Modeling The Electrical Resistance Of The Human Body: Towards More Accurate Hazard Assessments

Importance of Accurate Hazard Assessments

The human body’s interaction with electricity poses risks of shock, burns, and electrocution under hazardous conditions. Accurately modeling the body’s electrical resistance enables improved safety analysis when designing electrical systems and medical devices. More precise resistance estimates allow determining safe voltage and current limits to prevent injuries.

Electrical safety standards reference body resistance values determining permissible exposure thresholds. However, using oversimplified resistance models underestimates risks by assuming uniform characteristics. Improved physiological modeling provides nuanced hazard assessments accounting for individual differences across body geometries, tissue qualities, and contact scenarios.

Core Principles of Electrical Resistance

Resistance equates to the obstruction impeding electrical current flow through a conductive medium. The human body contains conductive tissues through which electricity can pass to varying degrees. Modeling this complex resistance requires applying core biophysical principles.

Ohm’s law defines the relationship where voltage equals current multiplied by resistance. Consequently, increased resistance across bodily tissues results in greater voltage drops for a given current. Higher sustained voltages enable damaging current flows increasing probability of hazardous bioeffects.

Resistance equals resistivity multiplied by length and divided by cross-sectional area. Humans exhibit substantial intra- and inter-subject variability along these dimensional measures. Modeling approaches must capture differences in anatomy contributing to individualized resistance properties.

Modeling Resistance of Human Tissues

Skin and Fat Layers

The skin acts as the primary contact point conducting current into the body. Epidermal layers exhibit scaling resistivities ranging from 100-1,000 ohm-cm matching low water compositions. Underlying fat also Demostrates high 1,000+ ohm-cm resistivities owing to nonconductive adipocytes.

Together, these superficial barriers account for over half of total body resistance. Equivalent models represent the skin-fat layers using variable numbers of parallel resistor-capacitor pairs. Improved modeling distributes these contact impedances across differential surface areas.

Muscle Tissue

Current penetrating beneath the skin reaches more conductive muscular tissues. Skeletal muscle primarily consists of long, tubular muscle fibers immersed in interstitial fluid. This anisotropic fibrous composition produces directionally-dependent “transverse” vs. “longitudinal” resistivity values.

Multiscale modeling approaches integrate small-scale cellular-level resistivities with the macrostructure. Gap junction resistances between fibers determine transverse resistance, while longitudinal values depend on fiber membrane properties. Realistic muscle shapes and densities derive person-specific aggregate resistances.

Internal Organs

Deeper current flows reaching the thoracic and abdominal cavities traverse organs of widely varying tissue consistency. Resistivities range from the low hundreds for vascularized kidney and liver to over 10,000 ohm-cm for insulating fat deposits.

Detailed anatomical modeling maps organ sizes, shapes, positions, and proximity to external contact points. Current flow simulations apply tissue-differentiated resistivities over matrix equation solvers. Individual organ resistance yields overall resistance by using parallel resistance calculations weighted by cross-sectional area.

Incorporating Body Geometry

Body resistance fundamentally depends on size and composition. Accurately modeling organ positions and spatial relationships enables quantifying current paths throughout tissue networks. Image-based mesh generation incorporates subject body geometry from medical scans.

MRI and CT images provide 3D volumetric sampling of anatomical structures. Tissue densities differentiate region-specific resistivities for finite-element models. Mesh elements discretize the body into adjacent voxels assigned unique resistance values based on contents. Solvers compute total impedances across pathways.

Incorporating age, height, weight, and body mass index correlates sample populations with body resistance distributions. Statistical variability quantification informs safety standards by predicting resistance ranges across vulnerable subgroups rather than using canonical values.

Sample Code for Multi-Layer Body Model

This sample Python code defines a multi-layer resistor network model estimating total resistance from contact point through subsequent skin, fat, muscle, and organ tissue layers:

import numpy as np

# Define layer thicknesses
skin_thick = 1e-3 # 1 mm  
fat_thick = 0.05 # 5 cm
muscle_thick = 0.2 # 20 cm

# Define layer resistivities
skin_rho = 1000 
fat_rho = 2000
muscle_rho = 300

# Calculate layer cross-sectional areas
torso_radius = 0.2 # 20 cm radius
skin_area = 2*np.pi*torso_radius*skin_thick 
fat_area = 2*np.pi*(torso_radius-skin_thick)*fat_thick
muscle_area = 2*np.pi*(torso_radius-skin_thick-fat_thick)*muscle_thick

# Compute layer resistances 
skin_resist = skin_rho*skin_thick/skin_area
fat_resist = fat_rho*fat_thick/fat_area  
muscle_resist = muscle_rho*muscle_thick/muscle_area  

# Model as series resistor network
R_model = skin_resist + fat_resist + muscle_resist  

print('Total modeled resistance =', R_model)

The script above calculates resistance contributions from concentric tissue layers. Parameter modifications enable configuring detailed sample-specific models.

Validating Models Through Testing

Effective human body resistance models require validation to ascertain accuracy. Testing procedures apply controlled voltage/current signals capturing resultant measurements for model comparisons.

Contact electrical impedance tomography uses electrode arrays measuring internal impedances through attached body segments. Alternating signals determine frequency-dependent resistive and reactive contributions across tissue types.

Comparisons with anatomically-detailed simulations based on individual medical images provide localized impedance validation data. This facilitates calibrating resistivity values and spatial distributions in computational models to match measured values.

Applications for Improved Hazard Analysis

Electrical Safety Standards

Consensus safety standards determine permissible electrical exposure thresholds for human contact scenarios. Updated standards incorporate recent scientific data on risks from current pathways associated with powerline contacts, device faults, and lightning strikes.

Accurately modeling tissue resistances and geometries better informs ballpark resistance figures used. Statistical distributions identify conservative boundaries covering higher vulnerability groups. Standards committees integrate computational model findings in ongoing guideline revisions.

Medical Device Design

Protecting patients from electrical hazards poses challenges when designing medical equipment. Improved organ-level modeling predicts localized current densities from low-voltage defects or electrical therapy equipment.

Simulating currents conducted through blood vessels and surrounding tissue identifies maximum safe ampacities. Engineers apply bioelectric models emulating patient anatomies validating safety margins for medical electronics attached externally or implanted inside the body.

Forensic Investigations

Analyzing electrical trauma requires reconstructing incident currents pathways through bodily tissues. Accurate resistance models help determine current flows needed to produce documented burns and cellular electroporation patterns.

Combined with tissue damage visualizations from scanned autopsy data, model-based current backtracing identifies likely attachment points. Findings assist forensic examiners assessing if injuries resulted from environmental contacts or deliberated directed assaults.