae/pathology , Magnetic Resonance Imaging , Muscular Atrophy/diagnostic imaging , Muscular Atrophy/etiology , Muscular Atrophy/pathology , Psoas Muscles/diagnostic imaging , Psoas Muscles/pathology , Retrospective StudiesABSTRACT
There is wide variation in the technique and type of contrast used for MR arthrography of shoulder. In this article, we discuss the current practice in UK and the reason for the change over the last few years.
Subject(s)
Contrast Media/administration & dosage , Joint Diseases/diagnostic imaging , Magnetic Resonance Imaging/methods , Practice Patterns, Physicians'/statistics & numerical data , Shoulder Joint/diagnostic imaging , Contrast Media/supply & distribution , Gadolinium , Humans , United KingdomABSTRACT
AIM: To validate an imaging protocol for the management of solitary central cartilage tumours (CCTs) of the proximal humerus and around the knee. MATERIALS AND METHODS: Over a 10-year period, 387 patients were identified with a CCT in the proximal humerus, distal femur, and proximal tibia, who were referred to a single unit either from primary/secondary care or tertiary care directly to Royal Orthopaedic Hospital, a specialist orthopaedic oncology service. The initial magnetic resonance imaging (MRI) images and any follow-up images were evaluated for length of tumour, presence/absence of endosteal scalloping, or aggressive/malignant features. The cases were categorised into one of seven types according to the Birmingham Atypical Cartilage Tumour Imaging Protocol (BACTIP). The outcome in the cases was assessed to ascertain if application of the protocol would have led to any delay in the diagnosis of malignant transformation to a chondrosarcoma. RESULTS: The incidence of malignancy (chondrosarcoma) increased with ascending BACTIP. There was a 100% benign diagnosis (enchondroma) in types IA and IB, 96% in IIA, and 83% in IIB. Fifty-seven percent of type IIC and 97% type III were diagnosed as malignant. In only one case would the application of the protocol have led to a 5-month delay in the diagnosis of chondrosarcoma. CONCLUSIONS: This retrospective study confirms the BACTIP as a useful tool for the general radiologist in the initial assessment of CCT in the proximal humerus and around the knee with the exception of the proximal fibula. In particular, determining which cases need prompt referral to a specialist orthopaedic oncology service for further assessment.
Subject(s)
Cartilage, Articular/diagnostic imaging , Humerus/diagnostic imaging , Knee Joint/diagnostic imaging , Neoplasms, Connective Tissue/diagnostic imaging , Adult , Age Factors , Aged , Aged, 80 and over , Bone Neoplasms/diagnostic imaging , Chondroma/diagnostic imaging , Chondrosarcoma/diagnostic imaging , Clinical Protocols , Humans , Magnetic Resonance Imaging , Male , Middle Aged , Reproducibility of Results , Retrospective Studies , Sex Factors , Young AdultABSTRACT
The master knot of Henry refers to a narrow space located between the anatomical crossover of the flexor hallucis longus and flexor digitorum longus tendons. This small space is prone to "intersection syndrome," as a result of tendinosis, tenosynovitis, and tears of the aforementioned tendons at the knot of Henry. The aim of this educational review is to detail the anatomy of the knot of Henry, including common variations in the tendon position and orientation. These complex interconnections can affect the outcome of surgical intervention if not appreciated at the time of treatment. We will also provide an overview of the common and rarer pathologies related to the knot of Henry. The aim of the present review is to make radiologists more aware of pathologies in this region, which are not routinely seen in daily practice.
Subject(s)
Foot/diagnostic imaging , Tendons/diagnostic imaging , Foot/anatomy & histology , Foot Diseases/diagnostic imaging , Foot Diseases/pathology , Foot Diseases/surgery , Humans , Magnetic Resonance Imaging , Tendon Transfer , Tendons/anatomy & histologyABSTRACT
AIM: To evaluate the frequency of the "flow-void" sign in a large series of pathologically proven renal cell carcinoma (RCC) bone metastases referred to a specialist unit and to evaluate its correlation with both lesion size and imaging sequence. A further aim was to describe a proposed grading system for the description of the "flow-void" sign. MATERIALS AND METHODS: A retrospective review of patients with magnetic resonance imaging (MRI) of pathologically proven RCC bone metastases between September 2007 and December 2017 was performed. MRI images were reviewed for the presence of the "flow-void" sign and a proposed grading system for this sign was applied. Statistical analysis was performed to determine the association between the presence of the "flow-void" sign and lesion size and MRI sequence. RESULTS: One hundred and forty bone lesions in 123 patients with histologically proven metastatic RCC were reviewed. One hundred and thirty-two (94.3%) lesions demonstrated the "flow-void" sign on at least one sequence in each study. A statistically significant difference was demonstrated between lesion size and the presence and type of "flow-void" sign. Lesions demonstrating type 3 "flow-void" sign had mean dimensions of 82.2 mm compared to 47.3 mm for lesions that did not demonstrate the "flow-void" sign (χ2(2) =11.4; p=0.01). T2-weighted, proton density and fat-saturated imaging also demonstrated the "flow-void" sign more frequently. CONCLUSION: The "flow-void" sign is a common imaging feature within RCC bone metastases. When observed, the "flow-void" sign can be a useful imaging feature in the diagnosis of RCC bone metastases.
Subject(s)
Bone Neoplasms/diagnostic imaging , Bone Neoplasms/secondary , Carcinoma, Renal Cell/pathology , Kidney Neoplasms/pathology , Magnetic Resonance Imaging/methods , Neoplasms, Second Primary/diagnostic imaging , Adult , Aged , Aged, 80 and over , Bone and Bones/diagnostic imaging , Female , Humans , Male , Middle Aged , Retrospective StudiesABSTRACT
OBJECTIVE: We describe a novel and safe needle-holding method that we have termed the 'dual steristrip technique'. This technique can be used to stabilize the bone biopsy needle without the need for the radiologist's hand to be in close proximity to the X-ray beam during CT-guided intervention. MATERIALS AND METHODS: The dual steristrip technique uses steristrips to stabilize the bone biopsy needle and allows for accurate assessment of needle position and trajectory. This involves affixing one end of a steristrip to the skin 2 cm from the needle skin entry point, wrapping the mid-section of the steristrip around the biopsy needle and affixing the other end of the steristrip to the skin at the opposite side of the needle 2 cm from the needle skin entry point. A second steristrip is then applied in a similar fashion at 90° to the first steristrip. RESULTS: In our institution, we have used the dual steristrip technique to stabilize the biopsy needle in certain cases where assessment of needle position/trajectory can be more challenging. This includes cases where there is a paucity of soft tissues overlying the bone or if the bone lesion is located in the superficial cortex. We have found it to be successful in 80% of cases. CONCLUSIONS: The dual steristrip technique is a safe and effective needle stabilization method that should be considered by the interventional radiologist in challenging CT-guided bone biopsy cases.
Subject(s)
Bandages , Bone Diseases/pathology , Radiation Dosage , Radiography, Interventional/methods , Tomography, X-Ray Computed/methods , Biopsy, Needle , Humans , Image-Guided BiopsyABSTRACT
Numerous corticosteroid preparations are available, but the type and dose administered is frequently at the discretion of the clinician. This is often based on anecdotal evidence and experience rather than formal clinical guidelines. In order to better understand current practice, we anonymously surveyed 100 members of the British Society of Skeletal Radiologists. The results of the survey demonstrated the arbitrary use of all types of steroid preparation at different anatomical locations. In this article, we review the commonly used corticosteroids and propose a guideline to help practitioners decide on the type and dose of steroid depending on the treatment location.
Subject(s)
Adrenal Cortex Hormones/administration & dosage , Musculoskeletal Diseases/drug therapy , Adrenal Cortex Hormones/therapeutic use , Humans , Injections, Intra-ArticularABSTRACT
Magnetic resonance imaging (MRI) is the established technique for evaluating the spine. Unfortunately, the supine position of the patient during conventional MRI scanning does not truly reflect the physiological forces experienced by the discoligamentous structures during normal upright posture and ambulation. Upright MRI is a relatively new technique that allows the patient to be scanned in several different weight-bearing positions, which may potentially demonstrate occult pathology not visualised in the supine position. The imaging technique and current clinical indications of upright spinal MRI would be discussed.
Subject(s)
Magnetic Resonance Imaging/methods , Posture/physiology , Humans , Standing Position , Weight-BearingABSTRACT
Unfortunately, the legend of Fig. 5 was incorrectly published in original publication. The corrected legend is given below.