Tuesday, August 15, 2017

THE BUTTERFLY EFFECT

The Butterfly Effect

Weather prediction is an extremely difficult problem. Meteorologists can predict the weather for short periods of time, a couple days at most, but beyond that predictions are generally poor.
Edward Lorenz was a mathematician and meteorologist at the Massachusetts Institute of Technology who loved the study of weather. With the advent of computers, Lorenz saw the chance to combine mathematics and meteorology. He set out to construct a mathematical model of the weather, namely a set of differential equations that represented changes in temperature, pressure, wind velocity, etc. In the end, Lorenz stripped the weather down to a crude model containing a set of 12 differential equations.
On a particular day in the winter of 1961, Lorenz wanted to re-examine a sequence of data coming from his model. Instead of restarting the entire run, he decided to save time and restart the run from somewhere in the middle. Using data printouts, he entered the conditions at some point near the middle of the previous run, and re-started the model calculation. What he found was very unusual and unexpected. The data from the second run should have exactly matched the data from the first run. While they matched at first, the runs eventually began to diverge dramatically — the second run losing all resemblance to the first within a few "model" months. A sample of the data from his two runs in shown below:
Lorenz's Sample Data
At first Lorenz thought that a vacuum tube had gone bad in his computer, a Royal McBee — an extremely slow and crude machine by today's standards. After discovering that there was no malfunction, Lorenz finally found the source of the problem. To save space, his printouts only showed three digits while the data in the computer's memory contained six digits. Lorenz had entered the rounded-off data from the printouts assuming that the difference was inconsequential. For example, even today temperature is not routinely measured within one part in a thousand.
This led Lorenz to realize that long-term weather forecasting was doomed. His simple model exhibits the phenomenon known as "sensitive dependence on initial conditions." This is sometimes referred to as the butterfly effect, e.g. a butterfly flapping its wings in South America can affect the weather in Central Park. The question then arises — why does a set of completely deterministic equations exhibit this behavior? After all, scientists are often taught that small initial perturbations lead to small changes in behavior. This was clearly not the case in Lorenz's model of the weather. The answer lies in the nature of the equations; they were nonlinear equations. While they are difficult to solve, nonlinear systems are central to chaos theory and often exhibit fantastically complex and chaotic behavior.

Friday, August 11, 2017

NERVES OF BODY

Alphabetical list

Related topic




    NERVES OF HEAD AND NECK

    NERVEPARENT NERVEMOTORINNERVATIONSENSORY INNERVATIONPATHWAY / DESCRIPTION / CLINICAL / NOTES / ETC
    Abducens (CN VI)Lateral Rectus muscle of the eyeRuns through the CAVERNOUS SINUS IN THE MIDDLE -- NOT ALONG THE LATERAL WALL; Injury = eye on affected side rotates inward
    Ansa CervicalesCervical Plexus ---> Ansa Cervicales; Hypoglossal (XII) ---> Ansa CervicalesStrap (Infrahyoid) musclesSuperior (C1-C2) hitch along Hypoglossus (XII) to innervate Strap Muscles
    Anterior EthmoidalTrigeminal (V) ---> Ophthalmic (V1) ---> Nasociliary ---> Anterior EthmoidalExternal Nose, anterior nasal cavityGives off internal and external nasal branches to supply sensory innervation to nose
    AuriculotemporalTrigeminal (V) ---> Mandibular (V3) ---> AuriculotemporalParasympathetic secretomotor to Parotid Gland via LESSER PETROSAL (IX)Outer ear and temporal region.Gives off Superficial Temporal Branches to supply sensory to the temporal region going up the side of the head; Receives parasympathetic fibers from Lesser Petrosal via OTIC GANGLION; It wraps around the MIDDLE MENINGEAL ARTERY
    BuccalTrigeminal (V) ---> Mandibular (V3) ---> BuccalCheek and oral mucosaRuns parallel with the Parotid duct
    Chorda TympaniFacial (VII) ---> Chorda TympaniParasympathetic secretomotor innervation to submandibular and sublingual glandsTaste to anterior 2/3 of tongueOne of the two parasympathetic branches of Facial N. (VII); Taste innervation excludes the Circumvallate Papillae; Exits middle ear out the PETROTYMPANIC FISSURE, before the Facial Canal. Then it synapses in SUBMANDIBULAR GANGLION, where it (1) joins up with Lingual N. (V3) to provide taste, and (2) sends secretomotor branches to target glands
    Deep Petrosal NerveInternal Carotid Plexus ---> Deep PetrosalSympathetic (inhibitory) to nasal mucosa and lacrimal glandsCarries SYMPATHETIC innervation from the Internal Carotid Plexus; Joins with Greater Petrosal to form Nerve of Pterygoid Canal; passes through the Sphenopalatine Ganglion but does NOT SYNAPSE; Gives branches to Nasopalatine N.
    External LaryngealVagus (X) ---> Superior Laryngeal ---> External LaryngealInferior Pharyngeal Muscle and CricothyroidGiven off of the Superior Laryngeal Nerve while it is within the CAROTID SHEATH
    External NasalTrigeminal (V) ---> Ophthalmic (V1) ---> Nasociliary ---> Anterior Ethmoidal ---> External Nasal; Trigeminal (V) ---> Maxillary (V2) ---> Infraorbital ---> External NasalExternal surface of noseHas anastomotic branches from both Ophthalmic (via Anterior Ethmoidal and Infratrochlear) and Maxillary (via Infraorbital) branches of the Trigeminal
    Facial (CN VII)BRANCHIAL motor (Arch II) to all muscles of facial expression; Secretomotor to all glands in head EXCEPT Parotid; Stapedius muscleTaste to anterior 2/3 of tongue (SVA); Somatic sensation to ear canal and ear drumTASTE Cell bodies are housed in GENICULATE GANGLION; Passes through Parotid Gland but does not innervate it; BELL'S PALSY = loss of facial expression; Branchial motor branches go out the STYLOMASTOID FORAMEN, and secretomotor branches DON'T.
    FrontalTrigeminal (V) ---> Ophthalmic (V1) ---> FrontalGives off Supratrochlear and Supraorbital branches.
    Glossopharyngeal (CN IX)Parasympathetic secretomotor to Parotid Gland; BRANCHIAL motor to Stylopharyngeus Muscle (Branchial Arch III)Taste to posterior 1/3 of tongue; Somatic sensation to posterior tongue, pharynx, and inner part of ear; Visceral Sensation to baroreceptors in the CAROTID SINUS; Somatic sensation to tympanic membraneExits Posterior Cranial Fossa through JUGULAR FORAMEN; Damage may ruin sensory to Oropharynx, which impairs SWALLOWING REFLEX; The nerve travels adhered to the STYLOPHARYNGEUS MUSCLE, then penetrates pharynx between Superior and Middle Constrictor muscles; Watch it when performing TONSILLECTOMY
    Great AuricularCervical Plexus (C2-C3) ---> Great AuricularExternal ear, region inferior to ear2nd nerve to penetrate investing fascia of Posterior Triangle of neck; Crosses Sternocleidomastoid and heads upward and toward anterior triangle
    Greater OccipitalCervical Dorsal Primary Ramus (C1) ---> Greater OccipitalBack of neckDistinguished from Lesser Occipital in that it is DORSAL PRIMARY RAMUS; Penetrates Trapezius to innervate back of neck
    Greater Petrosal NerveFacial (VII) ---> Greater PetrosalParasympathetic secretomotor to nasal mucosa and lacrimal glandsOne of the two parasympathetic branches of the Facial N,; Forms Nerve of Pterygoid Canal; synapses in PTERYGOPALATINE GANGLION, then gives branches to Nasopalatine N. (from V2)
    Hypoglossal (CN XII)All intrinsic and extrinsic muscles of the tongue, EXCEPT the PalatoglossusExits the posterior cranial fossa through HYPOGLOSSAL CANAL; a portion of Ansa Cervicales hangs off the Hypoglossal but does not intermix with it. Can be found lateral to and below the tongue, near the Lingual Nerve
    Inferior AlveolarTrigeminal (V) ---> Mandibular (V3) ---> Inferior AlveolarMylohyoid and Anterior Belly of DigastricMandibular (lower) teethThe continuation of the mandibular branch of the Trigeminal, after it has exited through FORAMEN OVALE. It reaches the lower teeth through the MANDIBULAR FORAMEN; Gives off a MYLOHYOID nerve and INCISIVE nerve to incisor teeth and continues onto Mental Foramen and out as Mental Nerve
    InfraorbitalTrigeminal (V) ---> Maxillary (V2)Cutaneous region beneath the eyes; external nose via External NasalExits INFRAORBITAL FORAMEN; gives off Superior Alveolar and External Nasal branches
    InfratrochlearTrigeminal (V) ---> Ophthalmic (V1) ---> Nasociliary ---> InfratrochlearInferomedial orbit, sometimes external nose via External NasalDivides into Internal and External nasal branches; it is the primary SENSORY supplier to the external nose
    Internal LaryngealVagus (X) ---> Superior Laryngeal ---> Internal LaryngealVisceral sensory from larynx and laryngeal mucosa in Supraglottic CavityPasses between the MIDDLE and INFERIOR pharyngeal constrictors; Pierces the THYROHYOID MEMBRANE
    Internal Nasal, Medial and LateralTrigeminal (V) ---> Ophthalmic (V1) ---> Nasociliary ---> Anterior Ethmoidal ---> Internal NasalInternal surface of nose, lower dorsum of noseThe Lateral Internal Nasal nerve continues to become the External Nasal Nerve, to innervate the tip of the nose
    LacrimalTrigeminal (V) ---> Ophthalmic (V1) ---> Frontal ---> LacrimalParasympathetic secretomotor to Lacrimal glands via GREATER PETROSAL VII)Parasympathetic fibers originate from the Greater Petrosal Nerve, which joins with the Ophthalmic (V1) in the orbit
    Lesser OccipitalCervical Plexus (C2-C3) ---> Lesser OccipitalPosterior to ear and back of neck1st nerve to penetrates investing fascia of Posterior Triangle of neck
    Lesser PetrosalGlossopharyngeal (IX) ---> Tympanic ---> Lesser PetrosalSecretomotor to Parotid GlandPasses out the LESSER PETROSAL HIATUS of Temporal Bone, then passes forward and out FORAMEN OVALE; Synapses in OTIC GANGLION, and then innervates the Parotid Gland via Auriculotemporal Nerve (V3)
    LingualTrigeminal (V) ---> Mandibular (V3) ---> LingualSomatic sensation to anterior 2/3 of tongue; Taste to anterior 2/3 via the Chorda TympaniChorda Tympani (from CN VII) joins the Lingual Nerve to provide the SVA fibers to the tongue; it wraps around the Submandibular Duct in the mouth
    Long CiliaryTrigeminal (V) ---> Ophthalmic (V1) ---> Nasociliary ---> Long CiliarySYMPATHETIC to the Dilator Pupillae Muscle, via Internal Carotid PlexusPain information from the surface of the CorneaCarries SYMPATHETIC innervation from the Internal Carotid Plexus to the dilator muscle from the sympathetic Internal Carotid Plexus
    Mandibular (V3)Trigeminal (V) ---> Mandibular (V3)BRANCHIAL motor to Muscles of Mastication; Tensor Tympani; Tensor Palati; Mylohyoid and Anterior Belly of DigastricSomatic sensation to anterior 2/3 of tongue; cutaneous chin; mandibular teethSensory components exit through FORAMEN OVALE of the Sphenoid; motor components do not; It is the only branch of CN III-VI to NOT go through cavernous sinus
    Maxillary (V2)Trigeminal (V) ---> Maxillary (V2)Cutaneous upper lip, nose, and infraorbital region; maxillary teeth; Nasopharynx; Soft PalateExits skull through FORAMEN ROTUNDUM to enter Sphenopalatine Fossa; Sensory innervation to nasopharynx is important during SWALLOWING; Branches into Zygomatic, Posterior Superior Alveolar, Greater and Lesser Palatine, and Nasopalatine branches; Runs through CAVERNOUS SINUS along lateral wall
    MentalTrigeminal (V) ---> Mandibular (V3) ---> Inferior Alveolar ---> MentalCutaneous chin, lower lip, and side of mandibleUltimately from Mandibular (V3), a terminal branch of the Inferior Alveolar past the MENTAL FORAMEN of the mandible
    NasociliaryTrigeminal (V) ---> Ophthalmic (V1) ---> NasociliaryNose, and pain information from corneaRuns along the medial side of the orbit, and divides into anterior ethmoidal and infratrochlear. It also gives off posterior ethmoidal; it is the sensory root to the CILIARY GANGLION
    NasopalatineTrigeminal (V) ---> Maxillary (V2) ---> NasopalatineBoth parasympathetic and sympathetic to Nasal Mucosa, via GREATER PETROSAL (VII) and DEEP PETROSAL, respectivelyAnterior potion of hard palate behind incisors (front teeth); perhaps some internal nasal cavityReceives Greater Petrosal and Deep Petrosal fibers from SPHENOPALATINE GANGLION; Enters nasal cavity through SPHENOPALATINE FORAMEN, where it gives off lateral and septal branches to nose; Continues through INCISIVE FORAMEN along the SEPTAL WALL, to innervate anterior hard palate
    Oculomotor (CN III)Extrinsic eye muscles, EXCEPT Lateral Rectus and Superior Oblique; Intrinsic Sphincter Pupillae and Ciliary MusclesEnters the orbit through the SUPERIOR ORBITAL FISSURE; Synapses in Ciliary Ganglion; Carries PARASYMPATHETIC innervation to the Sphincter Pupillae and Ciliary Muscles; Runs through the CAVERNOUS SINUS along the lateral wall
    Olfactory (CN I)OlfactionCell bodies are in Olfactory Mucosa of Superior Conchae; axons go through CRIBRIFORM PLATE of Ethmoid; Then they go back to CNS along OLFACTORY TRACTS
    OphthalmicTrigeminal (V) ---> Ophthalmic (V1)Cutaneous nose, supraorbital region, and foreheadRuns through the CAVERNOUS SINUS along the lateral wall; Synapses in CILIARY GANGLION. Enters the orbit in the SUPERIOR ORBITAL FISSURE
    Optic (CN II)SightEnters the orbit through the OPTIC CANAL, in the Lesser Wing of the Sphenoid; The optic nerve is only that portion between the eye and the Optic Chiasm; TUNNEL VISION = lesion at Optic Chiasm
    Palatine, Greater and LesserTrigeminal (V) ---> Maxillary (V2) ---> Infraorbital ---> Descending PalatineHard and soft palate, lateral nasal wallAlso called descending Palatine Branches of the Infraorbital; Goes through PALATINE FORAMEN to reach hard palate in back of mouth
    PharyngealVagus (X) ---> PharyngealBranchial motor to all muscles of the pharynx and soft palateEnters the pharynx between the superior and middle pharyngeal constrictors
    PhrenicCervical Plexus (C3-C5) ---> PhrenicDiaphragmIt is plastered on top of the Anterior Scalene muscle
    Recurrent LaryngealVagus (X) ---> Recurrent LaryngealAll intrinsic muscles of the Larynx EXCEPT the CricothyroidLaryngeal Mucosa in Infraglottic CavityTravels under Subclavian Artery and the right side, and under the Aortic Arch on the left side; can be found inferior to the Inferior Pharyngeal Constrictor; Easily damaged due to long course
    Short CIliaryTrigeminal (V) ---> Ophthalmic (V1) ---> Nasociliary ---> Short CiliaryParasympathetic to Constrictor Pupillae and Ciliary Muscle, via OCULOMOTOR (III). Also carried SYMPATHETICSReceives PARASYMPATHETIC fibers from the Oculomotor (III), via the Ciliary Ganglion. Also some sensory to the cornea + sympathetic to dilator
    Spinal Accessory (CN XI)Trapezius and Sternocleidomastoid BRANCHIAL MusclesCell Bodies are in SPINAL CHORD (C1-C5): They enter skull through FORAMEN MAGNUM, and then exit again through JUGULAR FORAMEN.
    Superior AlveolarTrigeminal (V) ---> Maxillary (V2) ---> Infraorbital ---> Superior AlveolarMaxillary teethGives off Anterior, Middle (through infraorbital sulcus) and Posterior (in pterygopalatine fossa) branches
    Superior LaryngealVagus (X) ---> Superior LaryngealInferior Pharyngeal Muscle and CricothyroidVisceral sensory from larynx, via the Internal LaryngealDivides into Internal Laryngeal and External Laryngeal branches; Damage can be tested by touching laryngeal mucosa to test for sensation
    SupraorbitalTrigeminal (V) ---> Ophthalmic (V1) ---> Frontal ---> SupraorbitalCutaneous region above the eyes
    SupratrochlearTrigeminal (V) ---> Ophthalmic (V1) ---> Frontal ---> SupratrochlearSuperolateral portion of orbit
    SupraclavicularCervical Plexus (C3-C4) ---> SupraclavicularAnterolateral shoulder, clavicular region4th nerve to penetrate investing fascia of Posterior Triangle of neck; heads downward and anteriorly
    Transverse CervicalCervical Plexus (C2-C3) ---> Transverse CervicalNeck around sternocleidomastoid3rd nerve to penetrate investing fascia of Posterior Triangle of neck; Crosses Sternocleidomastoid and heads directly anteriorly.
    Trigeminal (CN V)BRANCHIAL motor (Arch I) to Muscles of Mastication; Tensor Tympani; Tensor Palati; Mylohyoid and Anterior Belly of DigastricAll sensory innervation for the faceThe four parasympathetic ganglia hang off the various branches of the trigeminal; Divides into three principle branches: Opthalmic (V1), Maxillary (V2), and Mandibular (V3)
    Trochlear (CN IV)Superior Oblique muscle of the eyeIt is easily injured due to its long tortuous path (it arises from opposite side of brain and exits dorsally); it is difficult to test due to redundant action; Runs through CAVERNOUS SINUS along lateral wall
    TympanicGlossopharyngeal (IX) ---> TympanicSecretomotor to Parotid GlandGiven off from CN IX at Jugular Foramen; forms TYMPANIC PLEXUS; Exits out LESSER PETROSAL HIATUS, after which it is known as Lesser Petrosal Nerve
    Vagus (CN X)BRANCHIAL (Arches IV-VI) motor to all muscles of larynx, pharynx, and palate, EXCEPT Stylopharyngeus and Tensor Veli Palati; Parasympathetics to Thoracic and Abdominal visceraVisceral from part of tongue, pharynx and larynx, lungs and heart, CAROTID BODY, stomach; General sensory from larynx, pharynx, and part of external auditory canalExits posterior cranial fossa through JUGULAR FORAMEN; Travels in CAROTID SHEATH; Some say Vagus carries SVA taste fibers from a few taste buds in the tongue; Superior and Inferior Vagus Ganglia house SENSORY cell bodies, located inside and just beneath the Jugular Foramen, respectively
    Vestibulocochlear (CN VIII)Visceral sensory from Semicircular Canals, Utricle, and Saccule; SSA from cochlea = HearingReally two nerves: Auditory innervates the cochlea and Vestibular innervates the semi-circular canals; exits cranium through INTERNAL ACOUSTIC MEATUS
    Vidian's (Nerve of Pterygoid Canal)FACIAL (VII) ---> Greater Petrosal; and INTERNAL CAROTID PLEXUS ---> Deep PetrosalNasal, Lacrimal.Goes through PTERYGOID CANAL to PTERYGOPALATINE GANGLION, and on to innervate nasal + lacrimal glands via nasopalatine and lacrimal nerves, respectively; Parasympathetic from Greater Petrosal (VII) and sympathetic from Deep Petrosal
    ZygomaticTrigeminal (V) ---> Maxillary (V2) ---> ZygomaticParasympathetics to the Lacrimal GlandsFacial and temporal regions inferolateral to eyesSplits into zygomaticofacial and zygomaticotemporal branches; carries PARASYMPATHETICS to the lacrimal glands for a short time, before they join with the Lacrimal N.
    ZygomaticofacialTrigeminal (V) ---> Maxillary (V2) ---> Zygomatic ---> ZygomaticofacialFacial (anterior) part of Zygomatic archGoes out ZYGOMATICOFACIAL FORAMEN, in the prominence of the Zygomatic bone, right past Pterygopalatine Ganglion
    ZygomaticotemporalTrigeminal (V) ---> Maxillary (V2) ---> Zygomatic ---> ZygomaticotemporalTemporal (posterior) part of Zygomatic archGoes out ZYGOMATICOFACIAL FORAMEN, right past Pterygopalatine Ganglion

    MAIN MUSCLES OF HEAD AND NECK