Polar Radial
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Polar Radial
Leprosy etiology and pathogenesis
Leprosy (Hansen's disease) is a chronic infection of theskin and cutaneous nerves caused by M. leprae. The manifestationsin the patient may be localized or generalized,and are determined largely by the host response to theinfecting organism.
Aetiology Mycobacterium leprae is an acid-fast bacillus that cannotbe cultured in vitro. Ziehl-Neelsen staining of smears ofthe organism differentiates viable (solid staining) fromnon-viable (granular) organisms. In humans the coolersuperficial regions of the body are the preferred sites for bacterial proliferation. The generation time is about 13days. M. leprae was one of the first pathogenic bacteria tobe identified, and yet in vitro culture remains elusive. Ourknowledge of the organism's sensitivity to antimicrobialagents is gained from the response of mouse foot-padlesions induced by injection of suspensions of M. leprae toantileprosy drugs given in water. It is known that M. lepraeis a very hardy organism capable of surviving prolongeddrying in the shade in south India, and capable ofprolonged carriage in the noses of 5% of the generalpopulation and 16% of leprosy workers.Distribution and incidenceLeprosy is mainly a disease of the tropics and subtropics. It is relatively common in Africa and Asia, witha prevalence of 2-9 per 1000 in most areas and higher ratesin a few countries. There are about 600000 new cases peryear, including a considerable number of childhood cases,which indicates persistence of transmission. Lepromin skintest positivity rates in endemic areas are much higher thanrates of clinical cases, suggesting that host factors do muchto influence the outcome of the disease. The disease hasalmost completely disappeared from Europe, althoughcases do occur in Europeans who have had prolongedexposure in an endemic area.Transmission and epidemiologyThere is little evidence to support skin-skin contact as theroute of infection. Aerosol spread from the upper respiratorytract of patients with multibacillary (lepromatous)leprosy is the likely source of infection.There is considerable variation in the course of infectionfrom person to person, and the majority of those infecteddevelop no clinical disease. Among those developing clinical disease there appearsto be a racial variation in the type of leprosy occurring: upto 50% of cases in Asia have lepromatous disease, comparedwith 10% in Africa. The male-to-female ratio is 2:1in adults and unity in children.Pathogenesis and pathologyThe host's cellular immune response determines theoutcome of infection. If macrophages are able to kill theinfecting organisms there is either no clinical disease or thelesions of indeterminate leprosy at most . Thosein whom the infection progresses further develop one ofthe forms of disease described in Table 9.30 and classifiedas one of the following:• Tuberculoid (TT)• Borderline tuberculoid (BT)• Borderline (BB)• Borderline lepromatous (BL)• Lepromatous (LL).It should be noted that the clinical disease is a biologicalcontinuum between the two polar extremes of pure tuberculoidand pure lepromatous. Few bacilli are found in thetuberculoid forms, whereas large numbers are found inpatients with lepromatous leprosy. Host cellular responsesto mycobacterial antigens determine the form of diseasethat develops, with delayed-type hyper sensitivity at thetuberculoid end of the spectrum and anergy at the lepromatousend. The borderline forms are immunologicallyunstable, and without treatment will deteriorate to thelepromatous end of the spectrum.The pathology of leprosy is a granulomatous response.At the lepromatous end of the spectrum the granulomacomprises macrophages laden with solid staining bacilliand globules of fatty products of bacillary metabolism,including phenolic glycolipid 1. This appearance of themacrophages is called foamy macrophages. Although lymphocytesare conspicuous by their absence from lepromatouslesions they are well represented in tuberculoidlesions. The earliest lesions in leprosy begin in cutaneousnerves in the Schwann cells which have phagocytic functionsand ingest bacilli. The most marked damage to nervetrunks is seen in TT leprosy. At the lepromatous end ofthe spectrum the involved nerves are not so large. Theauriculotemporal, ulnar, median, radial cutaneous, lateralpopliteal and sural nerves are preferentially involved atsites where the nerve trunks are close to the skin and thereforecooler.The bacterial load and the morphology of the organismsneed to be assessed, initially for classification purposes andsubsequently to determine the response to treatment. Slitskin smears are obtained from the edges of lesions.Numbers of bacilli and their viability can be graded. Leprominis a skin test antigen obtained from M. leprae. Theantigen is injected intradermally and the test is read at 3weeks; a nodule at the site of injection indicates a positiveresponse, meaning delayed hypersensitivity and supportinga classification at the tuberculoid end of the spectrum. Two types of acute reaction are recognized in leprosy:• Erythema nodosum leprosum (ENL) is an immunecomplex-mediated vasculitis that occurs in LL patientsand, less often, in BL, either during treatment or in theuntreated patient. There is inflammation with oedemaand a prominent infiltrate of neutrophils.• A reversal reaction indicates a change in cellularresponsiveness to the infecting organism, either increasing(after starting treatment) or decreasing responsiveness.Skin lesions and affected nerves become moreinflamed. The swollen lesion resolves completely intime, becoming smaller in 'upgrading' and bigger with'downgrading'.Clinical featuresIndeterminate leprosyIndeterminate leprosy is manifest as a hypopigmentedmacule on a dark skin, and as a slightly reddened maculeon a light skin, with either normal or mildly reduced sensation.The lesions may regress spontaneously or progressto one of the stages described below.Tuberculoid leprosyTuberculoid leprosy (TT) is characterized by a hairless,hypopigmented anaesthetic lesion with a flat centre and awell-defined raised edge with minimal inflammation. 1The skin of the lesion does not sweat. Single lesions areusual, but up to three may be found. Common sites are theextensor aspect of the arms, around the elbow and theknee. A thickened cutaneous nerve supplying the affectedarea may be felt. 2 To feel an enlarged nerve the examiningfingertip should be moved to and fro over the nervetrunk at right-angles to the direction of the nerve. NeuralTT leprosy occurs with a single thickened nerve as the onlyphysical sign.Borderline tuberculoid leprosyBorderline tuberculoid (BT) lesions are similar to those ofTT but more numerous and asymmetrically distributed.The edges of the lesions are inflamed and irregular. 3 Thenerves preferentially involved in leprosy are usually thickenedand damaged, causing anaesthesia, loss of functionand deformity to a variable extent in hands and feet. Penetratingulcers in the soles of the feet, burns and skin sepsisare often present. There may be osteomyelitis of the bonesof the feet caused by an infected penetrating ulcer.Borderline leprosyBorderline leprosy (BB) produces multiple lesions thatvary in form, size and shape. Papules, plaques and lesionswith elevated wide outer rims and depressed, well-definedanaesthetic centres are seen. The lesions may be hypopigmentedor hyperpigmented. 4 There is diffuse involvementof the peripheral nerves.Borderline lepromatous leprosyBorderline lepromatous leprosy (BL) causes numerousasymmetrically distributed inflamed or hyperpigmentedlesions, which may be papules, nodules or plaques. sation over the lesions may be normal. Vague macules thatvary in size are present in some patients. Peripheral nervesmay only show slight enlargement.Lepromatous leprosyLepromatous leprosy (LL) is associated with numeroussymmetrically distributed skin lesions. 1 At the earlieststage, numerous slightly reddened hypopigmented maculesand nodules occur. Without treatment these evolve intopapules and plaques. The eyebrows are lost and the skin ofthe face and ears becomes diffusely thickened (leoninefacies). Involvement of the nasal mucosae may block thenose and cause a bloodstained nasal discharge. Destructionof the nasal cartilage may occur later. Iritis and keratitisare often present. The voice may alter because of inflammationand thickening of the laryngeal mucosa. Testicularatrophy and gynaecomastia occur because of testiculardamage. Bilateral oedema of the legs is often present.Nerve involvement occurs late in the course of the disease.Renal failure due to glomerulonephritis and amyloiddisease are late complications in LL. Reactional statesIn reversal reactions the skin lesions and involved nervesbecome more inflamed and swollen. These reactions mayalso be accompanied by swelling of the face, hands andfeet. Involved nerves become very tender, often withfurther deterioration in function. This type of reaction maypersist for 2-3 months before subsiding.ENL produces acute inflammation of existing skinlesions in BL. The lesions become swollen and painful andslowly evolve through a livid appearance to residual hyperpigmentationof the affected skin. Bullae form over somelesions; these ulcerate and are slow to heal. New papulesappear in LL cases, typically on the extensor aspects of thelimbs. They may evolve over 2-3 days, through a bullousstage, to indolent ulcers which are slow to heal. Uveitis, lymphadenitis,orchitis and neuritis are also features of ENL.DiagnosisDiagnosis is based on the clinical features, characteristichistology, a positive lepromin test (at the tuberculoid endof the spectrum) and acid-fast bacilli in slit skin smearstaken from the edge of lesions and other sites, the earlobes,elbows and knees (BB, BL and LL). In pure neural leprosythe diagnosis can be made from a biopsy of a few fasciclesof an affected distal cutaneous nerve with no motor function,such as the radial cutaneous nerve at the wrist, or thesural nerve.ManagementMultidrug therapy is now the rule and the current WHO recommendations are set out in Table 9.31. These drugsare generally well tolerated. Dapsone occasionally causeshaemolysis. Clofazimine may stain the skin a ratherreddish hue.Mild upgrading reactions may be controlled with aspirinor non-steroidal anti-inflammatory drugs. More severereactions that threaten nerve function require oral steroids.ENL may be controlled by steroids, but sometimes thalidomideis needed.The patient needs careful instruction regarding the careof hands and feet, prevention of cracking and infection ofthe skin of the feet and appropriate footwear. Where thecornea is exposed as a result of facial nerve palsy, earlylateral tarsorrhaphy is essential to prevent corneal damage.Tendon transplants may help in managing foot and handdeformities.Prevention and controlThere is still a considerable stigma attached to leprosy; thisis based on ignorance. Education of the public regardingthe disease and the efficacy of treatment is beingattempted. BCG vaccination reduces the incidence ofleprosy. Currently there are efforts to define protectiveantigens which may result in a genetically engineeredvaccine.
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Schrodinger equation, in planar polar coords.?
A particle of mass m is confined to a planar circular region of radius R.
Show that the Schrodinger equation is separable into an equation that only depends on the radial coordinate and another that depends only upon the angular coordinate.
How would I begin doing this?
Keep in mind that separation of variables is a key concept in the understanding of series solutions to partial differential equations. Don't skimp on this concept by throwing it out to YA and transcribing someone's answer. Master this now or suffer later.
Review T separation. Express all operators of time independent form of SE in polar coordinates. Assume a solution of the form RO where R depends only on r and O depends only on theta. move all R and r terms to lhs of = and all O and theta terms to right. That equals the separation constant.
Blender 2.5 Radial Array ( Polar Array )
