Subject: dose-response damage-repair (fwd)
Date: Wed, 22 Apr 1998 022446 -0500 (CDT)
From: "Roy L. Beavers" <rbeavers@llion.org>
To: emfguru@hotmail.com
--------------------------------------------------
.......Perhaps some of you will also know other experts to whom this
message should be forwarded....... It suggests a pretty good line
of thought about the math of "cell damage" repair..... I am not
qualified to say, but I hope Haldun's effort will get into the right
hands...... Cheerio [guru]
---------- Forwarded message ----------
Date: Tue, 21 Apr 1998 19:20:51 +0400 (EET DST)
From: Haldun Ozaktas
To: rbeavers@llion.org
Cc: haldun ozaktas ,
haldun ozaktas
Subject: dose-response damage-repair
Hi everyone,
The following represents some of the "analysis" I have been doing
ever since they recently put up an FM radio antenna on our campus
(about 500 meters to both my apartment and office), making me ponder
the consequences of this continual exposure.
If anybody takes the ideas seriously, I may consider developing it.
(If not, I can always send it to "Journal of Irreproducible Results".)
And please let me know if you know of any place you would suggest
me to post this.
Haldun Ozaktas
___________________________________________________________________________
***Elementary considerations on dose-response relationships
in the simultaneous presence of damage and repair mechanisms***
----Note: The subject matter of this working paper lies
beyond my scope of expertise and I am totally unaware of the
techniques experts in these areas actually use and what the
state of the art is. I am presenting them only to initiate
a possibly useful brainstorming.----
It seems it is being suggested that some health effects of EM fields
and waves is subject to a damage-repair effect. The fields act on the
body and cause some direct/indirect but--within certain limits--
reversible effect. Meanwhile, the body tries to heal itself as much as
it can. To the extent that and wherever such a mechanism is in effect,
this will have consequences on the kinds of dose-response relations
one would expect to see.
I will try to illustrate the essential point under overly simplified
assumptions. If anyone believes there is a correspondence with reality,
I might consider a full analytic elaboration.
But even before this simple formulation, a truly elementary example
to get across the main point:
Elementary example:
-------------------
Let us say I am exposed H hours a day and not exposed (24-H) hours
a day. When I am exposed, the rate of damage is d per hour. Thus
the damage I accumulate per day is dH. When I am not exposed, the
rate of healing or repair is r per hour. Thus the healing that
happens in a day is r(24-H). Thus the net damage n in excess of
repair, per day is
n = dH - r(24-H)
If we assume the body cannot accumulate "repair", we may take the
net damage as zero whenever this formula is less than zero.
The net damage n depends on two things:
(i) The ratio of repair rate to damage rate: r/d
(ii) The exposure time H in comparison to 24.
Since units of d and r are so far arbitrary, it is useful to
plot (n/d) = H - (r/d)(24-H) as a function of H with r/d as a
parameter. (For instance, we may take three representative values
for r/d as 0.1, 1, 10.)
(*) r/d=0.1, repair is much slower than damage.
No damage accumulated for very short exposure times, otherwise
damage accumulated per day increases linearly with H.
(*) r/d=1, repair is equal to damage.
No damage as long as H is less than 12 hours, otherwise
damage accumulated per day increases linearly with (H-12).
That is, the damage increases linearly with exposure in excess
of 12 hours. Someone exposed for 14 hours will have damage twice
that of someone exposed for 13 hours, although they are exposed
for approximately the same duration (14 ~ 13).
(*) r/d=10, repair is much faster than damage.
No damage as long as H is not very close to 24 hours.
This does not exclude very large damages to those exposed around
the clock and who never get a break from the constant exposure.
Someone exposed for 21 hours may get no damage, whereas someone
exposed for 22 hours or more may get severe damage. Someone
exposed for 24 hours may get more than 10 times the damage that
someone exposed for 22 hours does. These considerations may be
especially important in low but chronic exposure situations.
It is evident that these considerations indicate that even with
a linear dose-damage and dose-repair mechanism, we are led to
nonlinear dose-net damage relations because damage and repair
mechanisms steal time from each other. Those at greatest danger
may be those that never get a break from the EM fields and waves.
Consequently, simple linear assumptions on damage and repair
result in a nonlinear dose-response relationship.
The following are the elements of a more formal model. It can be
readily turned into a full blown model, but I see a point in doing
that only if anyone suggests that such a model might indeed have a
bearing on reality.
Elementary analysis:
--------------------
Let d(I) denote the "rate of damage" caused by a "cause" whose
"intensity" is I. When the cause is zero (I=0), the rate of damage
will be denoted d(0)=d0. Let r(I) denote the rate of repair under
instensity I. When the cause is zero (I=0), the rate of repair
will be denoted r(0)=r0.
The intensity I is in units of Joules/second or Tesla/second but
in any case something/second. It is a function of time so it
may be more explicitly written I(t).
Both d(I) and r(I) are in units of damage/second, where damage
is something which you can relate to risk of disease or death etc.
It may be initially presumed that d(I) is an increasing function
of I and that d0=0; there is no damage when I=0.
It may be presumed that r(I) is a decreasing function of I and
that r0 is its maximum value; repair mechanisms are hindered by
increasing intensity.
These presumptions are not essential and not assumed in the following.
Now, I will assume that the total net damage rate n(I) is given by
the difference of d(I) and r(I):
n(I) = d(I) - r(I)
(It is also possible to assume it is given by ratios but that simply
leads to an equivalent formulation under logarithms.)
Now, I further assume that the cumulative damage between time 0
and time T, denoted D(0,T) is given by the time integral
D(0,T) = integral_(0)^(T) [d(I) - r(I)] dt
where we remember that I is a function of time. It may be presumed
that illness occurs when D(0,T) exceeds a certain threshold D0.
Thus illness occurs when
int_(0)^(T) [d(I) - r(I)] dt = D0
(Note: I think it should be assumed that unlike damage, "repair"
cannot be accumulated. Thus D(0,T) > 0 for all T. If
[d(I) - r(I)] is negative for a sufficiently long time, this will
tend to bring D(0,T) below zero in the above formula. In this case,
we simply hard limit D(0,T) to zero from below and do not allow
it to become negative. While this peculiarity is easy to handle
numerically on a computer, I could not think of a compact notation
to represent it in the above equation. In the event that repair can
be accumulated, but only up to a certain amount, then we may simply
replace the hard limit with the appropriate negative number.)
Applications of the model:
__________________________
The final equation is a relation between D0, T and d(I),
r(I), and I(t). The researcher may measure the intensity
exposure as a function of time, thus knowing I(t).
The time T at which illness occurs can also be measured.
D0 is not an independent parameter, as it reflects the choice
of units of d(I) and r(I). These functions d(I) and r(I) are
the unknowns, which we desire to find. If we propose a plausible
parametric form for these functions, and if we have data
pertaining to a large number of cases, then we can numerically
solve for these damage rate and repair rate functions.
Of course, in reality different people will have different thresholds
and different functions d(I) and r(I) so the analysis must
statistically account for this and lead to some appropriate average.
(C) April 1998
Haldun M. Ozaktas, Associate Professor
Bilkent University (90) (312) 266 40 00 / 1619
Department of Electrical Engineering (90) (312) 266 43 07 (secretary)
TR-06533 Bilkent, Ankara, Turkey (90) (312) 266 41 26 (fax)
www.ee.bilkent.edu.tr/~haldun haldun@ee.bilkent.edu.tr
___________________________________________________________________________
Archive provided courtesy of WaveGuide, http://www.wave-guide.org
Reprinted with permission of Roy Beavers, http://www.feb.se/EMF-L/EMF-L.html