Assessment of medical response capacity in the time of disaster: the estimated formula of Hospital Treatment Capacity (HTC), the maximum receivable number of patients in hospital

Abstract

INTRODUCTION: For the assessment on medical response capacity for disaster in local area (such as rescue capacity, transport capacity and treatment capacity), it is necessary to assess it in peace time, and understand how many sufferers from disaster the hospital can respond to. Here the estimated formula of Hospital Treatment Capacity (hereinafter shortened to HTC), the maximum receivable number of patients in hospital (hereinafter shortened to MRN) was showed, which derived from the assessment on emergency medical response in Kobe University Hospital as an example. MATERIALS AND METHODS: We treated a total of 12,032 patients transferred and admitted to Kobe University Hospital from April 2003 to January 2005. We calculated the required number of medical personnel, equipment and length of treatment time in order to respond to 410 severe traumas, 35 burn injuries, and 28 patients with blood purification, which were considered to be main clinical conditions in disaster. Beside, the occupation of emergency room and the operation room per hour were also investigated in our hospital. RESULTS: HTC (MRN) for each clinical condition within H hours is expressed by following formula: (1) HTC (MRN) for burn injuries = The maximum integer of (≤Doctors/2∩≤Respirators/1∩≤outpatient beds/1∩≤inpatient beds/1∩≤monitors/1) x the minimum integer of (≥H/1.85) (2) HTC (MRN) for patients with blood purification = The maximum integer of (≤doctors/2∩≤ blood purification systems/1∩≤ outpatient beds/1∩≤inpatient beds/1∩≤monitors/1) x the minimum integer of (≥H/2.00) (3) HTC (MRN) for severe traumas =The maximum integer of (≤doctors-a/2∩≤surgeons/1∩≤anesthetists/ 1∩≤radiologists/1∩≤respirators/1∩≤outpatient beds/1∩≤inpatient beds/1∩≤monitors/1∩≤operation rooms/1∩≤angiography rooms/1) x the minimum integer of (≥H/2.82+b) CONCLUSION: The treatment capacity within local area is able to be assessed by adopting the estimated formula of HTC (MRN).

Full text

Kobe J. Med. Sci., Vol. 53, No. 5, pp. 189-198, 2007
Phone: 81-78-382-6521 FAX: 81-78-341-5254 E-mail: akirame@med.kobe-u.ac.jp
189
Assessment of Medical Response Capacity in the time of
Disaster: the Estimated Formula of Hospital Treatment
Capacity (HTC), the Maximum Receivable Number of
Patients in Hospital
AKIRA TAKAHASHI, NOBORU ISHII,
TAKAHISA KAWASHIMA, and HIROYUKI NAKAO
Department of Emergency and Disaster Medicine, Kobe University Graduate School of
Medicine
Received 25 December 2006/ Accepted 16 January 2007
Key words: disaster, estimated formula, assessment, preparedness, treatment capacity,
medical response
INTRODUCTION For the assessment on medical response capacity for disaster in
local area (such as rescue capacity, transport capacity and treatment capacity), it is
necessary to assess it in peace time, and understand how many sufferers from disaster
the hospital can respond to. Here the estimated formula of Hospital Treatment
Capacity (hereinafter shortened to HTC), the maximum receivable number of patients
in hospital (hereinafter shortened to MRN) was showed, which derived from the
assessment on emergency medical response in Kobe University Hospital as an example.
MATERIALS AND METHODS We treated a total of 12,032 patients transferred
and admitted to Kobe University Hospital from April 2003 to January 2005. We
calculated the required number of medical personnel, equipment and length of
treatment time in order to respond to 410 severe traumas, 35 burn injuries, and 28
patients with blood purification, which were considered to be main clinical conditions
in disaster. Beside, the occupation of emergency room and the operation room per hour
were also investigated in our hospital.
RESULTS HTC (MRN) for each clinical condition within H hours is expressed by
following formula:
(1) HTC (MRN) for burn injuries
= The maximum integer of
(≤Doctors/2∩≤Respirators/1∩≤outpatient beds/1∩≤inpatient beds/1∩≤monitors/1)
x the minimum integer of (≥H/1.85)
(2) HTC (MRN) for patients with blood purification
= The maximum integer of
(≤doctors/2∩≤ blood purification systems/1∩≤ outpatient beds/1∩
≤inpatient beds/1∩≤monitors/1)
x the minimum integer of (≥H/2.00)
(3) HTC (MRN) for severe traumas
=The maximum integer of
(≤doctors-a/2∩≤surgeons/1∩≤anesthetists/1∩≤radiologists/1∩≤respirators/1∩
≤outpatient beds/1∩≤inpatient beds/1∩≤monitors/1∩≤operation rooms/1∩
≤angiography rooms/1)

A. TAKAHASHI et al.
190
x the minimum integer of (≥H/2.82+b)
CONCLUSION The treatment capacity within local area is able to be assessed by
adopting the estimated formula of HTC (MRN).
The concept of a disaster medical plan and its management has been improved since the
Great Hanshin-Awaji Earthquake on 17 January 1995 in Japan. Based on the lesson learned
in coping with the earthquake, proactive efforts to improve the emergency management
system have been made, such as introducing an information system for emergency medicine,
designating more key disaster hospitals and implementing disaster medicine education and
trainings. However, even after the earthquake, delays in early response were identified in
mass-casualty incidents like the Tokyo Sarin gas attack, the O-157 mass food poisoning, the
Wakayama curry poisoning, the flood Nagoya, and the mass-gathering disaster at Akashi
fireworks festival. These delays occurred because, under current system, in the initial stage
of a disaster, the assessment of medical response is made first in the local area, and only after
it turned out that the amounts and types of damage are beyond the capacity of local
emergency management, they request support to neighbor cities.
Therefore, in order to shorten response times, it is necessary to assess the capacity for
emergency medical response in local areas during normal times, and share the results in
order to determine the capacity for deal with disasters and major accidents in the local area.
For the assessment on medical response capacity for disaster in local area, (such as rescue
capacity, transport capacity and treatment capacity), it is necessary to assess it in peace time,
and understand how many sufferers from disaster the hospital can respond to. In Japan, most
of the severe injuries are transported to the tertial emergency hospital such as critical care
center. Here we show the estimated formulas of Hospital Treatment Capacity (hereinafter
shortened to HTC), the maximum receivable number of patients in hospital (hereinafter
shortened to MRN), which derived from the assessment on emergency medical response in
the tertial emergency hospital, Kobe University hospital as an example.
MATERIALS AND METHODS
We treated a total of 12,032 patients transferred and admitted to Kobe University
Hospital from April 2003 to January 2005. Then we calculated the required number of
medical personnel, equipment and length of treatment time to respond to clinical conditions
from the daily emergency medical care. The subjects of clinical conditions were severe
traumas, burn injuries, and patients with blood purification, which were considered to be
main clinical conditions in disaster. Based on the result, we developed estimated formulas,
which could suggest MRN during a certain time. As a premise, we focused on the period for
treatment (treatment time) from the emergency room to the admission. The time is measured
by computer system in Kobe University Hospital, and the past average time during patient’s
stay in ER was adopted as treatment time.
For the response of emergency visit in Kobe University Hospital, basically 2 emergency
doctors are required to respond to 1 patient with severe trauma. If one needs to have an
operation, 2 emergency doctors, 1 surgeon, and 1 anesthetist are required. If one needs to
take angiography, 2 emergency doctors and 1 radiologist will respond. If one needs neither
operation nor angiography, 2 emergency doctors will respond (Figure 1). Besides, 2
emergency doctors are required to 1 patient with burn injury or needed blood purification
(Figure 2).
There are the facilities in Kobe University hospital, there are 6 beds in ER, 34 in
Intensive Care Unit, 13 operation rooms, 4 angiography rooms, 60 respirators, 14 anesthetic

ESTIMATED FORMULAS OF HOSPITAL CAPACITY
191
machines, 30 portable monitors, 37 fixed bedside monitors, central monitors for 144 patients,
26 blood purification systems, 11 beds in dialysis and 5 PCPS (Table 1).
The occupation of emergency room and the operation room per hour were also
investigated in our hospital.
Figure 1. 2 emergency doctors are required to respond to 1 patient with severe trauma. If
one needs to have an operation, 2 emergency doctors, 1 surgeon, and 1 anesthetist are required.
If one needs to take angiography, 2 emergency doctors and 1 radiologist will respond. If one
needs neither operation nor angiography, 2 emergency doctors will respond.
Figure 2. 2 emergency doctors are required to 1 patient with burn injury or needed blood
purification in Kobe University Hospital.
Required Medical Personnel (in Kobe University Hospital)
1 patient with severe trauma
2 emergency doctors (EMDs)
Operation or angiography required?
Yes No
・Operation: 2EMDs+1Surgeon+1Anesthetist
・Angiography: 2EMDs+1Radiologist
2 EMDs
Required Medical Personnel (in Kobe University Hospital)
1 patient with burn injury or blood purification
2 emergency doctors (EMDs)

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192
Table 1. Facilities in Kobe University Hospital
RESULTS
The number of patients and the average length of treatment time for the three types of
conditions in ER were showed at Table 2. The patients with these three types of conditions
need to be admitted. There were 35 burn injuries, and the average time of their treatment was
1.85 hours per patient. There were 28 patients required blood purification, and the average
time of their treatment was 2 hours per patient. There were 410 severe traumas, and the
average time of their treatment was 2.82 hours per patient.
The average number of patients in the emergency room per hour was showed in Figure 3.
The number increased during the beginning of day and twilight shift.
The average number of occupied operation rooms was showed in Figure 4. They were
mostly used during day-time and not much during night-time hours.
Table 2. The average length of treatment time for the three types of conditions in ER
The time is measured by computer system in Kobe University Hospital, and the past
average time during patient’s stay in the ER was adopted as treatment time
There were 35 burn injuries, and the average time of their treatment was 1.85
hours per patient. There were 28 patients required blood purification, and the
average time of their treatment was 2 hours per patient. There were 410 severe
traumas, and the average time of their treatment was 2.82 hours per patient.
34 bedsICU
30 portable
37 fixed bedside monitors
Central monitors for 144 patients
Monitor
13 CHDF
11 beds in dialysis room
Blood purification
system
13 roomsOperation Room
4 roomsAngiography room
5PCPS
14Anesthetic Machine
60Respirator
6 bedsEmerg ency room
34 bedsICU
30 portable
37 fixed bedside monitors
Central monitors for 144 patients
Monitor
13 CHDF
11 beds in dialysis room
Blood purification
system
13 roomsOperation Room
4 roomsAngiography room
5PCPS
14Anesthetic Machine
60Respirator
6 bedsEmerg ency room

ESTIMATED FORMULAS OF HOSPITAL CAPACITY
193
The number increases during the beginning of day and twilight shift.
They are mostly used during daytime and not much during nighttime hours.
The maximum receivable number of patients in hospital at once can be expressed by the
following formula. Setting the required number of medical personnel per patient as A1 . . .
An, the actual number of personnel to participate as B1 . . . Bn, the required number of
facilities to accept 1patient as C1 . . . Cn, and the actual number of facilities to use as D1 . . .
Dn (Table 3), then
MRN (HTC) in view of only element A1 = The maximum integer of (≤B1/A1).
MRN (HTC) in view of only element A2 = The maximum integer of (≤B2/A2).
MRN (HTC) in view of only element An = The maximum integer of (≤Bn/An).
MRN (HTC) in view of only element C1 = The maximum integer of (≤D1/C1).
MRN (HTC) in view of only element C2 = The maximum integer of (≤D2/C2).
MRN (HTC) in view of only element Cn = The maximum integer of (≤Dn/Cn).

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Table 3. The estimated Formula for Hospital Treatment Capacity (HTC)
The maximum receivable number of patients in hospital (MRN)
= HTC = The maximum integer of
(≤B1/A1∩≤B2/A2∩…∩≤Bn/An∩≤D1/C1∩≤D2/C2∩…∩≤Dn/Cn)
The mathematical symbols mean as follows: ≤ : and under ≥ : and over ∩. And
in view of all element A1…An, C1…Cn, MRN (HTC) can be expressed by the next formula:
MRN (HTC) in view of all element A1…An, C1…Cn
= The maximum integer of (≤B1/A1∩≤B2/A2∩...∩≤Bn/An∩≤D1/C1∩≤D2/C2∩...∩≤Dn/Cn)
If the treatment time is set as E hours, because E hours later, medical personnel and facilities
become free, the maximum receivable number of the patients in hospital within H hours will
be expressed by the following formula:
MRN within H hours
= The maximum integer of (≤B1/A1∩≤B2/A2∩...∩≤Bn/An∩≤D1/C1∩≤D2/C2∩...∩≤Dn/Cn)
x The minimum integer of (≥H/E)
If we look at the aspect of facilities (ex, inpatient beds), which are irrelevant to the time and
occupied by patients, MRN will be described by the following formula:
MRN defined by the facilities without time constraints
= The maximum integer of (≤D’1/C’1∩≤D’2/C’2∩...∩≤D’n/C’n)
D’n/C’n: without time constraints (Figure 5)
Figure 5. The estimated Formula for HTC (MRN) within H hours
Next, we would like to explain these formulas adopting for each clinical condition.
(1) In the case of burn injuries:
HTC (MRN) for burn injuries
= The maximum integer of
(≤Doctors/2∩≤Respirators/1∩≤outpatient beds/1∩≤inpatient beds/1∩≤monitors/1)

ESTIMATED FORMULAS OF HOSPITAL CAPACITY
195
x The minimum integer of (≥H/1.85)
MRN without time constraints
= The maximum integer of (≤respirators/1∩≤inpatient beds/1∩≤monitors/1)
(2) In the case of patients with blood purification:
HTC (MRN) for Patients with blood purification
= The maximum integer of
(≤doctors/2∩≤blood purification systems/1∩≤outpatient beds/1∩
≤inpatient beds/1∩≤monitors/1)
x The minimum integer of (≥H/2.00)
MRN without time constraints
= The maximum integer of (≤blood purification systems/1∩≤inpatient beds/1∩≤monitors/1)
(3) In the case of severe traumas:
HTC (MRN) for severe traumas
= The maximum integer of
(≤doctors-a/2∩≤surgeons/1∩≤anesthetists/1∩≤radiologists/1∩≤respirators/1∩
≤outpatient beds/1∩≤inpatient beds/1∩≤monitors/1∩≤operation rooms/1∩
≤angiography rooms/1)
x The minimum integer of (≥H/2.82 +b)
with operation: add the number of surgeons, anesthetists and operation room
a=the number of surgeons + anesthetists.
b=3(operation time: which was based on past data in our hospital)
with angiography: add the number of radiologists and angiography rooms
a=the number of radiologists.
b=0
without operation and angiography
: Delete the parts indicated with underline.
a=b=0
MRN without time constraints
= The maximum integer of (≤respirators/1∩≤inpatient beds/1∩≤monitors/1)
Next we present the actual case as an example. The train derailment occurred at 9:18 a.m.
on April 25, 2005 on JR Hukuchiyama railway line in Amagasaki city, causing many people
injured. The available number of personnel and facilities in Kobe University Hospital is as
follows: Set B1 equal to 31 doctors, who are able to participate. Among of them, set B2 as 5
surgeons, B3 as 3 anesthetists, and B4 as 2 radiologists. Regarding facilities, 5 vacant beds in
emergency room shows as D1, 1 available angiography room as D2, and 4 available
operation rooms as D3. For the facilities, without time constraints are: Set D4 equal to 8
available inpatient beds, D5 to 35 available respirators, D6 to 13 available monitors, D7 to
12 available blood purification systems. Then MRN in each condition within 5 hours is next
numbers:
MRN for severe traumas (need operation)
=The maximum integer of (≤31-5-3/2∩≤5/1∩≤3/1∩≤35/1∩≤5/1∩≤8/1∩≤13/1∩≤4/1)

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x The minimum integer of (≥5/5.04)= 3 x 1 (≤8) = 3
MRN for severe traumas (need angiography)
= The maximum integer of (≤31-2/2∩≤2/1∩≤35/1∩≤5/1∩≤8/1∩≤13/1∩≤1/1)
x The minimum integer of (≥5/2.04) =1 x 3 (≤8) = 3
MRN for burn injuries
= The maximum integer of (≤31/2∩≤35/1∩≤5/1∩≤8/1∩≤13/1)
x The minimum integer of (≥5/1.11)=5 x 5(≤8)= 8
MRN for patients with blood purification
= The maximum integer of (≤31/2∩≤12/1∩≤5/1∩≤8/1∩≤13/1)
x The minimum integer of (≥5/1.58)=5 x 4(≤8)= 8
The actual number of patients transferred to Kobe University Hospital was 4 all together:
1 patient with aortic injury, fracture of rib and spine;
1 patient with hemopneumothorax and fracture of the clavicle and scapula;
1 patient with head contusion and peroneal nerve palsy;
1 patient with fracture of rib and whiplash.
DISCUSSION
Early emergency medical response capacity at the time of major disasters and
mass-gathering disasters consists of these three capacities: rescue capacity, transport capacity
and medical treatment capacity. Rescue capacity and transport capacity are depended on fire
department capacity, which has comparatively enough support system.
This time, medical treatment capacity was assessed mathematically. Hospital
preparedness assessment and planning or surge capacity at the time of major disasters and
mass-gathering disasters have been reported previously. With regard to hospital preparedness
assessment and planning, Higgins and colleagues published an article on a hospital
assessment tool that was piloted in 116 hospitals (4). In order to assess the receivable number
of patients in hospital, the questionnaire survey is useful, but there are so many hospitals that
it is difficult to carry out the survey (317 hospitals in Hyogo prefecture only, in which 182
are designated emergency hospitals). Besides, because the questionnaire survey tends to be
subjective, and has difficulty to decide the suitable man who answers the questionnaire, it is
not considered to be suitable for this research. Chaffee and colleague presented a program
designed to assess and strengthen hospital preparedness in US hospitals (2). But they did not
present receivable number of patients in hospital. Hutchinson, Christopher and colleagues
published an article on mass casualty prediction methodology (5). De Boer examined 416
disasters over a 40-year period using the disaster severity scale (3). With regard to surge
capacity, the ability of an organization to rapidly increase its operating capability during a
disaster, Hick and colleagues published a state of the science review on surge capacity that
included strategies for increasing capacity (6). Community preparedness, including
emergency preparedness funding, was examined by McHugh and colleagues (9). Developing
community surge capacity also was explored by Bekemeier and Dahl (1). McKenzie and
colleagues documented the number and configuration of trauma centers in the United States
gaps in coverage (10). Posner and colleagues presented a strategy to expand burn unit
capacity based on work in Israel (11). The often-overlooked capacity of long-term care
facilities was described by Saliba and colleagues (12). Milsten A compiled and reviewed

ESTIMATED FORMULAS OF HOSPITAL CAPACITY
197
lessons learned from past disaster-related operational failures and reviewed importance and
types of disaster planning by the available literature from 1977 through March 1999 (8).
There was no literature which presented MRN in his report, because most of these literatures
presented adequate response to disaster mainly, based on disaster experience. Ishida and
Ohtori presented a model of emergency medical networks at the time of disaster and the
examples of its analysis, which can set up the distribution of visiting patients, that of
treatment time, the number of departments and network hospitals, and the time of patients
transport (7). They presented patients shift with the passage of time. But they did not present
MRN, because they might think it is difficult to decide MRN. Although there are such
reports above, there has been no report that suggests the concrete receivable number of
patients in hospital in the time of disaster. Besides, we can come across some formulas to
suggest conceptual thought for disaster management occasionally, but such formulas are
unpractical, and cannot be used in real disasters. In real disasters, it is important to make
objective judgment in order to determine how many patients are able to be received to the
hospital. Such formulas enable each hospital, each municipal, and each prefecture to show
the receivable number of patients, and to determine the range of backup hospitals from their
receivable number of patients and that of casualties in the disaster.
This time we take Kobe University Hospital as an example and suggest the receivable
number of patients. Basic formula might gain consensus, but we need further discussion on
parameters of personnel and equipment. If the parameters, however, can obtain one’s consent,
they can use in a wide range. Because the estimated formula of HTC was considered to be
very complex by adding data of the occupation rate of emergency room and operation room
per hour, the data were not added to the formula. HTC may be decided by the maximum
receivable number of patients in hospital without time constraints (ex. Inpatient bed) in the
end. Moreover, regarding the concept of time, though there are gap between treatment times
because of different levels of ability, we can show MRN per hour. If the facilities without
time constraints are not occupied, MRN can be received over and over within a certain time
because the needed personnel and facilities become free every treatment time. Although we
did not discuss this time, if there are surveys on the means of transportation between
hospitals, and the time of transportation, we can suggest the receivable number of patients
per hour on a regional basis accurately. If this formula of HTC can be introduced to
information system, MRN may be able to be presented just by inputting some necessary
parameters at the time of disaster. We established a precedent of the train derailment in
results, but the actual number of patients transferred to Kobe University Hospital was less
than MRN. Thus, it may be useful to decide support area by calculating MRN every hospital
or every local area (for example: Kobe city, Hyogo prefecture). This formula of HTC is also
considered to be useful for the preparedness assessment of disaster. The weak point at each
local area may be able to be clear by HTC assessment there at a certain time. The weak point
may be useful for judging the suitable place that new hospital is established.
CONCLUSION
The estimated formula to assess Hospital Treatment Capacity (HTC), the maximum
receivable number of patients in hospital (MRN), was presented according to the examples in
Kobe University Hospital. HTC (MRN) within H hours can be calculated as follows.
Set A1 . . . An equal to the required number of personnel per patient, B1 . . . Bn to the actual
number of personnel to participate, C1. . .Cn to the required number of facilities, and D1 . . .
Dn to the actual number of facilities to use, and treatment time are E hours,

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HTC (MRN) within H hours
= The maximum integer of
(≤B1/A1∩≤B2/A2∩…∩≤Bn/An∩≤D1/C1∩≤D2/C2∩… ∩≤Dn/Cn)
x The minimum integer of (≥H/E)
While further examination is necessary for the parameter of personnel and facilities, the
treatment capacity within local area is able to be assessed by adopting the estimated formula
of HTC (MRN).
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