Question

what is allometric? how does it work

human drug dose is 25 mg/ kg, what is the dog dose using that

Answer 1

what is allometric?

Ans: Allometry is the study of how these processes scale with body size and with each other, and the impact this has on ecology and evolution.

Allometry, in its broadest sense, describes how the characteristics of living creatures change with size. The term originally referred to the scaling relationship between the size of a body part and the size of the body as a whole, as both grow during development. However, more recently the meaning of the term allometry has been modified and expanded to refer to biological scaling relationships in general, be it for morphological traits (e.g., the relationship between brain size and body size among adult humans), physiological traits (e.g., the relationship between metabolic rate and body size among mammal species) or ecological traits (e.g., the relationship between wing size and flight performance in birds). Indeed, allometric relationships can be described for almost any co-varying biological measurements, resulting in broad usage of the term. However, a unifying theme is that allometry describes how traits or processes scale with one another. The study of allometry concerns the functional mechanisms that generate these scaling relationship, how they impact ecology, and how they respond to and influence evolution.

how does it work:

Allometric scaling relationships can be described using an allometric equation of the form,
	f (s) = c s d,	(1)
where c and d are constants. The variables s and f (s) represent the two different attributes that we are comparing (e.g., body mass and skeletal mass).

his equation can be used to understand the relationship between two attributes. Specifically, the constant d in this model determines the relative growth rates of the two attributes represented by s and f (s). For simplicity, let's consider the case d > 0 only.

• If d > 1, the attribute given by f (s) increases out of proportion to the attribute given by s. For example, if s represents body size, then f (s) is relatively larger for larger bodies than for smaller bodies.
• If 0 < d < 1, the attribute f (s) increases with attribute s, but does so at a slower rate than that of proportionality.
• If d = 1, then attribute f (s) changes as a constant proportion of attribute s. This special case is called isometry, rather than allometry.

• Notice that (1) is a power function not an exponential equation (the constant d is in the exponent position instead of the variable s). Unlike other applications where we need logarithms to help us solve the equation, here we use logarithms to simplify the allometric equation into a linear equation. Here's how it works We rewrite (1) as a logarithmic equation of the form,
  	log (f (s)) = log (c s d).	(2)
  Then, using the properties of logarithms, we can rearrange (2) as follows,
  	log (f)	= log c + log (s d),
  		= log c + d log s.	(3)
  When we change variables by letting,
  	y	= log f,
  	b	= log c,
  	m	= d,
  	x	= log s.
  you can see that (3) is in fact the linear equation
  	y	= mx + b.	(4)
  Therefore, transforming an allometric equation into its logarithmic equivalent gives rise to a linear equation.

human drug dose is 25 mg/ kg, what is the dog dose using that:

ans: Human dose (mg/kg) to dog dose (mg/kg) - multiply by 1.8

human drug dose is 25 mg/ kg=25 multiply by 1.8

therefor Dog dose is 45 mg/kg

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