Examples of linear equations in nursing

Math Powerpoint

Linear Equations in the Medical Field

Names: Yurievna Rodriguez

Geydis Pizano

Guillermo Pupo

Prof: Brenda Gonzalez

Inter Algebra 1

A linear equation is an algebraic equation in which each term has an exponent of one and its graphing results into a straight line.

Linear equations focus on collecting and analyzing data and providing a result as the output.

The result can take numerical form i.e. numbers or in form of images such as in X-rays and MRI scans.

Linear equations have a wide application in medical fields such as in generation of images in X-rays and in calculations such as in the determination of dosages or body assessments( Abdlrazg, 2016).

Linear equations form part of applied mathematics in the medical field.

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Determination of BSA

First, linear equations are used in determination of body surface area (BSA) for patients.

BSA can be obtained through a nomogram or calculated by a computer or a scientific calculator.

For instance, medics commonly determine BSA by the use of Mosteller formula.

The formula uses the square root of the product of weight and height, divided by 3600.

Body surface area is important in areas related to body metabolic activities such as extracorporeal circulation, body fluid requirements, ventilation, among others.

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Determination of Dosage

Nurses use linear equations to calculate the doses to be administered to patients.

Determination of doses involves organizing information and using a linear equation to solve the problem.

Dosages can be calculated using three ways: desired over have or the formula method, dimensional analysis method, and ration and proportion method.

Of all the three, ration and proportion, as well as the formula method use linear equations (Toney-Butler & Wilcox, 2019).

Calculating the amount of drug to be administered to a patient is very essential as wrong doses cannot heal the patient cause adverse body reactions or even kill the patient.

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For example, the formula method relates the desired dose and the amount to be taken by the patient using the relationship: Desired amount/available amount × quantity= unknown amount (Butler & Wilcox, 2019).

It can be represented in another way as D/A × Q=X.

An example is 500 mg of medicine , available in 100 mg and in the form of tablets.

Inserting the values in the equation D/A × Q=X, will be 500 mg/100 mg × 1 tablet = X,

Solving the equation gives the value of X as 5 tablets.

The formula method can be used in calculation of doses for other medications such as IV and syrup solutions. In other words, it is not limited to tablets.

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The system of linear equations in CT scans are said to be overdetermined since there are more equations that unknows.

Specifically, in CT, the number of X-ray beams exceeds the number of pixels.

For instance, the human brain is divided into several grids during scanning. The X-ray source then rotates round the brain generating beams at different angles.

An amount of the X-ray’s intensity is lost when it travels through bones and tissues from each section (Rahman, 2018).

To get the best out of CT scans, the part aimed is divided into several zones or grids from which information arising from the beam of light is analyzed.

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Used in CT scans

Linear algebra, which comprises linear functions is also applied in computed tomography (CT) (Rahman, 2018).

Linear equations are used in generating X-ray images from different directions.

X-ray examinations from one angle are not good enough as they can crucial radiographic images such as tumors that lie behind a bone.

However, Computed Tomography (CT) solves that by generating a number of beams from different directions, creating a cross-sectional radiograph of the medium.

Computed CT uses a lot of algorithms, which represent linear equations in matrix form to reconstruct an image, making sure that a medium’s images do not cover each other.

Computerized tomography refers to a procedure in which a narrow beam of X-rays is focused at a part of a patient’s body and quickly rotated, producing signals which are then decoded by a computer to generate cross sectional images.

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Because of the lack of a scanner, the specific values of intensity cannot be determined.

Therefore, intensity which is lost is taken as a percentage of attenuation “x” which is then converted to linear attenuation units (LAUs) using the formula : L=-ln(1-x).

Where, x is the percentage attenuation and L is linear attenuation.

The beams usually pass through different sections or grids.

Lets say we have three grids (A, B, C) and hence three beams of light (B1, B2, B3). Also, intensity passing through grids A,B and C is reduced by a, b and c values respectively (Rahman, 2018).

The formula, L=-ln (1-x) is the foundation of generating other linear equations. The other equations arise from beams passing through other grids. The number of linear equations is equal to the number of grids or partitions made to the body aimed.

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If beam 1 passes through grids A and B, it leads to a reduction in intensity of a and b units which can be modelled in an equation: a +b = L1.

Further equations can be modeled for beams passing through various grids, hence generating a system of linear equations.

By using Gaussian elimination or gauss-Jordan elimination method, we can calculate the values of a, b and c.

The values are then compared with a reference table to identify the contents of the grids. For instance, if the contains soft tissues, bones, tumors, etc. (Rahman, 2018).

The generation and solving of the equations is done by algorithms.

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Dilution of solutions

Moreover, health officers use linear equations in dilution of solutions.

The solutions can then be diluted to suit different uses, e.g. for use by adults or infants.

To calculate the amount of required in making a particular volume from a stock solution, the following linear formula is used:

Amount of stock required=Strength Required/Stock strength × Volume required.

Water required in dilution is related with the formula: Water required= Volume Required –Stock Required.

Most medical solutions are stored in concentrated forms to reduce storage space and bulkiness. It also helps in custom diluting the solutions for specific uses or individuals such as infants and adults.

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Conclusion

In conclusion, linear equations are very critical in the field of medicine.

Nurses use algebraic equations to determine the correct amount of dosage through calculation of BSA, the actual dosages and dilution of medical solutions.

Linear equations also serve a crucial role as they are integrated into algorithms which help in CT scans.

In general, linear equations make the process of diagnosing and treatment a success.

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References

Abdlrazg, B. (2016). Linear Algebra With Applications (Doctoral Dissertation, Near East University).

Toney-Butler, T., & Wilcox, L. (2019). Dose Calculation (Desired Over Have or Formula). Retrieved 9 September 2019, from https://www.ncbi.nlm.nih.gov/books/NBK493162/

Rahman, A. F. M. (2018). System of linear equations in Computed Tomography (CT) (Doctoral dissertation, BRAC University).

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