English translation
HSE Analog Computer — A New Development for Biomedical Research
This document is an English translation of the original German brochure published by Hugo Sachs Elektronik, approximately 1977.
HSE Analog Computer
A New Development for Biomedical Research
Application possibilities: Model-based simulation of biochemical and biophysical functional systems, for example in cardiovascular physiology, pharmacokinetics, in biochemical control systems of the cell, in the biophysics of membranes, and in model-building within pathophysiology.
Nearly all biological fundamental processes can be formulated as differential equations — such as the excretion kinetics of a pharmacological agent, and likewise — at the molecular level — the movement of ions through membranes or the kinetics of an enzymatic reaction.
Biological functional systems can therefore in general be described by a system of differential equations, whose computer-based representation and analysis is the great domain of the analog computer. A further great advantage of the analog computer is that it requires neither specialized mathematical knowledge from its user nor the learning of a special programming system or computer language.
For the biomedical application of analog computers, special criteria have developed over time that were fully taken into account in the new development of the HSE Analog Computer.
First and foremost, the desire for high computational capacity must be mentioned without the device falling into the price class of large computers. This goal was achieved with the HSE Analog Computer by limiting computational accuracy to approximately 1%. The device therefore offers in its price class a computational capacity not even approximately achieved before, so that even very extensive programs (such as the system of Hodgkin-Huxley equations for describing ion movement through excitable membranes) can be computed without difficulty.
Individual Components
The device individually contains:
- 32 Integrators
- 32 Summers
- 16 Multipliers (shared with a comparator, also suitable for division)
- 8 Function generators
- 32 Coefficient potentiometers (wire-wound)
- 32 associated impedance converters
- 4 Comparators (each with 2 relay contacts)
- Various free elements, unity-value elements, and special connections
Features
- Overload display, acoustic and optical
- Trigger and time-axis output for oscilloscopes
- Digital voltmeter with addressing switch
- 2 outputs with separate addressing switches for connection of oscilloscopes or direct recorders (output voltage ±10 V, Ri < 10 Ohm)
- Separately adjustable compute time and pause time with convenient start-stop switching
- Variable calibration voltage from −1 to +1 in steps of 0.05
- Ramp voltage for setting function generators
- Mobile 19” rack with writing surface and swiveling holders for patch cords
Programming is accomplished by plug connections on an exchangeable programming patch board, so that multiple finished programs can be computed alternately with one device (programming examples in the appendix).
Delivery Scope
The delivery scope of the fully equipped device (in parentheses = ¼ equipped) consists of the following parts and assemblies:
Basic unit: Wired for 4/4 equipment in a mobile 19-inch cabinet approximately 1.7 m high, removable side panels, lockable rear door, table surface mounted below the control platform, 4 mains sockets for peripheral devices, holder for patch cords.
- 1 exchangeable programming patch board with color-coded fields
- 3 transistor-regulated power supplies
- 2 reference voltage power supplies
- 1 overload monitoring unit, optical and acoustic (switchable)
- 1 repetition unit with separately adjustable compute time (3 stages and 10-turn potentiometer ranges: 10…100 ms, 0.1…1 s, 1…10 s, and 1 continuous stage) and continuously adjustable pause time up to max. 10 sec, with start-stop switching
- 1 Digital voltmeter, 3½-digit, 0.1% accurate
- 2 addressing switches
- 1 ramp unit for setting function generators
- 1 calibration unit, DC 0 to 10 V in 20 steps, switchable to positive or negative
- 2 exchangeable programming patch boards
- 32 coefficient wire potentiometers
- 32 (8) impedance converters for the above potentiometers
- 32 (8) integrators
- 32 (8) summers
- 16 (4) multipliers (shared with a comparator, also suitable for division)
- 8 (2) function generators
- 4 (1) comparator(s)
- 8 (2) free diodes
- 8 (2) overload monitoring plug-in cards
- 1 service plug-in card
- Each 32 (8) patch cords, 20, 40, and 50 cm long
Output jacks for recording devices are also provided (flip-trigger impulse, compute-time, sawtooth signals).
¼ Upgrade Unit for the HSE Analog Computer
- 8 impedance converters for potentiometers
- 8 integrators
- 8 summers
- 4 multipliers (shared with a comparator, also suitable for division)
- 2 function generators
- 1 comparator
- 2 free diodes
- 2 overload monitoring plug-in cards
- Each 8 patch cords, 20, 40, and 50 cm long
Pricing
| Item | Price |
|---|---|
| Fully equipped device | DM 54,100.– |
| ¼ equipped basic unit | DM 36,600.– |
| One upgrade unit (¼) | DM 9,500.– |
Plus value-added tax.
Delivery time: 6–9 months.
Included in the price is an individually tailored programming course. Prerequisites: Secondary-school mathematics (also sufficient for complex differential equation systems). No electronics knowledge required.
1.1.1977 — Subject to changes.
HUGO SACHS ELEKTRONIK K.G., D-7801 March/Freiburg (BRD). Tel. (07665) 2011 + 2012
Programming Example from Pharmacokinetics
Substance Transport: Stomach (M) → Blood (B) → Urine (U)
(Transport from blood to general tissue and back was ignored for simplicity.)
Reaction model:
M → B → U
(k₁ and k₂ = rate constants, 1st order)
Mathematical formulation:
- dm/dt = −k₁·m (m = concentration in stomach)
- db/dt = k₁·m − k₂·b (b = concentration in blood)
- du/dt = k₂·b (u = concentration in urine)
Computational procedure and programming:
| Equation | Compute step |
|---|---|
| (1) −dm/dt = k₁·m | k₁ |
| (2) db/dt = k₁·m − k₂·b | k₁, k₂ |
| (3) du/dt = k₂·b | — |
Explanation:
The connecting lines are realized on the programming field with patch cords. Example at integrator I(1): When −S appears at the input (= left side of the equation), then after integration +m appears at the output (integrators — and also summers — invert the sign). If this output value is connected via a patch cord to potentiometer P1 (which is set to the value k₁), then k₁·m is available there. According to equation (1), however, k₁·m = −dm/dt, and therefore the output of P1 must be connected to the input of I1 (the line symbolizes the equals sign!). The circuit in the vicinity of integrator I(“I1”) now behaves like equation (1). At the output of “I1” the solution of equation (1) for m is available. Correspondingly, the solutions of equations (2) and (3) are obtained.
The following figures give an overview of the temporal course of substance concentration in the stomach, blood, and urine as a function of the values of the rate constants k₁ and k₂ — computed from equations (1) to (3).
Computed concentrations of a substance in the stomach (m), in the blood (b), and in the urine (u) for various rate constants k₁ and k₂ (see programming example above):
- Upper row: k₁ = 5, k₂ = parameter
- Lower row: k₁ = 5, k₂ = parameter
HUGO SACHS ELEKTRONIK K.G., D-7801 Hugstetten near Freiburg (BRD), Tel. (07665)