Helium atom

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Helium_atom 

Helium atom

Helium-4
Names
Systematic IUPAC name Helium
Identifiers
CAS Number	7440-59-7
3D model (JSmol)	Interactive image
ChEBI	CHEBI:33681
ChemSpider	22423
EC Number	231-168-5
Gmelin Reference	16294
KEGG	D04420
MeSH	Helium
PubChem CID	23987
RTECS number	MH6520000
UNII	206GF3GB41
UN number	1046

InChI

SMILES
Properties
Chemical formula	He
Molar mass	4.002602 g·mol−1
Appearance	Colourless gas
Boiling point	−269 °C (−452.20 °F; 4.15 K)
Thermochemistry
Std molar entropy (So298)	126.151-126.155 J K−1 mol−1
Pharmacology
ATC code	V03AN03 (WHO)
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).

A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with either one or two neutrons, depending on the isotope, held together by the strong force. Unlike for hydrogen, a closed-form solution to the Schrödinger equation for the helium atom has not been found. However, various approximations, such as the Hartree–Fock method, can be used to estimate the ground state energy and wavefunction of the atom.

Introduction

Schematic termscheme for Para- and Orthohelium with one electron in ground state 1s and one excited electron.

The quantum mechanical description of the helium atom is of special interest, because it is the simplest multi-electron system and can be used to understand the concept of quantum entanglement. The Hamiltonian of helium, considered as a three-body system of two electrons and a nucleus and after separating out the centre-of-mass motion, can be written as

$${\displaystyle H(\mathbf {r} _{1},\,\mathbf {r} _{2})=\sum _{i=1,2}\left(-{\frac {\hbar ^{2}}{2\mu }}\nabla _{r_{i}}^{2}-{\frac {Ze^{2}}{4\pi \varepsilon _{0}r_{i}}}\right)-{\frac {\hbar ^{2}}{M}}\nabla _{r_{1}}\cdot \nabla _{r_{2}}+{\frac {e^{2}}{4\pi \varepsilon _{0}r_{12}}}}$$

where ${\displaystyle \mu ={\frac {mM}{m+M}}}$ is the reduced mass of an electron with respect to the nucleus, ${\displaystyle \mathbf {r} _{1}}$ and ${\displaystyle \mathbf {r} _{2}}$ are the electron-nucleus distance vectors and ${\displaystyle r_{12}=|\mathbf {r} _{1}-\mathbf {r} _{2}|}$. The nuclear charge, ${\displaystyle Z}$ is 2 for helium. In the approximation of an infinitely heavy nucleus, ${\displaystyle M=\infty }$ we have ${\displaystyle \mu =m}$ and the mass polarization term ${\textstyle {\frac {\hbar ^{2}}{M}}\nabla _{r_{1}}\cdot \nabla _{r_{2}}}$ disappears. In atomic units the Hamiltonian simplifies to

$${\displaystyle H(\mathbf {r} _{1},\,\mathbf {r} _{2})=-{\frac {1}{2}}\nabla _{r_{1}}^{2}-{\frac {1}{2}}\nabla _{r_{2}}^{2}-{\frac {Z}{r_{1}}}-{\frac {Z}{r_{2}}}+{\frac {1}{r_{12}}}.}$$

It is important to note, that it operates not in normal space, but in a 6-dimensional configuration space ${\displaystyle (\mathbf {r} _{1},\,\mathbf {r} _{2})}$. In this approximation (Pauli approximation) the wave function is a second order spinor with 4 components ${\displaystyle \psi _{ij}(\mathbf {r} _{1},\,\mathbf {r} _{2})}$, where the indices ${\displaystyle i,j=\,\uparrow ,\downarrow }$ describe the spin projection of both electrons (z-direction up or down) in some coordinate system. It has to obey the usual normalization condition ${\textstyle \sum _{ij}\int d\mathbf {r} _{1}d\mathbf {r} _{2}|\psi _{ij}|^{2}=1}$. This general spinor can be written as 2×2 matrix ${\textstyle {\boldsymbol {\psi }}={\begin{pmatrix}\psi _{\uparrow \uparrow }&\psi _{\uparrow \downarrow }\\\psi _{\downarrow \uparrow }&\psi _{\downarrow \downarrow }\end{pmatrix}}}$ and consequently also as linear combination of any given basis of four orthogonal (in the vector-space of 2×2 matrices) constant matrices ${\displaystyle {\boldsymbol {\sigma }}_{k}^{i}}$ with scalar function coefficients ${\displaystyle \phi _{i}^{k}(\mathbf {r} _{1},\,\mathbf {r} _{2})}$ as ${\textstyle {\boldsymbol {\psi }}=\sum _{ik}\phi _{i}^{k}(\mathbf {r} _{1},\,\mathbf {r} _{2}){\boldsymbol {\sigma }}_{k}^{i}}$. A convenient basis consists of one anti-symmetric matrix (with total spin ${\displaystyle S=0}$, corresponding to a singlet state)

$${\displaystyle {\boldsymbol {\sigma }}_{0}^{0}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1\\-1&0\end{pmatrix}}={\frac {1}{\sqrt {2}}}(\uparrow \downarrow -\downarrow \uparrow )}$$

and three symmetric matrices (with total spin ${\displaystyle S=1}$, corresponding to a triplet state)

$${\displaystyle {\begin{aligned}&{\boldsymbol {\sigma }}_{0}^{1}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}={\frac {1}{\sqrt {2}}}(\uparrow \downarrow +\downarrow \uparrow )\;;\\[4pt]&{\boldsymbol {\sigma }}_{1}^{1}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}=\;\uparrow \uparrow \;;\;\;{\boldsymbol {\sigma }}_{-1}^{1}={\begin{pmatrix}0&0\\0&1\end{pmatrix}}=\;\downarrow \downarrow \;.\end{aligned}}}$$

It is easy to show, that the singlet state is invariant under all rotations (a scalar entity), while the triplet can be mapped to an ordinary space vector ${\displaystyle (\sigma _{x},\sigma _{y},\sigma _{z})}$, with the three components

$${\displaystyle \sigma _{x}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}1&0\\0&-1\end{pmatrix}},\quad \sigma _{y}={\frac {i}{\sqrt {2}}}{\begin{pmatrix}1&0\\0&1\end{pmatrix}},\quad \sigma _{z}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}.}$$

Since all spin interaction terms between the four components of ${\displaystyle {\boldsymbol {\psi }}}$ in the above (scalar) Hamiltonian are neglected (e.g. an external magnetic field, or relativistic effects, like angular momentum coupling), the four Schrödinger equations can be solved independently.

The spin here only comes into play through the Pauli exclusion principle, which for fermions (like electrons) requires antisymmetry under simultaneous exchange of spin and coordinates

$${\displaystyle {\boldsymbol {\psi }}_{ij}(\mathbf {r} _{1},\,\mathbf {r} _{2})=-{\boldsymbol {\psi }}_{ji}(\mathbf {r} _{2},\,\mathbf {r} _{1}).}$$

Parahelium is then the singlet state ${\displaystyle {\boldsymbol {\psi }}=\phi _{0}(\mathbf {r} _{1},\,\mathbf {r} _{2}){\boldsymbol {\sigma }}_{0}^{0}}$ with a symmetric function ${\displaystyle \phi _{0}(\mathbf {r} _{1},\,\mathbf {r} _{2})=\phi _{0}(\mathbf {r} _{2},\,\mathbf {r} _{1})}$ and orthohelium is the triplet state ${\displaystyle {\boldsymbol {\psi }}_{m}=\phi _{1}(\mathbf {r} _{1},\,\mathbf {r} _{2}){\boldsymbol {\sigma }}_{m}^{1},\;m=-1,0,1}$ with an antisymmetric function ${\displaystyle \phi _{1}(\mathbf {r} _{1},\,\mathbf {r} _{2})=-\phi _{1}(\mathbf {r} _{2},\,\mathbf {r} _{1})}$. If the electron-electron interaction term is ignored, both spatial functions ${\displaystyle \phi _{x},\;x=0,1}$ can be written as linear combination of two arbitrary (orthogonal and normalized) one-electron eigenfunctions ${\displaystyle \varphi _{a},\varphi _{b}}$:

$${\displaystyle \phi _{x}={\frac {1}{\sqrt {2}}}(\varphi _{a}(\mathbf {r} _{1})\varphi _{b}(\mathbf {r} _{2})\pm \varphi _{a}(\mathbf {r} _{2})\varphi _{b}(\mathbf {r} _{1}))}$$

or for the special cases of ${\displaystyle \varphi _{a}=\varphi _{b}}$ (both electrons have identical quantum numbers, parahelium only): ${\displaystyle \phi _{0}=\varphi _{a}(\mathbf {r} _{1})\varphi _{a}(\mathbf {r} _{2})}$. The total energy (as eigenvalue of ${\displaystyle H}$) is then for all cases ${\displaystyle E=E_{a}+E_{b}}$ (independent of the symmetry).

This explains the absence of the ${\displaystyle 1^{3}S_{1}}$ state (with ${\displaystyle \varphi _{a}=\varphi _{b}=\varphi _{1s}}$) for orthohelium, where consequently ${\displaystyle 2^{3}S_{1}}$ (with ${\displaystyle \varphi _{a}=\varphi _{1s},\varphi _{b}=\varphi _{2s}}$) is the metastable ground state. (A state with the quantum numbers: principal quantum number ${\displaystyle n}$, total spin ${\displaystyle S}$, angular quantum number ${\displaystyle L}$ and total angular momentum ${\displaystyle J=|L-S|,\dots ,L+S}$ is denoted by ${\displaystyle n^{2S+1}L_{J}}$.)

If the electron-electron interaction term ${\textstyle {\frac {1}{r_{12}}}}$ is included, the Schrödinger equation is non separable. However, even if it is neglected, all states described above (even with two identical quantum numbers, like ${\displaystyle 1^{1}S_{0}}$ with ${\displaystyle {\boldsymbol {\psi }}=\varphi _{1s}(\mathbf {r} _{1})\varphi _{1s}(\mathbf {r} _{2}){\boldsymbol {\sigma }}_{0}^{0}}$) cannot be written as a product of one-electron wave functions: ${\displaystyle \psi _{ik}(\mathbf {r} _{1},\,\mathbf {r} _{2})\neq \chi _{i}(\mathbf {r} _{1})\xi _{k}(\mathbf {r} _{2})}$ — the wave function is entangled. One cannot say, particle 1 is in state 1 and the other in state 2, and measurements cannot be made on one particle without affecting the other.

Nevertheless, quite good theoretical descriptions of helium can be obtained within the Hartree–Fock and Thomas–Fermi approximations (see below).

The Hartree–Fock method is used for a variety of atomic systems. However it is just an approximation, and there are more accurate and efficient methods used today to solve atomic systems. The "many-body problem" for helium and other few electron systems can be solved quite accurately. For example, the ground state of helium is known to fifteen digits. In Hartree–Fock theory, the electrons are assumed to move in a potential created by the nucleus and the other electrons.

Perturbation method

The Hamiltonian for helium with two electrons can be written as a sum of the Hamiltonians for each electron:

$${\displaystyle H=\sum _{i=1}^{2}h(i)=H_{0}+H'}$$

where the zero-order unperturbed Hamiltonian is

$${\displaystyle H_{0}=-{\frac {1}{2}}\nabla _{r_{1}}^{2}-{\frac {1}{2}}\nabla _{r_{2}}^{2}-{\frac {Z}{r_{1}}}-{\frac {Z}{r_{2}}}}$$

while the perturbation term:

$${\displaystyle H'={\frac {1}{r_{12}}}}$$

is the electron-electron interaction. H₀ is just the sum of the two hydrogenic Hamiltonians:

$${\displaystyle H_{0}={\hat {h}}_{1}+{\hat {h}}_{2}}$$

where

$${\displaystyle {\hat {h}}_{i}=-{\frac {1}{2}}\nabla _{r_{i}}^{2}-{\frac {Z}{r_{i}}},i=1,2}$$

E_ni, the energy eigenvalues and ${\displaystyle \psi _{n_{i},\ell _{i},m_{i}}(\mathbf {r} _{i})}$, the corresponding eigenfunctions of the hydrogenic Hamiltonian will denote the normalized energy eigenvalues and the normalized eigenfunctions. So:

$${\displaystyle {\hat {h}}_{i}\psi _{n_{i},\ell _{i},m_{i}}(\mathbf {r} _{i})=E_{n_{i}}\psi _{n_{i},\ell _{i},m_{i}}(\mathbf {r} _{i})}$$

where

$${\displaystyle E_{n_{i}}=-{\frac {1}{2}}{\frac {Z^{2}}{n_{i}^{2}}}{\text{ in a.u.}}}$$

Neglecting the electron-electron repulsion term, the Schrödinger equation for the spatial part of the two-electron wave function will reduce to the 'zero-order' equation

$${\displaystyle H_{0}\psi ^{(0)}(\mathbf {r} _{1},\mathbf {r} _{2})=E^{(0)}\psi ^{(0)}(\mathbf {r} _{1},\mathbf {r} _{2})}$$

This equation is separable and the eigenfunctions can be written in the form of single products of hydrogenic wave functions:

$${\displaystyle \psi ^{(0)}(\mathbf {r} _{1},\mathbf {r} _{2})=\psi _{n_{1},\ell _{1},m_{1}}(\mathbf {r} _{1})\psi _{n_{2},\ell _{2},m_{2}}(\mathbf {r} _{2})}$$

The corresponding energies are (in atomic units, hereafter a.u.):

$${\displaystyle E_{n_{1},n_{2}}^{(0)}=E_{n_{1}}+E_{n_{2}}=-{\frac {Z^{2}}{2}}\left[{\frac {1}{n_{1}^{2}}}+{\frac {1}{n_{2}^{2}}}\right]}$$

Note that the wave function

$${\displaystyle \psi ^{(0)}(\mathbf {r} _{2},\mathbf {r} _{1})=\psi _{n_{2},\ell _{2},m_{2}}(\mathbf {r} _{1})\psi _{n_{1},\ell _{1},m_{1}}(\mathbf {r} _{2})}$$

An exchange of electron labels corresponds to the same energy ${\displaystyle E_{n_{1},n_{2}}^{(0)}}$. This particular case of degeneracy with respect to exchange of electron labels is called exchange degeneracy. The exact spatial wave functions of two-electron atoms must either be symmetric or antisymmetric with respect to the interchange of the coordinates ${\displaystyle \mathbf {r} _{1}}$ and ${\displaystyle \mathbf {r} _{2}}$ of the two electrons. The proper wave function then must be composed of the symmetric (+) and antisymmetric(−) linear combinations:

$${\displaystyle \psi _{\pm }^{(0)}(\mathbf {r} _{1},\mathbf {r} _{2})={\frac {1}{\sqrt {2}}}\left[\psi _{n_{1},\ell _{1},m_{1}}(\mathbf {r} _{1})\psi _{n_{2},\ell _{2},m_{2}}(\mathbf {r} _{2})\pm \psi _{n_{2},\ell _{2},m_{2}}(\mathbf {r} _{1})\psi _{n_{1},\ell _{1},m_{1}}(\mathbf {r} _{2})\right]}$$

This comes from Slater determinants.

The factor ${\textstyle {\frac {1}{\sqrt {2}}}}$ normalizes ${\displaystyle \psi _{\pm }^{(0)}}$. In order to get this wave function into a single product of one-particle wave functions, we use the fact that this is in the ground state. So ${\displaystyle n_{1}=n_{2}=1,\,\ell _{1}=\ell _{2}=0,\,m_{1}=m_{2}=0}$. So the ${\displaystyle \psi _{-}^{(0)}}$ will vanish, in agreement with the original formulation of the Pauli exclusion principle, in which two electrons cannot be in the same state. Therefore, the wave function for helium can be written as

$${\displaystyle \psi _{0}^{(0)}(\mathbf {r} _{1},\mathbf {r} _{2})=\psi _{1}(\mathbf {r_{1}} )\psi _{1}(\mathbf {r_{2}} )={\frac {Z^{3}}{\pi }}e^{-Z(r_{1}+r_{2})}}$$

Where ${\displaystyle \psi _{1}}$ and ${\displaystyle \psi _{2}}$ use the wave functions for the hydrogen Hamiltonian. For helium, Z = 2 from

$${\displaystyle E_{0}^{(0)}=E_{n_{1}=1,\,n_{2}=1}^{(0)}=-Z^{2}{\text{ a.u.}}}$$

where E⁽⁰⁾
₀ = −4 a.u. which is approximately −108.8 eV, which corresponds to an ionization potential V⁽⁰⁾
_P = 2 a.u. (≅54.4 eV). The experimental values are E₀ = −2.90 a.u. (≅ −79.0 eV) and V_p = 0.90 a.u. (≅ 24.6 eV).

The energy that we obtained is too low because the repulsion term between the electrons was ignored, whose effect is to raise the energy levels. As Z gets bigger, our approach should yield better results, since the electron-electron repulsion term will get smaller.

So far a very crude independent-particle approximation has been used, in which the electron-electron repulsion term is completely omitted. Splitting the Hamiltonian showed below will improve the results:

$${\displaystyle H={\bar {H_{0}}}+{\bar {H'}}}$$

where

$${\displaystyle {\bar {H_{0}}}=-{\frac {1}{2}}\nabla _{r_{1}}^{2}+V(r_{1})-{\frac {1}{2}}\nabla _{r_{2}}^{2}+V(r_{2})}$$

and

$${\displaystyle {\bar {H'}}={\frac {1}{r_{12}}}-{\frac {Z}{r_{1}}}-V(r_{1})-{\frac {Z}{r_{2}}}-V(r_{2})}$$

V(r) is a central potential which is chosen so that the effect of the perturbation ${\displaystyle {\bar {H'}}}$ is small. The net effect of each electron on the motion of the other one is to screen somewhat the charge of the nucleus, so a simple guess for V(r) is

$${\displaystyle V(r)=-{\frac {Z-S}{r}}=-{\frac {Z_{e}}{r}}}$$

where S is a screening constant and the quantity Z_e is the effective charge. The potential is a Coulomb interaction, so the corresponding individual electron energies are given (in a.u.) by

$${\displaystyle E_{0}=-(Z-S)^{2}=-Z_{e}^{2}}$$

and the corresponding wave function is given by

$${\displaystyle \psi _{0}(r_{1}\,,r_{2})={\frac {Z_{e}^{3}}{\pi }}e^{-Z_{e}(r_{1}+r_{2})}}$$

If Z_e was 1.70, that would make the expression above for the ground state energy agree with the experimental value E₀ = −2.903 a.u. of the ground state energy of helium. Since Z = 2 in this case, the screening constant is S = 0.30. For the ground state of helium, for the average shielding approximation, the screening effect of each electron on the other one is equivalent to about ${\textstyle {\frac {1}{3}}}$ of the electric charge.

The variational method

To obtain a more accurate energy the variational principle can be applied to the electron-electron potential V_ee using the wave function

$${\displaystyle \psi _{0}(\mathbf {r} _{1},\,\mathbf {r} _{2})={\frac {8}{\pi a^{3}}}e^{-2(r_{1}+r_{2})/a}}$$

$${\displaystyle \langle H\rangle =8E_{1}+\langle V_{ee}\rangle =8E_{1}+\left({\frac {e^{2}}{4\pi \varepsilon _{0}}}\right)\left({\frac {8}{\pi a^{3}}}\right)^{2}\int {\frac {e^{-4(r_{1}+r_{2})/a}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}\,d^{3}\mathbf {r} _{1}\,d^{3}\mathbf {r} _{2}}$$

After integrating this, the result is:

$${\displaystyle \langle H\rangle =8E_{1}+{\frac {5}{4a}}\left({\frac {e^{2}}{4\pi \epsilon _{0}}}\right)=8E_{1}-{\frac {5}{2}}E_{1}=-109+34=-75{\text{ eV}}}$$

This is closer to the experimental value, but if a better trial wave function is used, an even more accurate answer could be obtained. An ideal wave function would be one that doesn't ignore the influence of the other electron. In other words, each electron represents a cloud of negative charge which somewhat shields the nucleus so that the other electron actually sees an effective nuclear charge Z that is less than 2. A wave function of this type is given by:

$${\displaystyle \psi (\mathbf {r} _{1},\mathbf {r} _{2})={\frac {Z^{3}}{\pi a^{3}}}e^{-Z(r_{1}+r_{2})/a}}$$

Treating Z as a variational parameter to minimize H. The Hamiltonian using the wave function above is given by:

$${\displaystyle \langle H\rangle =2Z^{2}E_{1}+2(Z-2)\left({\frac {e^{2}}{4\pi \varepsilon _{0}}}\right)\left\langle {\frac {1}{r}}\right\rangle +\left\langle V_{ee}\right\rangle }$$

After calculating the expectation value of ${\textstyle {\frac {1}{r}}}$ and V_ee the expectation value of the Hamiltonian becomes:

$${\displaystyle \langle H\rangle =\left[-2Z^{2}+{\frac {27}{4}}Z\right]E_{1}}$$

The minimum value of Z needs to be calculated, so taking a derivative with respect to Z and setting the equation to 0 will give the minimum value of Z:

$${\displaystyle {\frac {d}{dZ}}\left(\left[-2Z^{2}+{\frac {27}{4}}Z\right]E_{1}\right)=0}$$

$${\displaystyle Z={\frac {27}{16}}\sim 1.69}$$

This shows that the other electron somewhat shields the nucleus reducing the effective charge from 2 to 1.69. So we obtain the most accurate result yet:

$${\displaystyle {\frac {1}{2}}\left({\frac {3}{2}}\right)^{6}E_{1}=-77.5{\text{ eV}}}$$

Where again, E₁ represents the ionization energy of hydrogen.

By using more complicated/accurate wave functions, the ground state energy of helium has been calculated closer and closer to the experimental value −78.95 eV. The variational approach has been refined to very high accuracy for a comprehensive regime of quantum states by G.W.F. Drake and co-workers as well as J.D. Morgan III, Jonathan Baker and Robert Hill using Hylleraas or Frankowski-Pekeris basis functions. One needs to include relativistic and quantum electrodynamic corrections to get full agreement with experiment to spectroscopic accuracy.

Experimental value of ionization energy

Helium's first ionization energy is −24.587387936(25) eV. This value was derived by experiment. The theoretic value of Helium atom's second ionization energy is −54.41776311(2) eV. The total ground state energy of the helium atom is −79.005151042(40) eV, or −2.90338583(13) Atomic units a.u., which equals −5.80677166 (26) Ry.

Major trauma

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Major_trauma 

Major trauma
Health care providers attending to a person on a stretcher with a gunshot wound to the head; the patient is intubated, and a mechanical ventilator is visible in the background

Major trauma is any injury that has the potential to cause prolonged disability or death. There are many causes of major trauma, blunt and penetrating, including falls, motor vehicle collisions, stabbing wounds, and gunshot wounds. Depending on the severity of injury, quickness of management, and transportation to an appropriate medical facility (called a trauma center) may be necessary to prevent loss of life or limb. The initial assessment is critical, and involves a physical evaluation and also may include the use of imaging tools to determine the types of injuries accurately and to formulate a course of treatment.

In 2002, unintentional and intentional injuries were the fifth and seventh leading causes of deaths worldwide, accounting for 6.23% and 2.84% of all deaths. For research purposes the definition often is based on an injury severity score (ISS) of greater than 15.

Classification

Injuries generally are classified by either severity, the location of damage, or a combination of both. Trauma also may be classified by demographic group, such as age or gender. It also may be classified by the type of force applied to the body, such as blunt trauma or penetrating trauma. For research purposes injury may be classified using the Barell matrix, which is based on ICD-9-CM. The purpose of the matrix is for international standardization of the classification of trauma. Major trauma sometimes is classified by body area; injuries affecting 40% are polytrauma, 30% head injuries, 20% chest trauma, 10%, abdominal trauma, and 2%, extremity trauma.

Various scales exist to provide a quantifiable metric to measure the severity of injuries. The value may be used for triaging a patient or for statistical analysis. Injury scales measure damage to anatomical parts, physiological values (blood pressure etc.), comorbidities, or a combination of those. The abbreviated injury scale and the Glasgow coma scale are used commonly to quantify injuries for the purpose of triaging and allow a system to monitor or "trend" a patient's condition in a clinical setting. The data also may be used in epidemiological investigations and for research purposes.

Approximately 2% of those who have experienced significant trauma have a spinal cord injury.

Causes

Injuries may be caused by any combination of external forces that act physically against the body. The leading causes of traumatic death are blunt trauma, motor vehicle collisions, and falls, followed by penetrating trauma such as stab wounds or impaled objects. Subsets of blunt trauma are both the number one and two causes of traumatic death.

For statistical purposes, injuries are classified as either intentional such as suicide, or unintentional, such as a motor vehicle collision. Intentional injury is a common cause of traumas. Penetrating trauma is caused when a foreign body such as a bullet or a knife enters the body tissue, creating an open wound. In the United States, most deaths caused by penetrating trauma occur in urban areas and 80% of these deaths are caused by firearms. Blast injury is a complex cause of trauma because it commonly includes both blunt and penetrating trauma, and also may be accompanied by a burn injury. Trauma also may be associated with a particular activity, such as an occupational or sports injury.

Pathophysiology

The body responds to traumatic injury both systemically and at the injury site. This response attempts to protect vital organs such as the liver, to allow further cell duplication and to heal the damage. The healing time of an injury depends on various factors including sex, age, and the severity of injury.

The symptoms of injury may manifest in many different ways, including:

• Altered mental status
• Fever
• Increased heart rate
• Generalized edema
• Increased cardiac output
• Increased rate of metabolism

Various organ systems respond to injury to restore homeostasis by maintaining perfusion to the heart and brain. Inflammation after injury occurs to protect against further damage and starts the healing process. Prolonged inflammation may cause multiple organ dysfunction syndrome or systemic inflammatory response syndrome. Immediately after injury, the body increases production of glucose through gluconeogenesis and its consumption of fat via lipolysis. Next, the body tries to replenish its energy stores of glucose and protein via anabolism. In this state the body will temporarily increase its maximum expenditure for the purpose of healing injured cells.

Diagnosis

Radiograph of a close-range shotgun blast injury to the knee. Birdshot pellets are visible within and around the shattered patella, distal femur, and proximal tibia

The initial assessment is critical in determining the extent of injuries and what will be needed to manage an injury, and for treating immediate life threats.

Physical examination

Primary physical examination is undertaken to identify any life-threatening problems, after which the secondary examination is carried out. This may occur during transportation or upon arrival at the hospital. The secondary examination consists of a systematic assessment of the abdominal, pelvic, and thoracic areas, a complete inspection of the body surface to find all injuries, and a neurological examination. Injuries that may manifest themselves later, may be missed during the initial assessment, such as when a patient is brought into a hospital's emergency department. Generally, the physical examination is performed in a systematic way that first checks for any immediate life threats (primary survey), and then taking a more in-depth examination (secondary survey).

Imaging

Whole body radiograph of traumatic injuries notable for fractures of both femurs (thigh bones), indicating major trauma

Persons with major trauma commonly have chest and pelvic x-rays taken, and, depending on the mechanism of injury and presentation, a focused assessment with sonography for trauma (FAST) exam to check for internal bleeding. For those with relatively stable blood pressure, heart rate, and sufficient oxygenation, CT scans are useful. Full-body CT scans, known as pan-scans, improve the survival rate of those who have suffered major trauma. These scans use intravenous injections for the radiocontrast agent, but not oral administration. There are concerns that intravenous contrast administration in trauma situations without confirming adequate renal function may cause damage to kidneys, but this does not appear to be significant.

In the U.S., CT or MRI scans are performed on 15% of those with trauma in emergency departments. Where blood pressure is low or the heart rate is increased—likely from bleeding in the abdomen—immediate surgery bypassing a CT scan is recommended. Modern 64-slice CT scans are able to rule out, with a high degree of accuracy, significant injuries to the neck following blunt trauma.

Surgical techniques

Surgical techniques, using a tube or catheter to drain fluid from the peritoneum, chest, or the pericardium around the heart, often are used in cases of severe blunt trauma to the chest or abdomen, especially when a person is experiencing early signs of shock. In those with low blood-pressure, likely because of bleeding in the abdominal cavity, cutting through the abdominal wall surgically is indicated.

Prevention

Main article: Injury prevention

By identifying risk factors present within a community and creating solutions to decrease the incidence of injury, trauma referral systems may help to enhance the overall health of a population. Injury prevention strategies are commonly used to prevent injuries in children, who are a high risk population. Injury prevention strategies generally involve educating the general public about specific risk factors and developing strategies to avoid or reduce injuries. Legislation intended to prevent injury typically involves seatbelts, child car-seats, helmets, alcohol control, and increased enforcement of the legislation. Other controllable factors, such as the use of drugs including alcohol or cocaine, increases the risk of trauma by increasing the likelihood of traffic collisions, violence, and abuse occurring. Prescription drugs such as benzodiazepines may increase the risk of trauma in elderly people.

The care of acutely injured people in a public health system requires the involvement of bystanders, community members, health care professionals, and health care systems. It encompasses pre-hospital trauma assessment and care by emergency medical services personnel, emergency department assessment, treatment, stabilization, and in-hospital care among all age groups. An established trauma system network is also an important component of community disaster preparedness, facilitating the care of people who have been involved in disasters that cause large numbers of casualties, such as earthquakes.

Management

A Navy corpsmen listens for the correct tube placement on an intubated trauma victim during a search and rescue exercise

 

Typical trauma room

Pre-hospital

The pre-hospital use of stabilization techniques improves the chances of a person surviving the journey to the nearest trauma-equipped hospital. Emergency medicine services determines which people need treatment at a trauma center as well as provide primary stabilization by checking and treating airway, breathing, and circulation as well as assessing for disability and gaining exposure to check for other injuries.

Spinal motion restriction by securing the neck with a cervical collar and placing the person on a long spine board was of high importance in the pre-hospital setting, but due to lack of evidence to support its use, the practice is losing favor. Instead, it is recommended that more exclusive criteria be met such as age and neurological deficits to indicate the need of these adjuncts. This may be accomplished with other medical transport devices, such as a Kendrick extrication device, before moving the person. It is important to quickly control severe bleeding with direct pressure to the wound and consider the use of hemostatic agents or tourniquets if the bleeding continues. Conditions such as impending airway obstruction, enlargening neck hematoma, or unconsciousness require intubation. It is unclear, however, if this is best performed before reaching hospital or in the hospital.

Rapid transportation of severely injured patients improves the outcome in trauma. Helicopter EMS transport reduces mortality compared to ground-based transport in adult trauma patients. Before arrival at the hospital, the availability of advanced life support does not greatly improve the outcome for major trauma when compared to the administration of basic life support. Evidence is inconclusive in determining support for pre-hospital intravenous fluid resuscitation while some evidence has found it may be harmful. Hospitals with designated trauma centers have improved outcomes when compared to hospitals without them, and outcomes may improve when persons who have experienced trauma are transferred directly to a trauma center.

In-hospital

Management of those with trauma often requires the help of many healthcare specialists including physicians, nurses, respiratory therapists, and social workers. Cooperation allows many actions to be completed at once. Generally, the first step of managing trauma is to perform a primary survey that evaluates a person's airway, breathing, circulation, and neurologic status. These steps may happen simultaneously or depend on the most pressing concern such as a tension pneumothorax or major arterial bleed. The primary survey generally includes assessment of the cervical spine, though clearing it is often not possible until after imaging, or the person has improved. After immediate life threats are controlled, a person is either moved into an operating room for immediate surgical correction of the injuries, or a secondary survey is performed that is a more detailed head-to-toe assessment of the person.

Indications for intubation include airway obstruction, inability to protect the airway, and respiratory failure. Examples of these indications include penetrating neck trauma, expanding neck hematoma, and being unconscious. In general, the method of intubation used is rapid sequence intubation followed by ventilation, though intubating in shock due to bleeding can lead to arrest, and should be done after some resuscitation whenever possible. Trauma resuscitation includes control of active bleeding. When a person is first brought in, vital signs are checked, an ECG is performed, and, if needed, vascular access is obtained. Other tests should be performed to get a baseline measurement of their current blood chemistry, such as an arterial blood gas or thromboelastography. In those with cardiac arrest due to trauma chest compressions are considered futile, but still recommended. Correcting the underlying cause such as a pneumothorax or pericardial tamponade, if present, may help.

A FAST exam may help assess for internal bleeding. In certain traumas, such as maxillofacial trauma, it may be beneficial to have a highly trained health care provider available to maintain airway, breathing, and circulation.

Intravenous fluids

Traditionally, high-volume intravenous fluids were given to people who had poor perfusion due to trauma. This is still appropriate in cases with isolated extremity trauma, thermal trauma, or head injuries. In general, however, giving lots of fluids appears to increase the risk of death. Current evidence supports limiting the use of fluids for penetrating thorax and abdominal injuries, allowing mild hypotension to persist. Targets include a mean arterial pressure of 60 mmHg, a systolic blood pressure of 70–90 mmHg, or the re-establishment of peripheral pulses and adequate ability to think. Hypertonic saline has been studied and found to be of little difference from normal saline.

As no intravenous fluids used for initial resuscitation have been shown to be superior, warmed Lactated Ringer's solution continues to be the solution of choice. If blood products are needed, a greater use of fresh frozen plasma and platelets instead of only packed red blood cells has been found to improve survival and lower overall blood product use; a ratio of 1:1:1 is recommended. The success of platelets has been attributed to the fact that they may prevent coagulopathy from developing. Cell salvage and autotransfusion also may be used.

Blood substitutes such as hemoglobin-based oxygen carriers are in development; however, as of 2013 there are none available for commercial use in North America or Europe. These products are only available for general use in South Africa and Russia.

Medications

Tranexamic acid decreases death in people who are having ongoing bleeding due to trauma, as well as those with mild to moderate traumatic brain injury and evidence of intracranial bleeding on CT scan. It only appears to be beneficial, however, if administered within the first three hours after trauma. For severe bleeding, for example from bleeding disorders, recombinant factor VIIa—a protein that assists blood clotting—may be appropriate. While it decreases blood use, it does not appear to decrease the mortality rate. In those without previous factor VII deficiency, its use is not recommended outside of trial situations.

Other medications may be used in conjunction with other procedures to stabilize a person who has sustained a significant injury. While positive inotropic medications such as norepinephrine sometimes are used in hemorrhagic shock as a result of trauma, there is a lack of evidence for their use. Therefore, as of 2012 they have not been recommended. Allowing a low blood pressure may be preferred in some situations.

Surgery

The decision whether to perform surgery is determined by the extent of the damage and the anatomical location of the injury. Bleeding must be controlled before definitive repair may occur. Damage control surgery is used to manage severe trauma in which there is a cycle of metabolic acidosis, hypothermia, and hypotension that may lead to death, if not corrected. The main principle of the procedure involves performing the fewest procedures to save life and limb; less critical procedures are left until the victim is more stable. Approximately 15% of all people with trauma have abdominal injuries, and approximately 25% of these require exploratory surgery. The majority of preventable deaths from trauma result from unrecognised intra-abdominal bleeding.

Prognosis

Trauma deaths occur in immediate, early, or late stages. Immediate deaths usually are due to apnea, severe brain or high spinal cord injury, or rupture of the heart or of large blood vessels. Early deaths occur within minutes to hours and often are due to hemorrhages in the outer meningeal layer of the brain, torn arteries, blood around the lungs, air around the lungs, ruptured spleen, liver laceration, or pelvic fracture. Immediate access to care may be crucial to prevent death in persons experiencing major trauma. Late deaths occur days or weeks after the injury and often are related to infection. Prognosis is better in countries with a dedicated trauma system where injured persons are provided quick and effective access to proper treatment facilities.

Long-term prognosis frequently is complicated by pain; more than half of trauma patients have moderate to severe pain one year after injury. Many also experience a reduced quality of life years after an injury, with 20% of victims sustaining some form of disability. Physical trauma may lead to development of post-traumatic stress disorder (PTSD). One study has found no correlation between the severity of trauma and the development of PTSD.

Epidemiology

Further information: List of preventable causes of death

 

Deaths from injuries per 100,000 inhabitants in 2004

no data   < 25   25–50   50–75   75–100   100–125   125–150

150–175   175–200   200–225   225–250   250–275   > 275

Incidence of accidents by activity in Denmark

Trauma is the sixth leading cause of death worldwide, resulting in five million or 10% of all deaths annually. It is the fifth leading cause of significant disability. About half of trauma deaths are in people aged between 15 and 45 years and trauma is the leading cause of death in this age group. Injury affects more males; 68% of injuries occur in males and death from trauma is twice as common in males as it is in females, this is believed to be because males are much more willing to engage in risk-taking activities. Teenagers and young adults are more likely to need hospitalization from injuries than other age groups. While elderly persons are less likely to be injured, they are more likely to die from injuries sustained due to various physiological differences that make it more difficult for the body to compensate for the injuries. The primary causes of traumatic death are central nervous system injuries and substantial blood loss. Various classification scales exist for use with trauma to determine the severity of injuries, which are used to determine the resources used and, for statistical collection.

History

The human remains discovered at the site of Nataruk in Turkana, Kenya, are claimed to show major trauma—both blunt and penetrating—caused by violent trauma to the head, neck, ribs, knees, and hands, which has been interpreted by some researchers as establishing the existence of warfare between two groups of hunter-gatherers 10,000 years ago. The evidence for blunt-force trauma at Nataruk has been challenged, however, and the interpretation that the site represents an early example of warfare has been questioned.

Society and culture

Economics

The financial cost of trauma includes both the amount of money spent on treatment and the loss of potential economic gain through absence from work. The average financial cost for the treatment of traumatic injury in the United States is approximately US$334,000 per person, making it costlier than the treatment of cancer and cardiovascular diseases. One reason for the high cost of the treatment for trauma is the increased possibility of complications, which leads to the need for more interventions. Maintaining a trauma center is costly because they are open continuously and maintain a state of readiness to receive patients, even if there are none. In addition to the direct costs of the treatment, there also is a burden on the economy due to lost wages and productivity, which in 2009, accounted for approximately US$693.5 billion in the United States.

Low- and middle-income countries

Citizens of low- and middle-income countries (LMICs) often have higher mortality rates from injury. These countries accounted for 89% of all deaths from injury worldwide. Many of these countries do not have access to sufficient surgical care and many do not have a trauma system in place. In addition, most LMICs do not have a pre-hospital care system that treats injured persons initially and transports them to hospital quickly, resulting in most casualty patients being transported by private vehicles. Also, their hospitals lack the appropriate equipment, organizational resources, or trained staff. By 2020, the amount of trauma-related deaths is expected to decline in high-income countries, while in low- to middle-income countries it is expected to increase.

Special populations

Children

Main article: Pediatric trauma

Cause	Deaths per year
Traffic collision	260,000
Drowning	175,000
Burns	96,000
Falls	47,000
Toxins	45,000

Due to anatomical and physiological differences, injuries in children need to be approached differently from those in adults. Accidents are the leading cause of death in children between 1 and 14 years old. In the United States, approximately sixteen million children go to an emergency department due to some form of injury every year, with boys being more frequently injured than girls by a ratio of 2:1. The world's five most common unintentional injuries in children as of 2008 are road crashes, drowning, burns, falls, and poisoning.

Weight estimation is an important part of managing trauma in children because the accurate dosing of medicine may be critical for resuscitative efforts. A number of methods to estimate weight, including the Broselow tape, Leffler formula, and Theron formula exist.

Pregnancy

Trauma occurs in approximately 5% of all pregnancies, and is the leading cause of maternal death. Additionally, pregnant women may experience placental abruption, pre-term labor, and uterine rupture. There are diagnostic issues during pregnancy; ionizing radiation has been shown to cause birth defects, although the doses used for typical exams generally are considered safe. Due to normal physiological changes that occur during pregnancy, shock may be more difficult to diagnose. Where the woman is more than 23 weeks pregnant, it is recommended that the fetus be monitored for at least four hours by cardiotocography.

A number of treatments beyond typical trauma care may be needed when the patient is pregnant. Because the weight of the uterus on the inferior vena cava may decrease blood return to the heart, it may be very beneficial to lay a woman in late pregnancy on her left side. also recommended are Rho(D) immune globulin in those who are rh negative, corticosteroids in those who are 24 to 34 weeks and may need delivery or a caesarian section in the event of cardiac arrest.

Research

See also: Traumatology

Most research on trauma occurs during war and military conflicts as militaries will increase trauma research spending in order to prevent combat related deaths. Some research is being conducted on patients who were admitted into an intensive care unit or trauma center, and received a trauma diagnosis that caused a negative change in their health-related quality of life, with a potential to create anxiety and symptoms of depression. New preserved blood products also are being researched for use in pre-hospital care; it is impractical to use the currently available blood products in a timely fashion in remote, rural settings or in theaters of war.