HP 42S and HP Prime: Rabbits vs Foxes

HP 42S and HP Prime: Rabbits vs Foxes

Introduction

The program presented today is based on the Rabbits vs. Foxes program for the HP 25 (see source below).  The program determines the population of rabbits and foxes over time as modeled by the differential equations:

Change in Rabbits:
dr/dt = 2 * r - α * r * f

Change of Foxes:
df/dt = -f + α * r  * f

where:
r = population of rabbits
f = population of foxes
α = probability of a rabbit encounters a fox
h = step 

This is approximated by Euler's method.

The HP Prime program RABBIT25 displays a print screen of results of the desired amount of iterations.  The HP 42S program RAB25 displays the results one step at time in the format rrrrr.fffff  (rabbits.foxes), like the original HP 25 program.


HP Prime Program RABBIT25

EXPORT RABBIT25()
BEGIN
// 2020-01-20 EWS
// Based on the Rabbits vs
// Foxes HP 25 program
LOCAL α,h,r,f,k,n,a;

// initialize and input
INPUT({α,h,r,f,n},
"Rabbits vs Foxes",
{"α: ","h: ","r0:","f0:","n: "},
{"α","h","inital # rabbits",
"initial # foxes",
"# iterations"});
L0:={r}; L1:={f};


// compute data
MSGBOX("L0 = rabbit population,
L1 = fox population;
(0,1,2,...,n), size n+1");
HFormat:=0;
PRINT();
PRINT("Rabbits vs Foxes");
FOR k FROM 0 TO n DO
IF k≠0 THEN
a:=α*r*f;
r:=r+h*(2*r-a);
f:=f+h*(−f+a);
END;
PRINT(k+" R: "+IP(r)+" F: "+
IP(f));
END;


// end of program
END;


HP 42S/Free42/DM42 Program RAB25

00 { 58-Byte Prgm }
01▸LBL "RAB25"
02 STO 02
03 R↓
04 STO 03
05 FIX 05
06▸LBL 05
07 RCL 02
08 ENTER
09 ENTER
10 RCL 03
11 RCL 00
12 ×
13 ×
14 STO 04
15 X<>Y
16 -
17 RCL 01
18 ×
19 +
20 X<0 font="">
21 0
22 STO 02
23 RCL 03
24 2
25 ×
26 RCL 04
27 -
28 RCL 01
29 ×
30 RCL 03
31 +
32 X<0 font="">
33 0
34 STO 03
35 IP
36 RCL 02
37 IP
38 1ᴇ5
39 ÷
40 +
41 STOP
42 GTO 05
43 .END.

Note:  You can replace STOP with PSE, as many as you like, if you don't want to press R/S after each step. 

Instructions:
Store α in R00, store h in R01, enter initial rabbit population

Example

Initial Populations:
Rabbits:  r = 300
Fixes:  f = 150
α = 0.01
h = 0.02

Iter:   Rabbits.Foxes  (rrrrr.ffff)
0:  300.00150
1:  303.00156
2:  305.00162
3:  307.00169
4:  309.00176
5:  311.00183
6:  312.00191
7:  312.00199
8:  312.00207
9:  312.00216
10: 311.00225
11: 309.00235
12: 307.00245
13: 304.00255
14: 301.00265
15: 297.00276


Source:

Randall B. Neff and Lynn Tilman "An Example of HP-25 Programming" Hewlett-Packard Journal: November 1975.  pg. 6
Eddie


All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

HP 41C and DM41L: Basic EKG Calculations

HP 41C and DM41L: Basic EKG Calculations

Introduction

The program calculates the following:

*  Lead II magnification, in mm

*  The mean axis deviation

*  The mean axis magnitude 

Given:

*  Lead I positive deflection, in mm

*  Lead III negative deflection, in mm

The mean axis deviation and magnitude are calculated by a rectangular conversion by the following coordinates:

X: Lead I positive deflection - Lead I negative deflection

Y:  Net Lead I deflection * 0.5774 + Net Lead III deflection * 1.1547

Mean axis deviation:  θ - 57°

The program also:

* Converts between the heart rate (rpm) and the R-R interval

* Use either parameter to calculate the Q-T interval, in seconds

heart rate = 60/R-R

Q-T interval = √(R-R)*0.39

The program is a translation of HP 67/HP 97 Basic EKG Determination, which itself is a translation of Steven A. Conrad's HP-65 program (HP-65 Users' Library Program).  See the source listed below.

Notes:

1.  Clear the assignments of keys A (Σ+) through E (LN) before running the program.  This must be done outside the programming environment.  Clear assignments to keys by ASN (blank) (designated key).  

Example:  Clear assignment from A: [ shift ] (ASN)  [ALPHA] [ALPHA] [ Σ+ ]

2.  Running EKG will turn the User Keyboard on.

3.  The program will set the calculator to degrees mode. 

4.  This program was entered on an HP 41C, and it should work on any simulator and Swiss Micros DM41.  

Instructions

1.  Run EKG.

2.  Determine Lead I net deviation and store it to register 01:

(in User's Mode) positive deviation Lead I [ENTER] negative deviation Lead I ( A )  

3.  Determine Lead II net deviation, storing net Lead III net deviation to register 03 and Lead II net deviation to register 02:

(in User's Mode)  positive deviation Lead III [ENTER] negative deviation Lead III ( B )

Result:  Lead II net deviation

4.  Compute Mean Axis:

(in User's Mode)   ( C )  deviation is displayed [ R/S ] magnitude is displayed

5a.  Convert heart rate to R-R:   

(in User's Mode) heart rate (bpm) ( D )

-or-

5b.  Convert R-R to heart rate:

(in User's Mode)  R-R ( D )

6.  Compute Q-T.  

(in User's Mode)  ( E )

HP 41C/DM41 Program:  EKG

01 LBL T^EKG

02 SF 27

03 GTO 00

04 LBL A

05 - 

06 STO 01

07 ^T III:_ 

08 ARCL X

09 AVIEW

10 RTN

11 LBL B

12 -

13 STO 03

14 RCL 01

15 +

16 STO 02

17 ^T II:_ 

18 ARCL X

19 AVIEW

20 RTN

21 LBL C

22 RCL 01

23 ENTER↑

24 0.5774

25 *

26 RCL 03

27 ENTER↑

28 1.1547

29 *

30 +

31 ENTER↑

32 RCL 01

33 R-P

34 X<>Y

35 57

36 -

37 ^T DEV=

38 ARCL X

39 AVIEW 

40 STOP

41 X<>Y

42 ABS

43 ^T MAG=

44 ARCL X

45 AVIEW

46 RTN

47 LBL D

48 ENTER↑

49 ENTER↑

50 60

51 X<>Y

52 /

53 X<=Y?

54 GTO 05

55 ^T RATE=

56 ARCL X

57 AVIEW

58 RTN

59 LBL 05

60 ^T R-R=

61 ARCL X

62 AVIEW

63 RTN

64 LBL E

65 X>Y?

66 X<>Y

67 SQRT

68 0.39

69 *

70 ^T Q-T=

71 ARCL X

72 AVIEW 

73 RTN

74 LBL 00

75 RTN

76 END

Example

I+ = 2.8 mm,  I- = 1.1 mm

III+ = 2.5 mm, III- = 1.4 mm

Heart Rate = 86 bpm

Keystrokes:

XEQ "EKG"

(User Mode is On)

2.8 [ENTER] 1.1 ( A ) 

Display:  III: 1.7000

2.5 [ENTER] 1.4 ( B )

Display:  II:  2.8000

( C )

Display:  DEV=-4.0516

[ R/S ]

Display:  MAG=2.8214

86 (D)

Display:  R-R=0.6977

(E)

Display:  Q-T=0.3258

Source:

"Basic EKG Determinations"  HP-67/97 User's Library Solutions:  Cardiac.  Hewlett Packard.  Corvallis, OR.  (no date given, but I estimate this to be circa 1974)

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP Prime: Fick Cardiac Output (The Blog Turns Six!)

HP Prime:  Fick Cardiac Output  (The Blog Turns Six!)

A Special Note

Happy sixth birthday to my mathematics blog!   And a big reason why blog has turned six on April 11, 2017 is because of all of you readers!  Words can’t explain how appreciated I am. 

Thank you!  Cheers to everyone!

Fun fact:  The most popular blog entry is my TI-36X Pro review (my fourth blog entry, 4/27/2011).  Link:  http://edspi31415.blogspot.com/2011/04/ti-36-pro-review.html

Now let’s get to today’s subject. 

Fick Cardiac Output Equations

The program FICK will calculate:

* CO: Cardiac Output (L/min)

* SV: Stroke Volume (ml)

* CI:  Cardiac Index (L/(min/m^2))

* SI:  Stroke Index (ml/m^2)

Given the following inputs:

* C_a:  Arterial blood oxygen (O₂) content percentage

* C_vO₂:  Venous blood oxygen (O₂) content percentage

* VO₂:  Oxygen compulsion (in ml per pure oxygen gas per minute, STPD)

* HR:  Heart Rate in beats per minute (BPM)

* Height in cm

* Weight in kg

STPD: Standard Temperature Pressure Density

Conversion factors:  1 in = 2.54 cm, 12 in = 1 ft, 1 lb = 0.45359237 kg

Formulas: 

CO = VO₂ / (10 * (C_a - C_vO₂))

SV = CO * 1000/HR

CI = CO/BSA

SI = SV/BSA

BSA:  body surface area, measured in cm^3.  There are several formulas, but the Fick program uses the simple approximation formula:

BSA = √(weight * height)/60

HP Prime Program FICK

EXPORT FICK()

BEGIN

// Fick Cardiac Output

// HP 65, 1972

// EWS 2017-04-10

// inputs

LOCAL ca,cv,vo,hr,h,w;

INPUT({ca,cv,vo,hr,h,w},

"Fick Cardiac Output",

{"Ca O_2:","C_v O_2:","VO_2:","HR:",

"Height:","Weight:"},

{"Arterial blood (%)",

"Venous blood (%)",

"O_2 compulsion (ml/min)",

"Heart Rate (BPM)",

"Height (cm)",

"Weight (kg)"});

// calculation

LOCAL co:=vo/(10*(ca-cv));

LOCAL sv:=co*1000/hr;

// simple BSA

LOCAL bsa:=√(w*h)/60;

LOCAL ci:=co/bsa;

LOCAL si:=sv/bsa;

// output

PRINT();

PRINT("Cardiac Output (l/min)");

PRINT(co);

PRINT("Stroke Volume (ml)");

PRINT(sv);

PRINT("Cardiac Index (L/(min/m^2))");

PRINT(ci);

PRINT("Stroke Index (ml/m^2)");

PRINT(si);

END;

Example:

Inputs:

* C_a:  19%

* C_vO₂:  15%

* VO₂:  250 ml/min

* HR:  64

* Height: 5 ft 11 in, 180.34 cm

* Weight 196 lb, 88.90410452 kg

Results:

* CO: 6.25 L/min

* SV: 97.65625 ml

* CI:  2.96158586825 L/(min/m^2)

* SI:  46.2747791914 ml/m^2

Source:

Hewlett Packard.  HP-67/97 User’s Library Solutions: Cardiac Corvallis, OR 1976  pg. 20

Here’s to many more years!

Eddie

This blog is property of Edward Shore, 2017.