Gauss–Newton algorithm

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https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm

Fitting of a noisy curve by an asymmetrical peak model ${\displaystyle f_{\beta }(x)}$ with parameters ${\displaystyle \beta }$ by mimimizing the sum of squared residuals ${\displaystyle r_i(\beta )=y_i-f_{\beta }(x_i)}$ at grid points ${\displaystyle x_i}$, using the Gauss–Newton algorithm.
Top: Raw data and model.
Bottom: Evolution of the normalised sum of the squares of the errors.

The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively approximate zeroes of the components of the sum, and thus minimizing the sum. In this sense, the algorithm is also an effective method for solving overdetermined systems of equations. It has the advantage that second derivatives, which can be challenging to compute, are not required.

Non-linear least squares problems arise, for instance, in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations.

The method is named after the mathematicians Carl Friedrich Gauss and Isaac Newton, and first appeared in Gauss's 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum.

Description

Given ${\displaystyle m}$ functions ${\displaystyle \mathbf{\text{r}}=(r_1,\dots ,r_m)}$ (often called residuals) of ${\displaystyle n}$ variables ${\displaystyle \mathit{\beta }=({\beta }_1,\dots {\beta }_n),}$ with ${\displaystyle m\ge n,}$ the Gauss–Newton algorithm iteratively finds the value of ${\displaystyle \beta }$ that minimize the sum of squares^[3] $${\displaystyle S(\mathit{\beta })=\sum _{i=1}^m{r}_i(\mathit{\beta }{)}^2.}$$

Starting with an initial guess ${\displaystyle {\mathit{\beta }}^{(0)}}$ for the minimum, the method proceeds by the iterations $${\displaystyle {\mathit{\beta }}^{(s+1)}={\mathit{\beta }}^{(s)}-{\left({{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\right)}^{-1}{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}\mathbf{r}\left({\mathit{\beta }}^{(s)}\right),}$$

where, if r and β are column vectors, the entries of the Jacobian matrix are $${\displaystyle {\left({\mathbf{J}}_{\mathbf{r}}\right)}_{ij}=\frac{\mathrm{\partial }{r}_i\left({\mathit{\beta }}^{(s)}\right)}{\mathrm{\partial }{\beta }_j},}$$

and the symbol ${\displaystyle {}^{\mathrm{T}}}$ denotes the matrix transpose.

At each iteration, the update ${\displaystyle \mathrm{\Delta }={\mathit{\beta }}^{(s+1)}-{\mathit{\beta }}^{(s)}}$ can be found by rearranging the previous equation in the following two steps:

• ${\displaystyle \mathrm{\Delta }=-{\left({{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\right)}^{-1}{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}\mathbf{r}\left({\mathit{\beta }}^{(s)}\right)}$
• ${\displaystyle {{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\mathrm{\Delta }=-{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}\mathbf{r}\left({\mathit{\beta }}^{(s)}\right)}$

With substitutions $A={{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}$, ${\displaystyle \mathbf{b}=-{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}\mathbf{r}\left({\mathit{\beta }}^{(s)}\right)}$, and ${\displaystyle \mathbf{x}=\mathrm{\Delta }}$, this turns into the conventional matrix equation of form ${\displaystyle A\mathbf{x}=\mathbf{b}}$, which can then be solved in a variety of methods (see Notes).

If m = n, the iteration simplifies to

$${\displaystyle {\mathit{\beta }}^{(s+1)}={\mathit{\beta }}^{(s)}-{\left({\mathbf{J}}_{\mathbf{r}}\right)}^{-1}\mathbf{r}\left({\mathit{\beta }}^{(s)}\right),}$$

which is a direct generalization of Newton's method in one dimension.

In data fitting, where the goal is to find the parameters ${\displaystyle \mathit{\beta }}$ such that a given model function ${\displaystyle \mathbf{f}(\mathbf{x},\mathit{\beta })}$ best fits some data points ${\displaystyle (x_i,y_i)}$, the functions ${\displaystyle r_i}$are the residuals: $${\displaystyle r_i(\mathit{\beta })=y_i-f\left(x_i,\mathit{\beta }\right).}$$

Then, the Gauss–Newton method can be expressed in terms of the Jacobian ${\displaystyle {\mathbf{J}}_{\mathbf{f}}=-{\mathbf{J}}_{\mathbf{r}}}$ of the function ${\displaystyle \mathbf{f}}$ as $${\displaystyle {\mathit{\beta }}^{(s+1)}={\mathit{\beta }}^{(s)}+{\left({{\mathbf{J}}_{\mathbf{f}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{f}}\right)}^{-1}{{\mathbf{J}}_{\mathbf{f}}}^{\mathrm{T}}\mathbf{r}\left({\mathit{\beta }}^{(s)}\right).}$$

Note that ${\displaystyle {\left({{\mathbf{J}}_{\mathbf{f}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{f}}\right)}^{-1}{{\mathbf{J}}_{\mathbf{f}}}^{\mathrm{T}}}$ is the left pseudoinverse of ${\displaystyle {\mathbf{J}}_{\mathbf{f}}}$.

Notes

The assumption m ≥ n in the algorithm statement is necessary, as otherwise the matrix ${\displaystyle {{\mathbf{J}}_{\mathbf{r}}}^T{\mathbf{J}}_{\mathbf{r}}}$ is not invertible and the normal equations cannot be solved (at least uniquely).

The Gauss–Newton algorithm can be derived by linearly approximating the vector of functions r_i. Using Taylor's theorem, we can write at every iteration: $${\displaystyle \mathbf{r}(\mathit{\beta })\approx \mathbf{r}\left({\mathit{\beta }}^{(s)}\right)+{\mathbf{J}}_{\mathbf{r}}\left({\mathit{\beta }}^{(s)}\right)\mathrm{\Delta }}$$

with ${\displaystyle \mathrm{\Delta }=\mathit{\beta }-{\mathit{\beta }}^{(s)}}$. The task of finding ${\displaystyle \mathrm{\Delta }}$ minimizing the sum of squares of the right-hand side; i.e., $${\displaystyle min{\Vert \mathbf{r}\left({\mathit{\beta }}^{(s)}\right)+{\mathbf{J}}_{\mathbf{r}}\left({\mathit{\beta }}^{(s)}\right)\mathrm{\Delta }\Vert }_2^2,}$$

is a linear least-squares problem, which can be solved explicitly, yielding the normal equations in the algorithm.

The normal equations are n simultaneous linear equations in the unknown increments ${\displaystyle \mathrm{\Delta }}$. They may be solved in one step, using Cholesky decomposition, or, better, the QR factorization of ${\displaystyle {\mathbf{J}}_{\mathbf{r}}}$. For large systems, an iterative method, such as the conjugate gradient method, may be more efficient. If there is a linear dependence between columns of J_r, the iterations will fail, as ${\displaystyle {{\mathbf{J}}_{\mathbf{r}}}^T{\mathbf{J}}_{\mathbf{r}}}$ becomes singular.

When ${\displaystyle \mathbf{r}}$ is complex ${\displaystyle \mathbf{r}:{\mathbb{C}}^n\to \mathbb{C}}$ the conjugate form should be used: ${\displaystyle {\left({\overline{{\mathbf{J}}_{\mathbf{r}}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\right)}^{-1}{\overline{{\mathbf{J}}_{\mathbf{r}}}}^{\mathrm{T}}}$.

Example

Calculated curve obtained with ${\displaystyle {\hat{\beta }}_1=0.362}$ and ${\displaystyle {\hat{\beta }}_2=0.556}$ (in blue) versus the observed data (in red)

In this example, the Gauss–Newton algorithm will be used to fit a model to some data by minimizing the sum of squares of errors between the data and model's predictions.

In a biology experiment studying the relation between substrate concentration [S] and reaction rate in an enzyme-mediated reaction, the data in the following table were obtained.

i	1	2	3	4	5	6	7
[S]	0.038	0.194	0.425	0.626	1.253	2.500	3.740
Rate	0.050	0.127	0.094	0.2122	0.2729	0.2665	0.3317

It is desired to find a curve (model function) of the form $${\displaystyle \text{rate}=\frac{V_{\text{max}}\cdot [S]}{K_M+[S]}}$$

that fits best the data in the least-squares sense, with the parameters ${\displaystyle V_{\text{max}}}$ and ${\displaystyle K_M}$ to be determined.

Denote by ${\displaystyle x_i}$ and ${\displaystyle y_i}$ the values of [S] and rate respectively, with ${\displaystyle i=1,\dots ,7}$. Let ${\displaystyle {\beta }_1=V_{\text{max}}}$ and ${\displaystyle {\beta }_2=K_M}$. We will find ${\displaystyle {\beta }_1}$ and ${\displaystyle {\beta }_2}$ such that the sum of squares of the residuals $${\displaystyle r_i=y_i-\frac{{\beta }_1{x}_i}{{\beta }_2+x_i},(i=1,\dots ,7)}$$

is minimized.

The Jacobian ${\displaystyle {\mathbf{J}}_{\mathbf{r}}}$ of the vector of residuals ${\displaystyle r_i}$ with respect to the unknowns ${\displaystyle {\beta }_j}$ is a ${\displaystyle 7\times 2}$ matrix with the ${\displaystyle i}$-th row having the entries $${\displaystyle \frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_1}=-\frac{x_i}{{\beta }_2+x_i};\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_2}=\frac{{\beta }_1\cdot x_i}{{\left({\beta }_2+x_i\right)}^2}.}$$

Starting with the initial estimates of ${\displaystyle {\beta }_1=0.9}$ and ${\displaystyle {\beta }_2=0.2}$, after five iterations of the Gauss–Newton algorithm, the optimal values ${\displaystyle {\hat{\beta }}_1=0.362}$ and ${\displaystyle {\hat{\beta }}_2=0.556}$ are obtained. The sum of squares of residuals decreased from the initial value of 1.445 to 0.00784 after the fifth iteration. The plot in the figure on the right shows the curve determined by the model for the optimal parameters with the observed data.

Convergence properties

The Gauss-Newton iteration is guaranteed to converge toward a local minimum point ${\displaystyle \hat{\beta }}$ under 4 conditions: The functions ${\displaystyle r_1,\dots ,r_m}$ are twice continuously differentiable in an open convex set ${\displaystyle D\ni \hat{\beta }}$, the Jacobian ${\displaystyle {\mathbf{J}}_{\mathbf{r}}(\hat{\beta })}$ is of full column rank, the initial iterate ${\displaystyle {\beta }^{(0)}}$ is near ${\displaystyle \hat{\beta }}$, and the local minimum value ${\displaystyle |S(\hat{\beta })|}$ is small. The convergence is quadratic if ${\displaystyle |S(\hat{\beta })|=0}$.

It can be shown that the increment Δ is a descent direction for S, and, if the algorithm converges, then the limit is a stationary point of S. For large minimum value ${\displaystyle |S(\hat{\beta })|}$, however, convergence is not guaranteed, not even local convergence as in Newton's method, or convergence under the usual Wolfe conditions.

The rate of convergence of the Gauss–Newton algorithm can approach quadratic. The algorithm may converge slowly or not at all if the initial guess is far from the minimum or the matrix ${\displaystyle {\mathbf{J}}_{\mathbf{r}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}}$ is ill-conditioned. For example, consider the problem with ${\displaystyle m=2}$ equations and ${\displaystyle n=1}$ variable, given by $${\displaystyle \begin{array}{rl}{r}_1(\beta )& =\beta +1,\\ r_2(\beta )& =\lambda {\beta }^2+\beta -1.\end{array}}$$

For ${\displaystyle \lambda <1}$, ${\displaystyle \beta =0}$ is a local optimum. If ${\displaystyle \lambda =0}$, then the problem is in fact linear and the method finds the optimum in one iteration. If |λ| < 1, then the method converges linearly and the error decreases asymptotically with a factor |λ| at every iteration. However, if |λ| > 1, then the method does not even converge locally.

Solving overdetermined systems of equations

The Gauss-Newton iteration $${\displaystyle {\mathbf{x}}^{(k+1)}={\mathbf{x}}^{(k)}-J({\mathbf{x}}^{(k)}{)}^{†}\mathbf{f}({\mathbf{x}}^{(k)}),k=0,1,\dots }$$ is an effective method for solving overdetermined systems of equations in the form of ${\displaystyle \mathbf{f}(\mathbf{x})=\mathbf{0}}$ with $${\displaystyle \mathbf{f}(\mathbf{x})=\left[\begin{array}{c}{f}_1(x_1,\dots ,x_n)\\ ⋮\\ f_m(x_1,\dots ,x_n)\end{array}\right]}$$ and ${\displaystyle m>n}$ where ${\displaystyle J(\mathbf{x}{)}^{†}}$ is the Moore-Penrose inverse (also known as pseudoinverse) of the Jacobian matrix ${\displaystyle J(\mathbf{x})}$ of ${\displaystyle \mathbf{f}(\mathbf{x})}$. It can be considered an extension of Newton's method and enjoys the same local quadratic convergence toward isolated regular solutions.

If the solution doesn't exist but the initial iterate ${\displaystyle {\mathbf{x}}^{(0)}}$ is near a point ${\displaystyle \hat{\mathbf{x}}=({\hat{x}}_1,\dots ,{\hat{x}}_n)}$ at which the sum of squares $\sum _{i=1}^m|f_i(x_1,\dots ,x_n){|}^2\equiv \Vert \mathbf{f}(\mathbf{x}){\Vert }_2^2$ reaches a small local minimum, the Gauss-Newton iteration linearly converges to ${\displaystyle \hat{\mathbf{x}}}$. The point ${\displaystyle \hat{\mathbf{x}}}$ is often called a least squares solution of the overdetermined system.

Derivation from Newton's method

In what follows, the Gauss–Newton algorithm will be derived from Newton's method for function optimization via an approximation. As a consequence, the rate of convergence of the Gauss–Newton algorithm can be quadratic under certain regularity conditions. In general (under weaker conditions), the convergence rate is linear.

The recurrence relation for Newton's method for minimizing a function S of parameters ${\displaystyle \mathit{\beta }}$ is $${\displaystyle {\mathit{\beta }}^{(s+1)}={\mathit{\beta }}^{(s)}-{\mathbf{H}}^{-1}\mathbf{g},}$$

where g denotes the gradient vector of S, and H denotes the Hessian matrix of S.

Since $S=\sum _{i=1}^m{r}_i^2$, the gradient is given by $${\displaystyle g_j=2\sum _{i=1}^m{r}_i\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_j}.}$$

Elements of the Hessian are calculated by differentiating the gradient elements, ${\displaystyle g_j}$, with respect to ${\displaystyle {\beta }_k}$: $${\displaystyle H_{jk}=2\sum _{i=1}^m\left(\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_j}\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_k}+r_i\frac{{\mathrm{\partial }}^2{r}_i}{\mathrm{\partial }{\beta }_j\mathrm{\partial }{\beta }_k}\right).}$$

The Gauss–Newton method is obtained by ignoring the second-order derivative terms (the second term in this expression). That is, the Hessian is approximated by $${\displaystyle H_{jk}\approx 2\sum _{i=1}^m{J}_{ij}{J}_{ik},}$$

where $J_{ij}=\mathrm{\partial }{r}_i/\mathrm{\partial }{\beta }_j$ are entries of the Jacobian J_r. Note that when the exact hessian is evaluated near an exact fit we have near-zero ${\displaystyle r_i}$, so the second term becomes near-zero as well, which justifies the approximation. The gradient and the approximate Hessian can be written in matrix notation as $${\displaystyle \mathbf{g}=2{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}\mathbf{r},\mathbf{H}\approx 2{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}.}$$

These expressions are substituted into the recurrence relation above to obtain the operational equations $${\displaystyle {\mathit{\beta }}^{(s+1)}={\mathit{\beta }}^{(s)}+\mathrm{\Delta };\mathrm{\Delta }=-{\left({{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\right)}^{-1}{{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}\mathbf{r}.}$$

Convergence of the Gauss–Newton method is not guaranteed in all instances. The approximation $${\displaystyle \left|r_i\frac{{\mathrm{\partial }}^2{r}_i}{\mathrm{\partial }{\beta }_j\mathrm{\partial }{\beta }_k}\right|\ll \left|\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_j}\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_k}\right|}$$

that needs to hold to be able to ignore the second-order derivative terms may be valid in two cases, for which convergence is to be expected:

1. The function values ${\displaystyle r_i}$ are small in magnitude, at least around the minimum.
2. The functions are only "mildly" nonlinear, so that $\frac{{\mathrm{\partial }}^2{r}_i}{\mathrm{\partial }{\beta }_j\mathrm{\partial }{\beta }_k}$ is relatively small in magnitude.

Improved versions

With the Gauss–Newton method the sum of squares of the residuals S may not decrease at every iteration. However, since Δ is a descent direction, unless ${\displaystyle S\left({\mathit{\beta }}^s\right)}$ is a stationary point, it holds that ${\displaystyle S\left({\mathit{\beta }}^s+\alpha \mathrm{\Delta }\right)<S\left({\mathit{\beta }}^s\right)}$ for all sufficiently small ${\displaystyle \alpha >0}$. Thus, if divergence occurs, one solution is to employ a fraction ${\displaystyle \alpha }$ of the increment vector Δ in the updating formula: $${\displaystyle {\mathit{\beta }}^{s+1}={\mathit{\beta }}^s+\alpha \mathrm{\Delta }.}$$

In other words, the increment vector is too long, but it still points "downhill", so going just a part of the way will decrease the objective function S. An optimal value for ${\displaystyle \alpha }$ can be found by using a line search algorithm, that is, the magnitude of ${\displaystyle \alpha }$ is determined by finding the value that minimizes S, usually using a direct search method in the interval ${\displaystyle 0<\alpha <1}$ or a backtracking line search such as Armijo-line search. Typically, ${\displaystyle \alpha }$ should be chosen such that it satisfies the Wolfe conditions or the Goldstein conditions.

In cases where the direction of the shift vector is such that the optimal fraction α is close to zero, an alternative method for handling divergence is the use of the Levenberg–Marquardt algorithm, a trust region method. The normal equations are modified in such a way that the increment vector is rotated towards the direction of steepest descent, $${\displaystyle \left({\mathbf{J}}^{\mathrm{T}}\mathbf{J}\mathbf{+}\lambda \mathbf{D}\right)\mathrm{\Delta }=-{\mathbf{J}}^{\mathrm{T}}\mathbf{r},}$$

where D is a positive diagonal matrix. Note that when D is the identity matrix I and ${\displaystyle \lambda \to +\mathrm{\infty }}$, then ${\displaystyle \lambda \mathrm{\Delta }=\lambda {\left({\mathbf{J}}^{\mathrm{T}}\mathbf{J}+\lambda \mathbf{I}\right)}^{-1}\left(-{\mathbf{J}}^{\mathrm{T}}\mathbf{r}\right)=\left(\mathbf{I}-{\mathbf{J}}^{\mathrm{T}}\mathbf{J}/\lambda +\cdots \right)\left(-{\mathbf{J}}^{\mathrm{T}}\mathbf{r}\right)\to -{\mathbf{J}}^{\mathrm{T}}\mathbf{r}}$, therefore the direction of Δ approaches the direction of the negative gradient ${\displaystyle -{\mathbf{J}}^{\mathrm{T}}\mathbf{r}}$.

The so-called Marquardt parameter ${\displaystyle \lambda }$ may also be optimized by a line search, but this is inefficient, as the shift vector must be recalculated every time ${\displaystyle \lambda }$ is changed. A more efficient strategy is this: When divergence occurs, increase the Marquardt parameter until there is a decrease in S. Then retain the value from one iteration to the next, but decrease it if possible until a cut-off value is reached, when the Marquardt parameter can be set to zero; the minimization of S then becomes a standard Gauss–Newton minimization.

Large-scale optimization

For large-scale optimization, the Gauss–Newton method is of special interest because it is often (though certainly not always) true that the matrix ${\displaystyle {\mathbf{J}}_{\mathbf{r}}}$ is more sparse than the approximate Hessian ${\displaystyle {\mathbf{J}}_{\mathbf{r}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}}$. In such cases, the step calculation itself will typically need to be done with an approximate iterative method appropriate for large and sparse problems, such as the conjugate gradient method.

In order to make this kind of approach work, one needs at least an efficient method for computing the product $${\displaystyle {{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\mathbf{p}}$$

for some vector p. With sparse matrix storage, it is in general practical to store the rows of ${\displaystyle {\mathbf{J}}_{\mathbf{r}}}$ in a compressed form (e.g., without zero entries), making a direct computation of the above product tricky due to the transposition. However, if one defines c_i as row i of the matrix ${\displaystyle {\mathbf{J}}_{\mathbf{r}}}$, the following simple relation holds: $${\displaystyle {{\mathbf{J}}_{\mathbf{r}}}^{\mathrm{T}}{\mathbf{J}}_{\mathbf{r}}\mathbf{p}=\sum _i{\mathbf{c}}_i\left({\mathbf{c}}_i\cdot \mathbf{p}\right),}$$

so that every row contributes additively and independently to the product. In addition to respecting a practical sparse storage structure, this expression is well suited for parallel computations. Note that every row c_i is the gradient of the corresponding residual r_i; with this in mind, the formula above emphasizes the fact that residuals contribute to the problem independently of each other.

Related algorithms

In a quasi-Newton method, such as that due to Davidon, Fletcher and Powell or Broyden–Fletcher–Goldfarb–Shanno (BFGS method) an estimate of the full Hessian $\frac{{\mathrm{\partial }}^{2}S}{\mathrm{\partial }{\beta }_j\mathrm{\partial }{\beta }_k}$ is built up numerically using first derivatives $\frac{\mathrm{\partial }{r}_i}{\mathrm{\partial }{\beta }_j}$ only so that after n refinement cycles the method closely approximates to Newton's method in performance. Note that quasi-Newton methods can minimize general real-valued functions, whereas Gauss–Newton, Levenberg–Marquardt, etc. fits only to nonlinear least-squares problems.

Another method for solving minimization problems using only first derivatives is gradient descent. However, this method does not take into account the second derivatives even approximately. Consequently, it is highly inefficient for many functions, especially if the parameters have strong interactions.

Bioethics

From Wikipedia, the free encyclopedia

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

Bioethics is both a field of study and professional practice, interested in ethical issues related to health (primarily focused on the human, but also increasingly includes animal ethics), including those emerging from advances in biology, medicine, and technologies. It proposes the discussion about moral discernment in society (what decisions are "good" or "bad" and why) and it is often related to medical policy and practice, but also to broader questions as environment, well-being and public health. Bioethics is concerned with the ethical questions that arise in the relationships among life sciences, biotechnology, medicine, politics, law, theology and philosophy. It includes the study of values relating to primary care, other branches of medicine ("the ethics of the ordinary"), ethical education in science, animal, and environmental ethics, and public health.

Etymology

The term bioethics (Greek bios, "life"; ethos, "moral nature, behavior") was coined in 1927 by Fritz Jahr in an article about a "bioethical imperative" regarding the use of animals and plants in scientific research. In 1970, the American biochemist and oncologist Van Rensselaer Potter used the term to describe the relationship between the biosphere and a growing human population. Potter's work laid the foundation for global ethics, a discipline centered around the link between biology, ecology, medicine, and human values. Sargent Shriver, the spouse of Eunice Kennedy Shriver, claimed that he had invented the term "bioethics" in the living room of his home in Bethesda, Maryland, in 1970. He stated that he thought of the word after returning from a discussion earlier that evening at Georgetown University, where he discussed with others a possible Kennedy family sponsorship of an institute focused around the "application of moral philosophy to concrete medical dilemmas".

Purpose and scope

The discipline of bioethics has addressed a wide swathe of human inquiry; ranging from debates over the boundaries of lifestyles (e.g. abortion, euthanasia), surrogacy, the allocation of scarce health care resources (e.g. organ donation, health care rationing), to the right to refuse medical care for religious or cultural reasons. Bioethicists disagree among themselves over the precise limits of their discipline, debating whether the field should concern itself with the ethical evaluation of all questions involving biology and medicine, or only a subset of these questions. Some bioethicists would narrow ethical evaluation only to the morality of medical treatments or technological innovations, and the timing of medical treatment of humans. Others would increase the scope of moral assessment to encompass the morality of all moves that would possibly assist or damage organisms successful of feeling fear.

The scope of bioethics has evolved past mere biotechnology to include topics such as cloning, gene therapy, life extension, human genetic engineering, astroethics and life in space, and manipulation of basic biology through altered DNA, XNA and proteins. These (and other) developments may affect future evolution and require new principles that address life at its core, such as biotic ethics that values life itself at its basic biological processes and structures, and seeks their propagation. Moving beyond the biological, issues raised in public health such as vaccination and resource allocation have also encouraged the development of novel ethics frameworks to address such challenges. A study published in 2022 based on the corpus of full papers from eight main bioethics journals demonstrated the heterogeneity of this field by distinguishing 91 topics that have been discussed in these journals over the past half a century.

Principles

Hippocrates Refusing the Gifts of Artaxerxes by Anne-Louis Girodet-Trioson, 1792

One of the first areas addressed by modern bioethicists was human experimentation. According to the Declaration of Helsinki (1964) published by the World Medical Association, the essential principles in medical research involving human subjects are autonomy, beneficence, non-maleficence, and justice. The autonomy of individuals to make decisions while assuming responsibility for them and respecting the autonomy of others ought to be respected. For people unable to exercise their autonomy, special measures ought to be taken to protect their rights and interests.

In US, the National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research was initially established in 1974 to identify the basic ethical principles that should underlie the conduct of biomedical and behavioral research involving human subjects. However, the fundamental principles announced in the Belmont Report (1979)—namely, respect for persons, beneficence and justice—have influenced the thinking of bioethicists across a wide range of issues. Others have added non-maleficence, human dignity, and the sanctity of life to this list of cardinal values. Overall, the Belmont Report has guided lookup in a course centered on defending prone topics as properly as pushing for transparency between the researcher and the subject. Research has flourished within the past 40 years and due to the advance in technology, it is thought that human subjects have outgrown the Belmont Report, and the need for revision is desired.

Another essential precept of bioethics is its placement of cost on dialogue and presentation. Numerous dialogue based bioethics organizations exist in universities throughout the United States to champion precisely such goals. Examples include the Ohio State Bioethics Society and the Bioethics Society of Cornell. Professional level versions of these organizations also exist.

Many bioethicists, in particular scientific scholars, accord the easiest precedence to autonomy. They trust that every affected person ought to decide which direction of motion they think about most in line with their beliefs. In other words, the patient should always have the freedom to choose their own treatment.

Medical ethics

Medical ethics is a utilized department of ethics that analyzes the exercise of clinical medicinal drug and associated scientific research. Medical ethics is based on a set of values. These values consist of the appreciation for autonomy, beneficence, and justice.

Main article: Medical ethics

Ethics affects medical decisions made by healthcare providers and patients. Medical ethics is the study of moral values and judgments as they apply to medicine. The four main moral commitments are respect for autonomy, beneficence, nonmaleficence, and justice. Using these four principles and thinking about what the physicians' specific concern is for their scope of practice can help physicians make moral decisions. As a scholarly discipline, medical ethics encompasses its practical application in clinical settings as well as work on its history, philosophy, theology, and sociology.

Medical ethics tends to be understood narrowly as applied professional ethics; whereas bioethics has a more expansive application, touching upon the philosophy of science and issues of biotechnology. The two fields often overlap, and the distinction is more so a matter of style than professional consensus. Medical ethics shares many principles with other branches of healthcare ethics, such as nursing ethics. A bioethicist assists the health care and research community in examining moral issues involved in our understanding of life and death, and resolving ethical dilemmas in medicine and science. Examples of this would be the topic of equality in medicine, the intersection of cultural practices and medical care, ethical distribution of healthcare resources in pandemics, and issues of bioterrorism.

Medical ethical concerns frequently touch on matters of life and death. Patient rights, informed consent, confidentiality, competency, advance directives, carelessness, and many other topics are highlighted as serious health concerns.

The proper actions to take in light of all the circumstances are what ethics is all about. It discusses the difference between what is proper and wrong at a certain moment and a particular society. Medical ethics is concerned with the duties that doctors, hospitals, and other healthcare providers have to patients, society, and other health professionals.

The health profession has a set of ethical standards that are relevant to various organizations of health workers and medical facilities. Ethics are never stagnant and always relevant. What is seen as acceptable ethics now may not be so one hundred years ago. The hospital administrator is required to have a thorough awareness of their moral and legal obligations.

Medical sociology

The practice of bioethics in clinical care have been studied by medical sociology. Many scholars consider that bioethics arose in response to a perceived lack of accountability in medical care in the 1970s. Studying the clinical practice of ethics in medical care, Hauschildt and Vries found that ethical questions were often reframed as clinical judgments to allow clinicians to make decisions. Ethicists most often put key decisions in the hands of physicians rather than patients.

Communication strategies suggested by ethicists act to decrease patient autonomy. Examples include, clinicians discussing treatment options with one another prior to talking to patients or their family to present a united front limited patient autonomy, hiding uncertainty amongst clinicians. Decisions about overarching goals of treatment were reframed as technical matters excluding patients and their families. Palliative care experts were used as intermediaries to guide patients towards less invasive end-of-live treatment. In their study, Hauschild and Vries found that 76% of ethical consultants were trained as clinicians.

Studying informed consent, Corrigan found that some social processes resulted in limitations to patients choice, but also at times patients could find questions regarding consent to medical trials burdensome.

The most prevalent subject is how social stratification (based on SES, gender, class, ethnicity, and age) affects patterns of behavior related to health and sickness, illness risk, disability, and other outcomes related to health care. The study of health care organization and provision, which encompasses the evolving organizational structures of health care organizations and the social psychology of health and health care, is another important approach. These latter research cover topics including connections between doctors and patients, coping mechanisms, and social support. The description of other important fields of medical sociology study emphasizes how theory and research have changed in the twenty-first century.

Perspectives and methodology

Bioethicists come from a wide variety of backgrounds and have training in a diverse array of disciplines. The field contains individuals trained in philosophy such as Deryck Beyleveld of Durham University, Daniel Brock of Harvard University, Baruch Brody of Rice University, Arthur Caplan of NYU, Joseph Fins of Cornell University, Frances Kamm of Rutgers University, Daniel Callahan of the Hastings Center, Peter Singer of Princeton University, and Julian Savulescu of the University of Oxford; medically trained clinician ethicists such as Mark Siegler of the University of Chicago; lawyers such as Nancy Dubler of Albert Einstein College of Medicine and Jerry Menikoff of the federal Office for Human Research Protections; political scientists like Francis Fukuyama; religious studies scholars including James Childress; and theologians like Lisa Sowle Cahill and Stanley Hauerwas.

The field, formerly dominated by formally trained philosophers, has become increasingly interdisciplinary, with some critics even claiming that the methods of analytic philosophy have harmed the field's development. Leading journals in the field include The Journal of Medicine and Philosophy, the Hastings Center Report, the American Journal of Bioethics, the Journal of Medical Ethics, Bioethics, the Kennedy Institute of Ethics Journal, Public Health Ethics, and the Cambridge Quarterly of Healthcare Ethics. Bioethics has also benefited from the process philosophy developed by Alfred North Whitehead.

Another discipline that discusses bioethics is the field of feminism; the International Journal of Feminist Approaches to Bioethics has played an important role in organizing and legitimizing feminist work in bioethics.

Many religious communities have their histories of inquiry into bioethical issues and have developed rules and guidelines on how to deal with these issues from within the viewpoint of their respective faiths. The Jewish, Christian and Muslim faiths have each developed a considerable body of literature on these matters. In the case of many non-Western cultures, a strict separation of religion from philosophy does not exist. In many Asian cultures, for example, there is a lively discussion on bioethical issues. Buddhist bioethics, in general, is characterized by a naturalistic outlook that leads to a rationalistic, pragmatic approach. Buddhist bioethicists include Damien Keown. In India, Vandana Shiva is a leading bioethicist speaking from the Hindu tradition.

In Africa, and partly also in Latin America, the debate on bioethics frequently focuses on its practical relevance in the context of underdevelopment and geopolitical power relations. In Africa, their bioethical approach is influenced by and similar to Western bioethics due to the colonization of many African countries. Some African bioethicists are calling for a shift in bioethics that utilizes indigenous African philosophy rather than western philosophy. Some African bioethicists also believe that Africans will be more likely to accept a bioethical approach grounded in their own culture, as well as empower African people.

Masahiro Morioka argues that in Japan the bioethics movement was first launched by disability activists and feminists in the early 1970s, while academic bioethics began in the mid-1980s. During this period, unique philosophical discussions on brain death and disability appeared both in the academy and journalism. In Chinese culture and bioethics, there is not as much of an emphasis on autonomy as opposed to the heavy emphasis placed on autonomy in Western bioethics. Community, social values, and family are all heavily valued in Chinese culture, and contribute to the lack of emphasis on autonomy in Chinese bioethics. The Chinese believe that the family, community, and individual are all interdependent of each other, so it is common for the family unit to collectively make decisions regarding healthcare and medical decisions for a loved one, instead of an individual making an independent decision for his or her self.

Some argue that spirituality and understanding one another as spiritual beings and moral agents is an important aspect of bioethics, and that spirituality and bioethics are heavily intertwined with one another. As a healthcare provider, it is important to know and understand varying world views and religious beliefs. Having this knowledge and understanding can empower healthcare providers with the ability to better treat and serve their patients. Developing a connection and understanding of a patient's moral agent helps enhance the care provided to the patient. Without this connection or understanding, patients can be at risk of becoming "faceless units of work" and being looked at as a "set of medical conditions" as opposed to the storied and spiritual beings that they are.

Islamic bioethics

Bioethics in the realm of Islam differs from Western bioethics, but they share some similar perspectives viewpoints as well. Western bioethics is focused on rights, especially individual rights. Islamic bioethics focuses more on religious duties and obligations, such as seeking treatment and preserving life. Islamic bioethics is heavily influenced and connected to the teachings of the Qur'an as well as the teachings of Muhammad. These influences essentially make it an extension of Shariah or Islamic Law. In Islamic bioethics, passages from the Qur'an are often used to validate various medical practices. For example, a passage from the Qur'an states "whosoever killeth a human being ... it shall be as if he had killed all humankind, and whosoever saveth the life of one, it shall be as if he saved the life of all humankind." This excerpt can be used to encourage using medicine and medical practices to save lives, but can also be looked at as a protest against euthanasia and assisted suicide. A high value and worth are placed on human life in Islam, and in turn, human life is deeply valued in the practice of Islamic bioethics as well. Muslims believe all human life, even one of poor quality, needs to be given appreciation and must be cared for and conserved.

The Islamic education on sensible problems associated to existence in normal and human lifestyles in unique can be sought in Islamic bioethics. As we will see later, due to the fact of interconnectedness of the Islamic regulation and the Islamic ethics, the Islamic bioethics has to reflect on consideration on necessities of the Islamic regulation (Shari‘ah) in addition to ethical considerations.

To react to new technological and medical advancements, informed Islamic jurists regularly will hold conferences to discuss new bioethical issues and come to an agreement on where they stand on the issue from an Islamic perspective. This allows Islamic bioethics to stay pliable and responsive to new advancements in medicine. The standpoints taken by Islamic jurists on bioethical issues are not always unanimous decisions and at times may differ. There is much diversity among Muslims varying from country to country, and the different degrees to which they adhere by Shariah. Differences and disagreements in regards to jurisprudence, theology, and ethics between the two main branches of Islam, Sunni, and Shia, lead to differences in the methods and ways in which Islamic bioethics is practiced throughout the Islamic world. An area where there is a lack of consensus is brain death. The Organization of Islamic Conferences Islamic Fiqh Academy (OIC-IFA) holds the view that brain death is equivalent to cardiopulmonary death, and acknowledges brain death in an individual as the individual being deceased. On the contrary, the Islamic Organization of Medical Sciences (IOMS) states that brain death is an "intermediate state between life and death" and does not acknowledge a brain dead individual as being deceased.

Islamic bioethicists look to the Qur'an and religious leaders regarding their outlook on reproduction and abortion. It is firmly believed that the reproduction of a human child can only be proper and legitimate via marriage. This does not mean that a child can only be reproduced via sexual intercourse between a married couple, but that the only proper and legitimate way to have a child is when it is an act between husband and wife. It is okay for a married couple to have a child artificially and from techniques using modern biotechnology as opposed to sexual intercourse, but to do this out of the context of marriage would be deemed immoral.

Islamic bioethics is strongly against abortion and strictly prohibits it. The IOMS states that "from the moment a zygote settles inside a woman's body, it deserves a unanimously recognized degree of respect." Abortion may only be permitted in unique situations where it is considered to be the "lesser evil".

Islamic bioethics must take into account both moral concerns and the requirements of the Islamic law (Shari'ah) due to the interdependence of Islamic law and Islamic ethics. In order to avoid making a mistake, everything must be thoroughly examined, first against moral criteria and then against legal ones.

Despite the fact that Islamic law and morality are completely in agreement with one another, they may have distinct prescriptions because of their diverse ends and objectives. One distinction, for instance, is that Islamic ethics seeks to teach those with higher desires how to become more perfect and closer to God, but Islamic law seeks to decrease criteria for perfection or pleasure in both realms that are doable for the average or even lower than average. However, there may be situations where something is not against Islamic law but is nonetheless condemned by Islamic ethics. Or there can be circumstances that, while not required by Islamic law, are essential from an ethical standpoint. For instance, while idle conversation is not strictly forbidden by Islamic law, it is morally unacceptable since it wastes time and is detrimental to one's spiritual growth.

Islamic bioethics' first influences Islamic bioethics is founded on the Qur'an, the Sunnah, and reason (al-'aql), much like any other inquiry into Islam. Sunni Muslims may use terms like ijmaa' (consensus) and qiyas in place of reason (analogy). Ijmaa' and qiyas as such are not recognized by Shi'a since they are insufficient proofs on their own.

Christian bioethics

In Christian bioethics it is noted that the Bible, especially the New Testament, teaches about healing by faith. Healing in the Bible is often associated with the ministry of specific individuals including Elijah, Jesus and Paul. Being healed has been described as a privilege of accepting Christ's redemption on the cross. Jesus endorsed the use of the medical assistance of the time (medicines of oil and wine).

The principle of the sacredness of human life is at the basis of Catholic bioethics. On the subject of abortion, for example, Catholics and Orthodox are on very similar positions. Catholic bioethics insists on this concept, without exception, while Anglicans, Waldensians and Lutherans have positions closer to secular ones, for example with regard to the end of life.

In 1936, Ludwig Bieler argued that Jesus was stylized in the New Testament in the image of the "divine man" (Greek: theios aner), which was widespread in antiquity. It is said that many of the famous rulers and elders of the time had divine healing powers.

Contemporary bioethical and health care policy issues, including abortion, the distribution of limited resources, the nature of appropriate hospital chaplaincy, fetal experimentation, the use of fetal tissue in treatment, genetic engineering, the use of critical care units, distinctions between ordinary and extraordinary treatment, euthanasia, free and informed consent, competency determinations, the meaning of life, are being examined within the framework of traditional Christian moral commitments.

Feminist bioethics

Feminist bioethics critiques the fields of bioethics and medicine for its lack of inclusion of women's and other marginalized group's perspectives. This lack of perspective from women is thought to create power imbalances that favor men. These power imbalances are theorized to be created from the androcentric nature of medicine. One example of a lack of consideration of women is in clinical drug trials that exclude women due to hormonal fluctuations and possible future birth defects. This has led to a gap in the research on how pharmaceuticals can affect women. Feminist bioethicists call for the necessity of feminist approaches to bioethics because the lack of diverse perspectives in bioethics and medicine can cause preventable harm to already vulnerable groups.

This study first gained prevalence in the field of reproductive medicine as it was viewed as a "woman's issue". Since then, feminist approaches to bioethics has expanded to include bioethical topics in mental health, disability advocacy, healthcare accessibility, and pharmaceuticals. Lindemann notes the need for the future agenda of feminist approaches to bioethics to expand further to include healthcare organizational ethics, genetics, stem cell research, and more.

Notable figures in feminist bioethics include Carol Gilligan, Susan Sherwin, and the creators of the International Journal of Feminist Approaches to Bioethics, Mary C. Rawlinson and Anne Donchin. Sherwin's book No Longer Patient: Feminist Ethics in Health Care (1992) is credited with being one of the first full-length books published on the topic of feminist bioethics and points out the shortcomings in then-current bioethical theories. Sherwin's viewpoint incorporates models of oppression within healthcare that intend to further marginalize women, people of color, immigrants, and people with disabilities. Since created in 1992, the International Journal of Feminist Approaches to Bioethics has done much work to legitimize feminist work and theory in bioethics.

In 2001, American professor Mary C. Rawlinson published The Concept of A Feminist Bioethics, an article criticizing traditional male-centric views on ethics. Rawlinson points out that traditional philosophical thought centralizes men and leaves women as an "other" or an accessory to men. As a result, the philosophy of "feminist bioethics" contradicts bioethics because women's rights are seen as a separate order from human rights. Finally, Rawlinson makes several recommendations for how women's experiences and bodies could reshape fundamental ethical principles, including acceptance, mutual respect, and the establishment of bodily autonomy for women.

Environmental bioethics

Bioethics, the ethics of the life sciences in general, expanded from the encounter between experts in medicine and the laity, to include organizational and social ethics, environmental ethics. As of 2019 textbooks of green bioethics existed.Particular emphasis on responsibility toward ecosystems, including resource conservation, environmental protection, and considerations of intergenerational justice.

Animal bioethics

Main Article: Animal ethics

Animal bioethics is the study of animal-human dynamics, and how animals should be treated by humans. In a scientific framework, ethical issues of consideration include animal testing and eponymous taxonomy (the ethics of naming species after people). Biologists W. M. S. Russell and R. L. Burch developed the “3 R’s”, a set of 3 guidelines outlining recommended procedures to promote animal respect and reduce the amount of animals used in scientific research. They include determining alternatives to animal use (replacement), minimizing the number of animals used (reduction), and mitigating animal suffering if they are used in research (refinement).

Eponymous taxonomy

Taxonomy is the classification of animals in biological disciplines. Some species such as Aleiodes gaga are named after real people, which can be controversial, as in the case of Anophthalmus hitleri, a species of beetle hunted to endangerment by Nazi memorabilia collectors. Critics of eponymic naming conventions such as Guedes et. al argue that eponymous taxonomy is a form of scientific colonization because scientists from colonizing nations often had a stake in naming species native to countries in the Global South. Supporters of eponymous taxa argue that “famous” taxonomies are important for conservation efforts, as species of interest would be brought to public attention.

Ethical issues in gene therapy

Gene therapy involves ethics, because scientists are making changes to genes, the building blocks of the human body. Currently, therapeutic gene therapy is available to treat specific genetic disorders by editing cells in specific body parts. For example, gene therapy can treat hematopoietic disease. There is also a controversial gene therapy called "germline gene therapy", in which genes in a sperm or egg can be edited to prevent genetic disorder in the future generation. It is unknown how this type of gene therapy affects long-term human development. In the United States, federal funding cannot be used to research germline gene therapy.

The ethical challenges in gene therapy for rare childhood diseases underscore the complexity of initiating trials, determining dosage levels, and involving affected families. With over a third of gene therapies targeting rare, genetic, pediatric-onset, and life-limiting diseases, fair participant selection and transparent engagement with patient communities become crucial ethical considerations. Another concern involves the use of virus-derived vectors for gene transfer, raising safety and hereditary implications. Additionally, the ethical dilemma in gene therapy explores the potential harms of human enhancement, particularly regarding the birth of disabled individuals. Addressing these challenges is vital for responsible development, application, and equitable access to gene therapies. The experience with human growth hormone further illustrates the blurred lines between therapy and enhancement, emphasizing the importance of ethical considerations in balancing therapeutic benefits and potential enhancements, especially in the rapidly advancing field of genomic medicine. As gene therapies progress towards FDA approval, collaboration with clinical genetics providers becomes essential to navigate the ethical complexities of this new era in medicine.

Professional practice

Bioethics as a subject of expert exercise (although now not a formal profession) developed at the beginning in North America in the Nineteen Eighties and Nineteen Nineties, in the areas of clinical / medical ethics and research ethics. Slowly internationalizing as a field, since the 2000s professional bioethics has expanded to include other specialties, such as organizational ethics in health systems, public health ethics, and more recently Ethics of artificial intelligence. Professional ethicists may be called consultants, ethicists, coordinators, or even analysts; and they may work in healthcare organizations, government agencies, and in both the public and private sectors. They may also be full-time employees, unbiased consultants, or have cross-appointments with educational institutions, such as lookup centres or universities.

Models of bioethics

American ethicists Tom Beauchamp and James Childress developed Principles of Biomedical Ethics, a set of four principles that include autonomy, nonmaleficence (avoiding harm), beneficence (doing good), and justice. Today, the four principles are used by bioethicists to assess ethical considerations such as childhood vaccinations and patient autonomy. One facet of the principles that Beauchamp and Childress defend is the idea that a set of universal morals can be created and applied to a given situation. Critics of this philosophy argue that it is not possible to assign universal morality to social values.

According to Ihor Boyko's book "Bioethics", there are three models of bioethics in the world:

• Model 1 is "liberal" when there are no restrictions.
• Model 2 is "utilitarian", when what is prohibited is allowed for one person or a group of persons, if it is useful and beneficial for the majority of people.
• Model 3 is "personalistic", where the human person is considered an inviolable integrity.

Learned societies and professional associations

The field of bioethics has developed national and international learned societies and professional associations, such as the American Society for Bioethics and Humanities, the Canadian Bioethics Society, the Canadian Association of Research Ethics Boards, the Association of Bioethics Program Directors, the Bangladesh Bioethics Society and the International Association of Bioethics.

Education

Bioethics is taught in courses at the undergraduate and graduate level in different academic disciplines or programs, such as Philosophy, Medicine, Law, Social Sciences. It has become a requirement for professional accreditation in many health professional programs (Medicine, Nursing, Rehabilitation), to have obligatory training in ethics (e.g., professional ethics, medical ethics, clinical ethics, nursing ethics). Interest in the field and professional opportunities have led to the development of dedicated programs with concentrations in Bioethics, largely in the United States, Canada (List of Canadian bioethics programs) and Europe, offering undergraduate majors/minors, graduate certificates, and master's and doctoral degrees.

Training in bioethics (usually clinical, medical, or professional ethics) are part of core competency requirements for health professionals in fields such as nursing, medicine or rehabilitation. For example, every medical school in Canada teaches bioethics so that students can gain an understanding of biomedical ethics and use the knowledge gained in their future careers to provide better patient care. Canadian residency training programs are required to teach bioethics as it is one of the conditions of accreditation, and is a requirement by the College of Family Physicians of Canada and by the Royal College of Physicians and Surgeons of Canada.

Criticism

As a field of study, bioethics has also drawn criticism. For instance, Paul Farmer noted that bioethics tends to focus its attention on problems that arise from "too much care" for patients in industrialized nations while giving little or no attention to the ethical problem of too little care for the poor. Farmer characterizes the bioethics of handling morally difficult clinical situations, normally in hospitals in industrialized countries, as "quandary ethics". He does not regard quandary ethics and clinical bioethics as unimportant; he argues, rather, that bioethics must be balanced and give due weight to the poor.

Additionally, bioethics has been condemned for its lack of diversity in thought, particularly concerning race. Even as the field has grown to include the areas of public opinion, policymaking, and medical decision-making, little to no academic writing has been authored concerning the intersection between race–especially the cultural values imbued in that construct–and bioethical literature. John Hoberman illustrates this in a 2016 critique, in which he points out that bioethicists have been traditionally resistant to expanding their discourse to include sociological and historically relevant applications. Central to this is the notion of white normativity, which establishes the dominance of white hegemonic structures in bioethical academia and tends to reinforce existing biases.

These points and critiques, along with the neglect of women's perspectives within bioethics, have also been discussed amongst feminist bioethical scholars.

However, differing views on bioethics' lack of diversity of thought and social inclusivity have also been advanced. For example, one historian has argued that the diversity of thought and social inclusivity are the two essential cornerstones of bioethics, albeit they have not been fully realized.

In order to practice critical bioethics, bioethicists must base their investigations in empirical research, refute ideas with facts, engage in self-reflection, and be skeptical of the assertions made by other bioethicists, scientists, and doctors. A thorough normative study of actual moral experience is what is intended.

Issues

Research in bioethics is conducted by a broad and interdisciplinary community of scholars, and is not restricted only to those researchers who define themselves as "bioethicists": it includes researchers from the humanities, social sciences, health sciences and health professions, law, the fundamental sciences, etc. These researchers may be working in specialized bioethics centers and institutes associated with university bioethics training programs; but they may also be based in disciplinary departments without a specific bioethics focus. Notable examples of research centers include, amongst others, The Hastings Center, the Kennedy Institute of Ethics, the Yale Interdisciplinary Center for Bioethics, the Centre for Human Bioethics.

Areas of bioethics research that are the subject of published, peer-reviewed bioethical analysis include:

• Abortion
• Alternative medicine
• Animal rights
• Applied ethics
• Artificial insemination
• Artificial life
• Artificial womb
• Assisted suicide
• Biocentrism
• Biological agent
• Biological patent
• Biopiracy
• Biorisk
• Blood transfusion
• Body modification
• Brain–computer interface
• Chimeras
• Circumcision
• Cloning
• Cognitive liberty
• Confidentiality (medical records)
• Conflict of interest in the healthcare industry
• Consent
• Contraception (birth control)
• Cryonics
• Disability
• Ecocide
• End-of-life care
• Eugenics
• Euthanasia (human, non-human animal)
• Exorcism
• Faith healing
• Feeding tube
• Gain-of-function research
• Gene theft
• Gene therapy
• Genetic testing
• Genetically modified food
• Genetically modified organism
• Genomics
• Great Ape Project
• HeLa cells
• Human cloning
• Human enhancement
• Human experimentation in the United States
• Human genetic engineering
• Human population planning
• Iatrogenesis
• Infertility treatments
• Intersex
• Life extension
• Life support
• Lobotomy
• Medicalization
• Medical malpractice
• Medical research
• Medical torture
• Mediation
• Mitochondrial donation
• Moral obligation
• Moral status of animals
• Nanomedicine
• Neuroethics
• Neuroenhancement
• Nazi human experimentation
• Ordinary and extraordinary care
• Overtreatment
• Organ donation
• Organ transplant
• Pain management
• Parthenogenesis
• Patients' Bill of Rights
• Placebo
• Pharmacogenetics
• Political abuse of psychiatry
• Population control (non-human animals)
• Prescription drug prices in the United States
• Procreative beneficence
• Professional ethics
• Psychosurgery
• Quality of life (healthcare)
• Quaternary prevention
• Recreational drug use
• Reproductive rights
• Reproductive technology
• Reprogenetics
• Research ethics
• Resource allocation
• Sex reassignment therapy
• Sperm and egg donation
• Spiritual drug use
• Stem cell research
• Sterilization (medicine)
• Suicide
• Surrogacy
• Transsexuality
• Transhumanism
• Transplant trade
• Triage
• Tubal ligation
• Vaccination controversy
• Xenotransfusion
• Xenotransplantation

Quantum chemistry

From Wikipedia, the free encyclopedia

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

Simulated electron localization function (ELF) map of a furan (C₄H₄O) molecule. Colour indicates the magnitude of the ELF field, which reflects the degree of electron localisation at each point in the molecular plane.

Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics.

Quantum chemistry studies focused on the electronic ground state and excited states of atoms, molecules, and ions. Such calculations allow chemical reactions to be described with respect to pathways, intermediates, and transition states. Spectroscopic properties may also be predicted. Typically, such studies assume the electronic wave function is adiabatically parameterized by the nuclear positions (i.e., the Born–Oppenheimer approximation). A wide variety of approaches are used, including semi-empirical methods, density functional theory, Hartree–Fock calculations, quantum Monte Carlo methods, and coupled cluster methods.

Understanding electronic structure and molecular dynamics through the development of computational solutions to the Schrödinger equation is a central goal of quantum chemistry. Progress in the field depends on overcoming several challenges, including the need to increase the accuracy of the results for small molecular systems, and to also increase the size of large molecules that can be realistically subjected to computation, which is limited by scaling considerations — the computation time increases as a power of the number of atoms.

History

Some view the birth of quantum chemistry as starting with the discovery of the Schrödinger equation and its application to the hydrogen atom. However, a 1927 article of Walter Heitler (1904–1981) and Fritz London, is often recognized as the first milestone in the history of quantum chemistry. This was the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond. However, prior to this a critical conceptual framework was provided by Gilbert N. Lewis in his 1916 paper The Atom and the Molecule, wherein Lewis developed the first working model of valence electrons. Important contributions were also made by Yoshikatsu Sugiura and S.C. Wang. A series of articles by Linus Pauling, written throughout the 1930s, integrated the work of Heitler, London, Sugiura, Wang, Lewis, and John C. Slater on the concept of valence and its quantum-mechanical basis into a new theoretical framework. Many chemists were introduced to the field of quantum chemistry by Pauling's 1939 text The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry, wherein he summarized this work (referred to widely now as valence bond theory) and explained quantum mechanics in a way which could be followed by chemists. The text soon became a standard text at many universities. In 1937, Hans Hellmann appears to have been the first to publish a book on quantum chemistry, in the Russian  and German languages.

In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. In addition to the investigators mentioned above, important progress and critical contributions were made in the early years of this field by Irving Langmuir, Robert S. Mulliken, Max Born, J. Robert Oppenheimer, Hans Hellmann, Maria Goeppert Mayer, Erich Hückel, Douglas Hartree, John Lennard-Jones, and Vladimir Fock.

Electronic structure

The electronic structure of an atom or molecule is the quantum state of its electrons. The first step in solving a quantum chemical problem is usually solving the Schrödinger equation (or Dirac equation in relativistic quantum chemistry) with the electronic molecular Hamiltonian, usually making use of the Born–Oppenheimer (B–O) approximation. This is called determining the electronic structure of the molecule. An exact solution for the non-relativistic Schrödinger equation can only be obtained for the hydrogen atom (though exact solutions for the bound state energies of the hydrogen molecular ion within the B-O approximation have been identified in terms of the generalized Lambert W function). Since all other atomic and molecular systems involve the motions of three or more "particles", their Schrödinger equations cannot be solved analytically and so approximate and/or computational solutions must be sought. The process of seeking computational solutions to these problems is part of the field known as computational chemistry.

Valence bond theory

Main article: Valence bond theory

As mentioned above, Heitler and London's method was extended by Slater and Pauling to become the valence-bond (VB) method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of bonds. It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of orbital hybridization and resonance.

A covalent bond is formed when there is an overlap of half-filled atomic orbitals from two atoms, which together form an electron pair. The strength and energy of the system is dependent on the amount of overlap. As the atoms move together, their orbitals start to overlap and the electrons begin to feel the attraction of both nuclei. There is also a repulsion that begins to occur, which becomes very strong when the atoms are too close together. The ideal and most stable length between the two atoms is the bond distance, which is when the repulsive and attractive forces balance resulting in the lowest energy configuration.

Orientation of the orbitals can have a large affect on what bonds are formed, including if any is formed. When there is a direct overlap of one atomic orbital from each atom, a sigma (σ) bond is formed. This can be created from two s-orbitals, an s-orbital and a p-orbital, or two p-orbitals. A pi (π) bond is formed from a side-to-side overlap of two p-orbitals. The pi bond only forms if the phases of the overlapping p-orbitals are the same.

Molecular orbital theory

The MO diagram of the trihydrogen cation.

Main article: Molecular orbital theory

An alternative approach to valence bond theory was developed in 1929 by Friedrich Hund and Robert S. Mulliken, in which electrons are described by mathematical functions delocalized over an entire molecule. The Hund–Mulliken approach or molecular orbital (MO) method is less intuitive to chemists but predicts spectroscopic properties better than the VB method. As opposed to VB theory, MO theory does not focus just the overlap of electron density in one area causing a bond but instead describes the whole molecule as one system. This leads to a more complex understanding of the system. This approach is the conceptual basis of the Hartree–Fock method and further post-Hartree–Fock methods.

MO calculations result in orbitals or wavefunctions and energies for a molecule, which can be filled with electrons from two different atomic orbitals. These atomic orbitals come from separate atoms resulting in molecular orbitals being linear combinations of atomic orbitals.

Density functional theory

Main article: Density functional theory

The Thomas–Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attempt to describe many-electron systems on the basis of electronic density instead of wave functions, although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory (DFT). Modern day DFT uses the Kohn–Sham method, where the density functional is split into four terms; the Kohn–Sham kinetic energy, an external potential, exchange and correlation energies. A large part of the focus on developing DFT is on improving the exchange and correlation terms. Though this method is less developed than post Hartree–Fock methods, its significantly lower computational requirements (scaling typically no worse than n³ with respect to n basis functions, for the pure functionals) allow it to tackle larger polyatomic molecules and even macromolecules. This computational affordability and often comparable accuracy to MP2 and CCSD(T) (post-Hartree–Fock methods) has made it one of the most popular methods in computational chemistry.

Chemical dynamics

A further step can consist of solving the Schrödinger equation with the total molecular Hamiltonian in order to study the motion of molecules. Direct solution of the Schrödinger equation is called quantum dynamics, whereas its solution within the semiclassical approximation is called semiclassical dynamics. Purely classical simulations of molecular motion are referred to as molecular dynamics (MD). Another approach to dynamics is a hybrid framework known as mixed quantum-classical dynamics; yet another hybrid framework uses the Feynman path integral formulation to add quantum corrections to molecular dynamics, which is called path integral molecular dynamics. Statistical approaches, using for example classical and quantum Monte Carlo methods, are also possible and are particularly useful for describing equilibrium distributions of states.

Adiabatic chemical dynamics

Main article: Born–Oppenheimer approximation

In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energy surfaces. This is the Born–Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable simple estimates of unimolecular reaction rates from a few characteristics of the potential surface.

Non-adiabatic chemical dynamics

Main article: Vibronic coupling

Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surfaces (corresponding to different electronic quantum states of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by Stueckelberg, Landau, and Zener in the 1930s, in their work on what is now known as the Landau–Zener transition. Their formula allows the transition probability between two adiabatic potential curves in the neighborhood of an avoided crossing to be calculated. Spin-forbidden reactions are one type of non-adiabatic reactions where at least one change in spin state occurs when progressing from reactant to product.