**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**6.5.2 Thermogenic Limits
In Vivo**

Consider nanorobots at work inside a single biological cell
of size L_{cell}, volume V_{cell} = L_{cell}^{3},
and thermal conductivity K_{t} = 0.623 watts/m-K (water) immersed in
a large isothermal heat sink. The maximum temperature differential DT_{n}
between core and periphery caused by the intracellular release of P_{cell}
(watts) due to nanorobot activity is:

_{}
{Eqn. 6.52}

where D_{cell} is total cellular energy density (watts/m^{3}).
A typical ~20 micron diameter human tissue cell produces 30-480 pW, giving DT_{cell}
= 0.3-6.0 microkelvins. The data in Table
6.8 indicates that individual cells appear to safely tolerate internal energy
releases up to D_{cell} ~ 10^{6} watts/m^{3}, which
leads to the following proposed thermogenic limit for in cyto operations:

Thus, for example, using the proposed limit an isolated 20
micron tissue cell can safely host in its interior a set of active nanorobotic
machinery that in total generates P_{cell} ~ 8000 pW and raises cell
temperature by DT_{cell} ~ 100 microkelvins,
which seems extremely conservative.

If many cells in a given block of tissue contain active nanomachinery,
as will often be the case, then the assumption of an isothermal heat sink no
longer holds because the nanorobots will collectively warm up their operating
environment. In the limit of an entire human body, a 100-watt total nanorobot
power expenditure giving a whole-body 1000 watt/m^{3} incremental power
density (Table
6.8) seems quite conservative since 50,000-100,000 watts/m^{3} is
considered the safe therapeutic range for medical diathermy.^{ 819}
A temperature rise in the tissues triggers an increase in blood flow, which
in turn produces a cooling effect. The maximum thermal load that an adult can
dissipate under room temperature conditions without an increase in body temperature
is a whole-body exposure of 100 watts/m^{2},^{822}
or ~2000 watts/m^{3}. Thus a 100-watt whole-body nanorobot power budget
normally will produce no measurable increase in body temperature.

Operated at its peak output of 1600 watts,^{780,865}
the human body's core temperature rises ~3.5 K.^{821}
Even assuming a simple linear relation, a whole-body 100-watt nanorobot power
budget would correspond to an increase in core body temperature of at most ~0.2
K, far smaller than the mean normal diurnal variation of ~1 K (Section
6.3.1) and less than the ~0.2-0.5 K load error in the human thermoregulatory
control system.^{865} Since glucose-powered
nanorobots may compete with tissues for fuel, a 100-watt total withdrawal also
represents ~2000 Kcal/day, near the limit of what can be conveniently replaced
dietetically on a long-term basis.

A proper comprehensive analysis of energy flows^{818}
requires a detailed model of body geometry, incident radiation, skin emissivity,
convection currents, heat exchange by conduction, evaporative cooling, respiratory
heat losses, physiological and behavioral thermoregulatory responses, work done
by the patient, and the precise distribution, clumping patterns and activities
of in vivo nanorobots, all of which is very complex and quite beyond the scope
of this book. However, a simple log-linear interpolative relation with correct
endpoints (D_{tiss} = 10^{6} watts/m^{3} at L_{tiss}
= 20 microns and D_{tiss} = 10^{3} watts/m^{3} at L_{tiss}
= 0.5 meters) suggests the following proposed crude maximum thermogenic limits
for nanorobot operations in human soft tissue:

_{}
{Eqn. 6.56}

where V_{tiss} = L_{tiss}^{3} for
the total volume of soft tissue in which all deployed nanorobots are active.
(Eqns. 6.52 through 6.56
are summarized in Figs. 6.14
and
6.15). Thus, for example, medical nanorobots deployed solely in the thyroid
gland (L_{tiss} ~ 2.6 cm; Table
8.9) should be restricted to a maximum total power budget P_{tiss}
~ 0.1 watt which elevates thyroid temperature by DT_{tiss}
~ 0.02 K. Higher in vivo power densities may sometimes be justified in hospital
or emergency medical situations (Chapter 24), and
a few other special circumstances (e.g., Chapter 21).

Last updated on 18 February 2003